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xwyam 2013-04-17 14:34:39 +08:00
commit c911534928
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1000
base_exp.txt Normal file
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#include <iostream>
#include <string>
#include <math.h>
#include <stdlib.h>
#include <sys/timeb.h>
using namespace std;
typedef unsigned long long int uu; // 简化大整数定义
#define _eps 0.00001 // 设置最小值表示

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/** If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below 1000. */
#include "0.hpp"
const int _a = 3;
const int _b = 5;
const int _max = 1000;
int main()
{
int total = 0;
for(int i = 1; i < 1000; i++) // 循环体
if(i % _a == 0 || i % _b == 0) total += i; // 满足条件的数字加入到 total 中
cout << total << endl;
return 0;
}

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/** The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
Find the sum of all the primes below two million. */
#include "0.hpp"
#include <sys/timeb.h>
uu factor(uu a, uu min = 1)
{
uu temp = min;
uu sqr = (int)(sqrt((double)a) + _eps);
while(temp < sqr) if(a % ++temp == 0) break;
if(a % temp == 0) return temp;
else return 1;
}
int main()
{
const uu _max = 2000000;
uu sum = 0;
timeb start, end;
ftime(&start);
for(uu i = 3; i <= _max; i += 2) {
if(factor(i) == 1) {
//cout << i << "\t";
sum += i;
}
}
sum += 2;
ftime(&end);
cout << sum << endl;
cout << (end.time - start.time) * 1000 + end.millitm - start.millitm << endl;
return 0;
}

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/** In the 20 * 20 grid below, four numbers along a diagonal line have been marked in red.
08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
32 98 81 28 64 23 67 10 (26) 38 40 67 59 54 70 66 18 38 64 70
67 26 20 68 02 62 12 20 95 (63) 94 39 63 08 40 91 66 49 94 21
24 55 58 05 66 73 99 26 97 17 (78) 78 96 83 14 88 34 89 63 72
21 36 23 09 75 00 76 44 20 45 35 (14) 00 61 33 97 34 31 33 95
78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48
The product of these numbers is 26 * 63 * 78 * 14 = 1788696.
What is the greatest product of four adjacent numbers in any direction (up, down, left, right, or diagonally) in the 2020 grid? */
#include "0.hpp"
#define _unit 4
#define _maxh 20
#define _maxv 20
struct node {
int loch;
int locv;
int direc;
int value;
};
int vec[4][2] = {{0, 1}, {1, 1}, {1, 0}, {-1, 1}};
int matrix[_maxh][_maxv] = {
{8, 2, 22, 97, 38, 15, 0, 40, 0, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8},
{49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 4, 56, 62, 0},
{81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 3, 49, 13, 36, 65},
{52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 36, 91},
{22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80},
{24, 47, 32, 60, 99, 3, 45, 2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50},
{32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70},
{67, 26, 20, 68, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21},
{24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72},
{21, 36, 23, 9, 75, 0, 76, 44, 20, 45, 35, 14, 0, 61, 33, 97, 34, 31, 33, 95},
{78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92},
{16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 0, 17, 54, 24, 36, 29, 85, 57},
{86, 56, 0, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58},
{19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40},
{4, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66},
{88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69},
{4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36},
{20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16},
{20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54},
{1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48},
};
int calc(node a)
{
int temp = 1;
for(int i = 0; i < _unit; i++) {
temp *= matrix[a.loch + i * vec[a.direc][0]][a.locv + i * vec[a.direc][1]];
//cout << a.loch + i * vec[a.direc][0] << endl << a.locv + i * vec[a.direc][1] << endl;
//cout << temp << endl;
}
return temp;
}
int main()
{
node max;
max.loch = 0;
max.locv = 0;
max.direc = 0;
max.value = 0;
node temp;
for(int j = 0; j <= _maxv - _unit; j++) {
temp.locv = j;
for(int k = 0; k < 3; k++) {
temp.direc = k;
for(int i = 0; i <= _maxh - _unit; i++) {
temp.loch = i;
temp.value = calc(temp);
//cout << i << " " << j << " " << k << " " << temp.value << endl;
if(temp.value > max.value) max = temp;
}
}
temp.direc = 3;
for(int i = _unit - 1; i < _maxh; i++) {
temp.loch = i;
temp.value = calc(temp);
//cout << i << " " << j << " " << 4 << " " << temp.value << endl;
if(temp.value > max.value) max = temp;
}
}
//max.value = calc(max);
cout << max.value << endl;
return 0;
}

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#include <iostream>
using namespace std;
int judge1(int a)
{
int tmp = 10;
while(a != 0) {
if(tmp < a % 10) return 1;
tmp = a % 10;
a /= 10;
}
return 0;
}
int judge2(int a)
{
int tmp = 0;
while(a != 0) {
if(tmp > a % 10) return 1;
tmp = a % 10;
a /= 10;
}
return 0;
}
int main()
{
int nis = 0;
int nnot = 100;
int n = 100;
while(nis != nnot * 99) {
n += 1;
if(judge1(n) * judge2(n) > 0) nis += 1;
else nnot += 1;
}
cout << n << endl;
return 0;
}

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/** The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
Let us list the factors of the first seven triangle numbers:
1: 1
3: 1,3
6: 1,2,3,6
10: 1,2,5,10
15: 1,3,5,15
21: 1,3,7,21
28: 1,2,4,7,14,28
We can see that 28 is the first triangle number to have over five divisors.
What is the value of the first triangle number to have over five hundred divisors? */
#include "0.hpp"
int main()
{
uu n = 1;
uu max;
uu sqr;
timeb start, now;
ftime(&start);
do {
max = n * (n + 1) / 2;
sqr = (uu)(sqrt((double)max));
int count = 0;
uu temp = 1;
while(temp < sqr) {
if(max % temp == 0) count++;
temp++;
}
ftime(&now);
if(count >= 250) {
cout << n << " " << max << " time: " << (now.time * 1000 + now.millitm - start.time * 1000 - start.millitm) << "ms" << endl;
break;
}
n++;
} while(1);
return 0;
}

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/** Work out the first ten digits of the sum of the following one-hundred 50-digit numbers. */
#include "0.hpp"
#include "lib/lint.cpp"
#define _max 100
string str[_max] = {
"37107287533902102798797998220837590246510135740250",
"46376937677490009712648124896970078050417018260538",
"74324986199524741059474233309513058123726617309629",
"91942213363574161572522430563301811072406154908250",
"23067588207539346171171980310421047513778063246676",
"89261670696623633820136378418383684178734361726757",
"28112879812849979408065481931592621691275889832738",
"44274228917432520321923589422876796487670272189318",
"47451445736001306439091167216856844588711603153276",
"70386486105843025439939619828917593665686757934951",
"62176457141856560629502157223196586755079324193331",
"64906352462741904929101432445813822663347944758178",
"92575867718337217661963751590579239728245598838407",
"58203565325359399008402633568948830189458628227828",
"80181199384826282014278194139940567587151170094390",
"35398664372827112653829987240784473053190104293586",
"86515506006295864861532075273371959191420517255829",
"71693888707715466499115593487603532921714970056938",
"54370070576826684624621495650076471787294438377604",
"53282654108756828443191190634694037855217779295145",
"36123272525000296071075082563815656710885258350721",
"45876576172410976447339110607218265236877223636045",
"17423706905851860660448207621209813287860733969412",
"81142660418086830619328460811191061556940512689692",
"51934325451728388641918047049293215058642563049483",
"62467221648435076201727918039944693004732956340691",
"15732444386908125794514089057706229429197107928209",
"55037687525678773091862540744969844508330393682126",
"18336384825330154686196124348767681297534375946515",
"80386287592878490201521685554828717201219257766954",
"78182833757993103614740356856449095527097864797581",
"16726320100436897842553539920931837441497806860984",
"48403098129077791799088218795327364475675590848030",
"87086987551392711854517078544161852424320693150332",
"59959406895756536782107074926966537676326235447210",
"69793950679652694742597709739166693763042633987085",
"41052684708299085211399427365734116182760315001271",
"65378607361501080857009149939512557028198746004375",
"35829035317434717326932123578154982629742552737307",
"94953759765105305946966067683156574377167401875275",
"88902802571733229619176668713819931811048770190271",
"25267680276078003013678680992525463401061632866526",
"36270218540497705585629946580636237993140746255962",
"24074486908231174977792365466257246923322810917141",
"91430288197103288597806669760892938638285025333403",
"34413065578016127815921815005561868836468420090470",
"23053081172816430487623791969842487255036638784583",
"11487696932154902810424020138335124462181441773470",
"63783299490636259666498587618221225225512486764533",
"67720186971698544312419572409913959008952310058822",
"95548255300263520781532296796249481641953868218774",
"76085327132285723110424803456124867697064507995236",
"37774242535411291684276865538926205024910326572967",
"23701913275725675285653248258265463092207058596522",
"29798860272258331913126375147341994889534765745501",
"18495701454879288984856827726077713721403798879715",
"38298203783031473527721580348144513491373226651381",
"34829543829199918180278916522431027392251122869539",
"40957953066405232632538044100059654939159879593635",
"29746152185502371307642255121183693803580388584903",
"41698116222072977186158236678424689157993532961922",
"62467957194401269043877107275048102390895523597457",
"23189706772547915061505504953922979530901129967519",
"86188088225875314529584099251203829009407770775672",
"11306739708304724483816533873502340845647058077308",
"82959174767140363198008187129011875491310547126581",
"97623331044818386269515456334926366572897563400500",
"42846280183517070527831839425882145521227251250327",
"55121603546981200581762165212827652751691296897789",
"32238195734329339946437501907836945765883352399886",
"75506164965184775180738168837861091527357929701337",
"62177842752192623401942399639168044983993173312731",
"32924185707147349566916674687634660915035914677504",
"99518671430235219628894890102423325116913619626622",
"73267460800591547471830798392868535206946944540724",
"76841822524674417161514036427982273348055556214818",
"97142617910342598647204516893989422179826088076852",
"87783646182799346313767754307809363333018982642090",
"10848802521674670883215120185883543223812876952786",
"71329612474782464538636993009049310363619763878039",
"62184073572399794223406235393808339651327408011116",
"66627891981488087797941876876144230030984490851411",
"60661826293682836764744779239180335110989069790714",
"85786944089552990653640447425576083659976645795096",
"66024396409905389607120198219976047599490197230297",
"64913982680032973156037120041377903785566085089252",
"16730939319872750275468906903707539413042652315011",
"94809377245048795150954100921645863754710598436791",
"78639167021187492431995700641917969777599028300699",
"15368713711936614952811305876380278410754449733078",
"40789923115535562561142322423255033685442488917353",
"44889911501440648020369068063960672322193204149535",
"41503128880339536053299340368006977710650566631954",
"81234880673210146739058568557934581403627822703280",
"82616570773948327592232845941706525094512325230608",
"22918802058777319719839450180888072429661980811197",
"77158542502016545090413245809786882778948721859617",
"72107838435069186155435662884062257473692284509516",
"20849603980134001723930671666823555245252804609722",
"53503534226472524250874054075591789781264330331690",
};
int main()
{
lint a("0");
lint b;
for(int i = 0; i < _max; i++) {
b = str[i];
a = a + b;
}
cout << a.getd()/**.substr(0, 10)*/ << endl;
return 0;
}

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/** The following iterative sequence is defined for the set of positive integers:
n -> n/2 (n is even)
n -> 3n + 1 (n is odd)
Using the rule above and starting with 13, we generate the following sequence:
13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1
It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.
Which starting number, under one million, produces the longest chain?
NOTE: Once the chain starts the terms are allowed to go above one million. */
#include "0.hpp"
#define _max 1000000
#define _min 1
struct num {
uu value;
int ch;
};
int sq(uu a, int flag = 0)
{
int count = 0;
while(a != 1) {
count++;
//if(flag) cout << a << " -> ";
if(a % 2) a = a * 3 + 1;
else a /= 2;
}
//if(flag) cout << 1 << endl;
return count;
}
int main()
{
timeb start, end;
ftime(&start);
num max;
max.ch = 0;
for(uu i = _max; i >= _min; i--) {
if(sq(i) > max.ch) {
max.value = i;
max.ch = sq(i);
}
}
ftime(&end);
cout << max.value << endl;
cout << max.ch << " times calc" << endl;
sq(max.value, 1);
cout << endl << "cost " << (end.time - start.time) * 1000 + end.millitm - start.millitm << " ms" << endl;
return 0;
}

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/** Starting in the top left corner of a 2*2 grid, there are 6 routes (without backtracking) to the bottom right corner.
How many routes are there through a 20*20 grid? */
#include "0.hpp"
#define _max 20
int main()
{
double pro = 1.0;
for(int i = 1; i <= _max; i++) {
pro *= (i + (double)_max);
pro /= i;
}
cout << (long long int)pro << endl;
return 0;
}

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/** What is the sum of the digits of the number 2^1000 ? */
#include "0.hpp"
#include "lib/lint.cpp"
uint sum(string a)
{
uint suma = 0;
for(uint i = 0; i < a.size(); i++) suma += (a[i] - '0');
return suma;
}
int main()
{
lint a("2");
lint b("1000");
lint c = a ^ b;
cout << sum(c.getd()) << endl;
return 0;
}

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/** If the numbers 1 to 5 are written out in words: one, two, three, four, five, then there are 3 + 3 + 5 + 4 + 4 = 19 letters used in total.
If all the numbers from 1 to 1000 (one thousand) inclusive were written out in words, how many letters would be used?
NOTE: Do not count spaces or hyphens. For example, 342 (three hundred and forty-two) contains 23 letters and 115 (one hundred and fifteen) contains 20 letters. The use of "and" when writing out numbers is in compliance with British usage. */
#include "0.hpp"
int ele[20] = {0, 3, 3, 5, 4, 4, 3, 5, 5, 4, 3,
6, 6, 8, 8, 7, 7, 9, 8, 8};
int ten[11] = {0, 3, 6, 6, 5, 5, 5, 7, 6, 6, 7};
int dot[4] = {0, 8, 7, 7};
string eles[20] = {"", "one", "two", "three", "four", "five", "six", "seven", "eight", "nine", "ten", "eleven", "twelve", "thirteen", "fourteen", "fifteen", "sixteen", "seventeen", "eighteen", "nineteen"};
string tens[11] = {"", "ten", "twenty", "thirty", "forty", "fifty", "sixty", "seventy", "eighty", "nithty", "hundrad"};
string dots[4] = {"", "thousand", "million", "billion"};
int analyse(int x)
{
int a = x / 100;
int b = x % 100;
int out = 0;
if(a) {
if(a / 10) {
out += ele[a / 10] + dot[1]; // thousand
cout << eles[a / 10] + " " + dots[1] + " ";
}
if(a % 10) {
out += ele[a % 10] + ten[10]; // hundrad
cout << eles[a % 10] + " " + tens[10] + " ";
}
if(b) {
out += 3; // and
cout << "and ";
}
}
if(b >= 20) {
out += ele[b % 10] + ten[b / 10];
cout << tens[b / 10] + " " + eles[b % 10] + " ";
}
else {
out += ele[b];
cout << eles[b];
}
cout << endl;
return out;
}
int main()
{
int sum = 0;
for(int i = 1; i <= 1000; i++) sum += analyse(i);
cout << sum << endl;
return 0;
}

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/** 1 Jan 1900 was a Monday.
How many Sundays fell on the first of the month during the twentieth century (1 Jan 1901 to 31 Dec 2000)? */
#include "0.hpp"
#define _ori 1901
#define _base 1900
#define _end 2000
#define _moon 1
#define _day 0
//int month[13] = {1, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
int month[13] = {0, 3, 0, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3};
int year[2] = {1, 2};
string day[7] = {"Sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday"};
int leap(int a)
{
if(a % 100 == 0) {
if(a % 400 == 0) return 1;
else return 0;
}
else {
if(a % 4 == 0) return 1;
else return 0;
}
}
int main()
{
int count = 0;
int sum = 1;
int yearsum;
for(int i = _ori; i <= _end; i++) { // loop of year
sum += year[leap(i - 1)];
yearsum = 0;
cout << i << '\t';
//for(int j = 2; j <= _moon; j++) // loop of month
//yearsum += month[j - 1];
//if(_moon > 2 && leap(i)) yearsum += month[0];
for(int j = 0; j < 12; j++) {
yearsum += month[j];
if(j == 2 && leap(i)) yearsum++;
if((sum + yearsum) % 7 == _day) count++;
cout << (sum + yearsum) % 7 << " ";
}
cout << '\t' << count;
cout << endl;
//for(int k = 0; k < month[_moon]; k++) // loop of date
//if((sum + k + yearsum) % 7 == _day) count++;
//cout << i << " " << (sum + yearsum) % 7 << endl;
}
cout << count << endl;
return 0;
}

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/** Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms. */
#include "0.hpp"
int main()
{
const uu _max = 4000000;
uu fib[3] = {0, 1, 1}; // 设置 fib 数列循环的数组
uu count = 1; // fib 数列的项计数器
uu sum = 0; // 满足条件的数的和
while(fib[count] <= _max) { // fib 数列小于要求值时不断循环
if(fib[count] % 2 == 0) sum += fib[count]; // 满足条件的项计入总和
//cout << fib[count] << endl;
count = (count + 1) % 3; // 项计数器
fib[count] = fib[(count + 1) % 3] + fib[(count + 2) % 3]; // fib 数列递推公式
}
cout << sum << endl; // 输出结果
return 0;
}

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/** n! means n * (n - 1) * ... * 3 * 2 * 1
For example, 10! = 10 * 9 * ... * 3 * 2 * 1 = 3628800,
and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27.
Find the sum of the digits in the number 100! */
#include "0.hpp"
#include "lib/lint.cpp"
#define _max 100
uint sum(string a)
{
uint suma = 0;
for(uint i = 0; i < a.size(); i++) suma += (a[i] - '0');
return suma;
}
int main()
{
lint a("1");
lint b;
for(int i = 1; i <= _max; i++) {
b = itos(i);
a = a * b;
}
cout << sum(a.getd()) << endl;
}

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/** Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).
If d(a) = b and d(b) = a, where a b, then a and b are an amicable pair and each of a and b are called amicable numbers.
For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.
Evaluate the sum of all the amicable numbers under 10000. */
#include "0.hpp"
#define _max 10000
uu ami(uu x)
{
uu test = 1;
uu sqr = (uu)(sqrt((double)x) + _eps);
if(x == sqr * sqr) test += sqr;
for(uu i = 2; i < sqr; i++)
if(x % i == 0) {
test += i + x / i;
//cout << i << endl << x / i <<endl;
}
return test;
}
int main()
{
uu sum = 0;
for(uu temp = 100; temp <= _max; temp++) {
uu amip = ami(temp);
if(temp == ami(amip) && temp - amip) {
//cout << temp << '\t' << amip << endl;
sum += amip + temp;
}
}
cout << sum / 2 << endl;
return 0;
}

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/** Using names.txt (right click and 'Save Link/Target As...'), a 46K text file containing over five-thousand first names, begin by sorting it into alphabetical order. Then working out the alphabetical value for each name, multiply this value by its alphabetical position in the list to obtain a name score.
For example, when the list is sorted into alphabetical order, COLIN, which is worth 3 + 15 + 12 + 9 + 14 = 53, is the 938th name in the list. So, COLIN would obtain a score of 938 53 = 49714.
What is the total of all the name scores in the file? */

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/** A perfect number is a number for which the sum of its proper divisors is exactly equal to the number. For example, the sum of the proper divisors of 28 would be 1 + 2 + 4 + 7 + 14 = 28, which means that 28 is a perfect number.
A number n is called deficient if the sum of its proper divisors is less than n and it is called abundant if this sum exceeds n.
As 12 is the smallest abundant number, 1 + 2 + 3 + 4 + 6 = 16, the smallest number that can be written as the sum of two abundant numbers is 24. By mathematical analysis, it can be shown that all integers greater than 28123 can be written as the sum of two abundant numbers. However, this upper limit cannot be reduced any further by analysis even though it is known that the greatest number that cannot be expressed as the sum of two abundant numbers is less than this limit.
Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers. */
#include "0.hpp"
#define _max 20161
uu divsum(uu numin)
{
uu out = 0;
for(uu i = 1; i <= numin / 3; i++) {
if(numin % i == 0) out += i;
}
return out;
}
int main()
{
uu haha = 0;
for(uu i = 1; i <= _max; i += 2)
if(divsum(i) >= i) haha += i;
cout << haha << endl;
return 0;
}

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/** A permutation is an ordered arrangement of objects. For example, 3124 is one possible permutation of the digits 1, 2, 3 and 4. If all of the permutations are listed numerically or alphabetically, we call it lexicographic order. The lexicographic permutations of 0, 1 and 2 are:
012 021 102 120 201 210
What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9? */
#include "0.hpp"
#define _max 10
#define _end 1000000
string ch = "0123456789";
uu count[_max] = {};
uu num[_max] = {1, 1};
int main()
{
uu locale = _end - 1;
string out = "";
for(unsigned int i = 2; i < _max; i++) {
num[i] = num[i - 1] * i;
//cout << num[i] << endl;
}
for(unsigned int i = _max - 1; i >= 1; i--) {
count[i] = locale / num[i];
locale %= num[i];
//cout << count[i] << endl;
out += ch[count[i]];
ch = ch.substr(0, count[i]) + ch.substr(count[i] + 1);
//cout << out << '\t' << ch << endl;
}
cout << out + ch << endl;
return 0;
}

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/** The Fibonacci sequence is defined by the recurrence relation:
Fn = Fn1 + Fn2, where F1 = 1 and F2 = 1.
Hence the first 12 terms will be:
F1 = 1
F2 = 1
F3 = 2
F4 = 3
F5 = 5
F6 = 8
F7 = 13
F8 = 21
F9 = 34
F10 = 55
F11 = 89
F12 = 144
The 12th term, F12, is the first term to contain three digits.
What is the first term in the Fibonacci sequence to contain 1000 digits? */
#include "0.hpp"
#include "lib/lint.cpp"
void fib_matrix(unsigned int maxnum);
int main()
{
unsigned int max;
cin >> max;
//for(int i = 1; i <= max; i++) cout << fib_recursive(i) << endl;
fib_matrix(max);
return 0;
}
void fib_matrix(unsigned int maxnum)
{
string first = "1";
lint fib[2];
fib[0] = first;
fib[1] = first;
//for(int i = 1; i <= maxnum; i++) {
int i = 1;
while(1) {
//cout << fib[i % 2].getd() << endl;
if(fib[i % 2].getd().size() >= maxnum) break;
if(i >= 2) fib[(i + 1) % 2] = fib[(i + 1) % 2] + fib[i % 2];
i++;
}
//cout << fib[maxnum % 2].getd() << endl;
cout << i << endl;
}

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/** A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:
1/2 = 0.5
1/3 = 0.(3)
1/4 = 0.25
1/5 = 0.2
1/6 = 0.1(6)
1/7 = 0.(142857)
1/8 = 0.125
1/9 = 0.(1)
1/10 = 0.1
Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.
Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part. */
#include "0.hpp"
const int _max = 10000;
int cycle(int num)
{
int mod[_max] = {0};
int temp = 10;
int count = 0;
int flag = 1;
do {
if(temp == 0) break;
if(temp < num) temp *= 10;
//cout << temp / num;
temp %= num;
mod[count] = temp;
for(int i = 0; i <= count - 1; i++)
if(temp == mod[i]) {
flag = 0;
count -= i;
count--;
}
count++;
} while(flag);
//cout << '\t' << count << endl;
return count;
}
int main()
{
int max[2] = {0, 0};
for(int i = 2; i <= _max; i++) {
//cout << i << '\t';
int temp = cycle(i);
if(temp > max[1]) {
max[0] = i;
max[1] = temp;
}
}
cout << max[0] << '\t' << max[1] << endl;
return 0;
}

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/** The prime factors of 13195 are 5, 7, 13 and 29.
What is the largest prime factor of the number 600851475143 ? */
#include "0.hpp"
/* 分解因数，如果是素数返回 1 */
uu factor(uu a, uu min = 2)
{
uu temp = min;
uu sqr = (int)(sqrt((double)a) + _eps); // 定义尝试上界
while(temp < sqr) if(a % ++temp == 0) break; // 从最小值到上界开始尝试
if(a % temp == 0) return temp; // 如果 a 能分解则返回最小因子
else return 1; // 如果 a 是素数就返回 1，此处也可以设置为返回 x 本身
}
int main()
{
uu num = 600851475143;
uu temp = 2; // 尝试循环分解 num 的因子
do {
if(num % temp == 0) { // 如果满足 temp 整除 num
if(factor(num / temp) == 1) break; // 同时 num / temp 是素数则返回
else num /= temp; // 如果 num / temp 不为素数，就缩小 num 以减小运算量
}
temp++; // temp 增加
} while(1);
cout << (num / temp) << endl; // 输出结果
return 0;
}

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/** A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 * 99.
Find the largest palindrome made from the product of two 3-digit numbers.. */
/** 1001 = 7 * 11 * 13 */
#define _max 997
#include "0.hpp"
int main()
{
int pal = 0;
for(int i = _max; i >= 100; i--) {
int temp = i;
pal = 0;
while(temp > 0) {
pal = pal * 10 + temp % 10;
temp /= 10;
}
pal += i * 1000;
int m = 100;
do {
while(pal % m != 0) m++;
if(m < 1000 && pal / m < 1000) {
cout << pal << " = " << m << " * " << pal / m << endl;
return 0;
}
m++;
} while(m < 1000);
}
return 0;
}

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/** The series, 11 + 22 + 33 + ... + 1010 = 10405071317.
Find the last ten digits of the series, 1^1 + 2^2 + 3^3 + ... + 1000^1000. */
#include "0.hpp"
#include "lib/lint.cpp"
#define _max 1000
#define _mod 10000000000
#define _array 10
uu pow(uu a, uu b, uu mod = _mod)
{
int bi[_array] = {0};
for(int i = 0; i < _array; i++) {
bi[i] = b % 2;
b /= 2;
}
uu out = 1;
for(int i = _array - 1; i >= 0; i--) {
out = (out % mod) * out % mod;
if(bi[i] == 1) out = (out * a) % mod;
}
return out;
}
int main()
{
uu sum = 0;
for(uu i = 1; i <= _max; i++) {
sum += pow(i, i);
sum = sum % _mod;
}
cout << sum << endl;
return 0;
}

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/** 2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.
What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20? */
#include "0.hpp"
int main()
{
const int _max = 20;
uu num[_max] = {0};
for(int i = 0; i < _max; i++) num[i] = i + 1;
for(int i = 0; i < _max; i++)
if(num[i] > 1)
for(int j = i + 1; j < _max; j++)
if(num[j] % num[i] == 0) num[j] /= num[i];
uu divnum = 1;
for(int i = 0; i < _max; i++) {
divnum *= num[i];
cout << num[i] << " ";
}
cout << endl;
cout << divnum << endl;
return 0;
}

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/** The sum of the squares of the first ten natural numbers is,
1^2 + 2^2 + ... + 10^2 = 385
The square of the sum of the first ten natural numbers is,
(1 + 2 + ... + 10)^2 = 552 = 3025
Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 385 = 2640.
Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum. */
#include "0.hpp"
#define _max 100
int main()
{
uu sum = 0; // 最终的和
uu num[_max];
for(int i = 0; i < _max; i++) num[i] = i + 1;
for(int i = 0; i < _max; i++)
for(int j = i + 1; j < _max; j++)
sum += num[i] * num[j];
sum *= 2;
cout << sum << endl;
return 0;
}

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/** By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.
What is the 10001st prime number? */
#include "0.hpp"
#define _num 10001
uu factor(uu a, uu min = 1)
{
uu temp = min;
uu sqr = (int)sqrt((double)a);
while(temp < sqr) if(a % ++temp == 0) break;
if(a % temp == 0) return temp;
else return 1;
}
int main()
{
uu num = 1;
int count = 0;
do {
if(factor(++num) == 1) {
//cout << num << endl;
++count;
}
} while(count < _num);
cout << num << endl;
return 0;
}

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/** Discover the largest product of five consecutive digits in the 1000-digit number. */
#include "0.hpp"
string str = "731671765313306249192251196744265747423553491949349698352031277450632623957831801698480186947885184385861560789112949495459501737958331952853208805511125406987471585238630507156932909632952274430435576689664895044524452316173185640309871112172238311362229893423380308135336276614282806444486645238749303589072962904915604407723907138105158593079608667017242712188399879790879227492190169972088809377665727333001053367881220235421809751254540594752243258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450";
struct place {
string str;
int value;
int locale;
};
int sss(string ch)
{
int pro = 1;
for(int i = 0; i < _unit; i++) {
pro *= (int)(ch[i] - '0');
}
return pro;
}
int main()
{
const int _unit = 5;
int length = str.size() - _unit;
place max;
max.str = "";
max.value = 0;
max.locale = 0;
for(int i = 0; i <= length; i++) {
int valuetemp = sss(str.substr(i, _unit));
if(valuetemp > max.value) {
max.locale = i;
max.value = valuetemp;
max.str = str.substr(i, _unit);
}
}
cout << "max product is " + max.str << endl;
cout << "the value of product is " << max.value << endl;
cout << "locale is " << max.locale << endl;
return 0;
}

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/** A Pythagorean triplet is a set of three natural numbers, a b c, for which,
a^2 + b^2 = c^2
For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.
There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc. */
#include "0.hpp"
int main()
{
const uu _max = 1000;
uu _min = (int)((sqrt(2) - 1) * _max);
uu root;
uu i;
for(i = _min; i <= _max; i++) {
uu sqr = (i + _max) * (i + _max) - 2 * _max * _max;
root = (int)(sqrt((double)sqr) + _eps);
if(sqr == root * root) break;
}
cout << i << endl << (_max + root - i) / 2 << endl;
cout << abs(_max - i - root) / 2 << endl;
return 0;
}

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79,59,12,2,79,35,8,28,20,2,3,68,8,9,68,45,0,12,9,67,68,4,7,5,23,27,1,21,79,85,78,79,85,71,38,10,71,27,12,2,79,6,2,8,13,9,1,13,9,8,68,19,7,1,71,56,11,21,11,68,6,3,22,2,14,0,30,79,1,31,6,23,19,10,0,73,79,44,2,79,19,6,28,68,16,6,16,15,79,35,8,11,72,71,14,10,3,79,12,2,79,19,6,28,68,32,0,0,73,79,86,71,39,1,71,24,5,20,79,13,9,79,16,15,10,68,5,10,3,14,1,10,14,1,3,71,24,13,19,7,68,32,0,0,73,79,87,71,39,1,71,12,22,2,14,16,2,11,68,2,25,1,21,22,16,15,6,10,0,79,16,15,10,22,2,79,13,20,65,68,41,0,16,15,6,10,0,79,1,31,6,23,19,28,68,19,7,5,19,79,12,2,79,0,14,11,10,64,27,68,10,14,15,2,65,68,83,79,40,14,9,1,71,6,16,20,10,8,1,79,19,6,28,68,14,1,68,15,6,9,75,79,5,9,11,68,19,7,13,20,79,8,14,9,1,71,8,13,17,10,23,71,3,13,0,7,16,71,27,11,71,10,18,2,29,29,8,1,1,73,79,81,71,59,12,2,79,8,14,8,12,19,79,23,15,6,10,2,28,68,19,7,22,8,26,3,15,79,16,15,10,68,3,14,22,12,1,1,20,28,72,71,14,10,3,79,16,15,10,68,3,14,22,12,1,1,20,28,68,4,14,10,71,1,1,17,10,22,71,10,28,19,6,10,0,26,13,20,7,68,14,27,74,71,89,68,32,0,0,71,28,1,9,27,68,45,0,12,9,79,16,15,10,68,37,14,20,19,6,23,19,79,83,71,27,11,71,27,1,11,3,68,2,25,1,21,22,11,9,10,68,6,13,11,18,27,68,19,7,1,71,3,13,0,7,16,71,28,11,71,27,12,6,27,68,2,25,1,21,22,11,9,10,68,10,6,3,15,27,68,5,10,8,14,10,18,2,79,6,2,12,5,18,28,1,71,0,2,71,7,13,20,79,16,2,28,16,14,2,11,9,22,74,71,87,68,45,0,12,9,79,12,14,2,23,2,3,2,71,24,5,20,79,10,8,27,68,19,7,1,71,3,13,0,7,16,92,79,12,2,79,19,6,28,68,8,1,8,30,79,5,71,24,13,19,1,1,20,28,68,19,0,68,19,7,1,71,3,13,0,7,16,73,79,93,71,59,12,2,79,11,9,10,68,16,7,11,71,6,23,71,27,12,2,79,16,21,26,1,71,3,13,0,7,16,75,79,19,15,0,68,0,6,18,2,28,68,11,6,3,15,27,68,19,0,68,2,25,1,21,22,11,9,10,72,71,24,5,20,79,3,8,6,10,0,79,16,8,79,7,8,2,1,71,6,10,19,0,68,19,7,1,71,24,11,21,3,0,73,79,85,87,79,38,18,27,68,6,3,16,15,0,17,0,7,68,19,7,1,71,24,11,21,3,0,71,24,5,20,79,9,6,11,1,71,27,12,21,0,17,0,7,68,15,6,9,75,79,16,15,10,68,16,0,22,11,11,68,3,6,0,9,72,16,71,29,1,4,0,3,9,6,30,2,79,12,14,2,68,16,7,1,9,79,12,2,79,7,6,2,1,73,79,85,86,79,33,17,10,10,71,6,10,71,7,13,20,79,11,16,1,68,11,14,10,3,79,5,9,11,68,6,2,11,9,8,68,15,6,23,71,0,19,9,79,20,2,0,20,11,10,72,71,7,1,71,24,5,20,79,10,8,27,68,6,12,7,2,31,16,2,11,74,71,94,86,71,45,17,19,79,16,8,79,5,11,3,68,16,7,11,71,13,1,11,6,1,17,10,0,71,7,13,10,79,5,9,11,68,6,12,7,2,31,16,2,11,68,15,6,9,75,79,12,2,79,3,6,25,1,71,27,12,2,79,22,14,8,12,19,79,16,8,79,6,2,12,11,10,10,68,4,7,13,11,11,22,2,1,68,8,9,68,32,0,0,73,79,85,84,79,48,15,10,29,71,14,22,2,79,22,2,13,11,21,1,69,71,59,12,14,28,68,14,28,68,9,0,16,71,14,68,23,7,29,20,6,7,6,3,68,5,6,22,19,7,68,21,10,23,18,3,16,14,1,3,71,9,22,8,2,68,15,26,9,6,1,68,23,14,23,20,6,11,9,79,11,21,79,20,11,14,10,75,79,16,15,6,23,71,29,1,5,6,22,19,7,68,4,0,9,2,28,68,1,29,11,10,79,35,8,11,74,86,91,68,52,0,68,19,7,1,71,56,11,21,11,68,5,10,7,6,2,1,71,7,17,10,14,10,71,14,10,3,79,8,14,25,1,3,79,12,2,29,1,71,0,10,71,10,5,21,27,12,71,14,9,8,1,3,71,26,23,73,79,44,2,79,19,6,28,68,1,26,8,11,79,11,1,79,17,9,9,5,14,3,13,9,8,68,11,0,18,2,79,5,9,11,68,1,14,13,19,7,2,18,3,10,2,28,23,73,79,37,9,11,68,16,10,68,15,14,18,2,79,23,2,10,10,71,7,13,20,79,3,11,0,22,30,67,68,19,7,1,71,8,8,8,29,29,71,0,2,71,27,12,2,79,11,9,3,29,71,60,11,9,79,11,1,79,16,15,10,68,33,14,16,15,10,22,73

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#include <iostream>
using namespace std;
typedef unsigned long long int uu;
void function(uu n)
{
uu m, k, t;
t = 1;
m = n;
while (m > 1) {
k = 2;
while (m % k != 0) k++;
if (t) cout << k;
else cout << "*" << k;
m = m / k;
t = 0;
}
cout << endl;
}
int main()
{
cout << "use 0 to exit" << endl;
uu num;
do {
cin >> num;
if(num == 0) break;
function(num);
} while(1);
return 0;
}

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#include "lint.hpp"
void get(vector< complex<long double> > x)
{
for(uint i = x.size() - 1; i >= 0; i--) {
if(i > x.size()) break;
cout << x[i] << " ";
}
cout << endl << endl;
}
void get(vuint x)
{
for(uint i = x.size() - 1; i >= 0; i--) {
if(i > x.size()) break;
cout << x[i] << " ";
}
cout << endl << endl;
}
lint::lint() { }
lint::lint(string lintin)
{
operator =(lintin);
}
lint::~lint()
{ num.clear(); }
void lint::operator =(string strin)
{
sign = 1;
strin = del(strin);
if(strin[0] == '-') {
sign = -1;
strin = strin.substr(1, strin.size() - 1);
}
/* 整理输入，使其全是数字，并且首位无0 */
for(uint i = 0; i < strin.size(); i++)
if(strin[i] > '9' || strin[i] < '0') strin[i] = '0';
length = strin.size();
len = (length + unit - 1) / unit;
uint mod = length % unit;
if(num.capacity()) num.clear();
num.resize(len);
for(uint i = 0; i < len - 1; i++)
num[i] = atoi(strin.substr(length - (i + 1) * unit, unit).c_str());
num[len - 1] = atoi(strin.substr(0, (mod == 0) ? unit : mod).c_str());
}
/* 提取十进制数值 */
string lint::getd()
{ return vtos(num); }
vuint lint::getvec()
{
return num;
}
/* 提取 vector 中相应位置的数字 */
uint lint::operator [](uint locale)
{
if(locale >= len) return 0;
else return num[locale];
}
/* 提取 vector 的长度 */
uint lint::getlen()
{ return len; }
/* 提取整数长度 */
uint lint::getlength()
{ return length; }
int lint::getsign()
{ return sign; }
/* 定义加法 */
string lint::operator +(lint opnum)
{
if(sign * opnum.getsign() == -1) {
if(sign == -1) {
lint abs(getd());
return opnum - abs;
} else {
lint abs(opnum.getd());
lint absa(getd());
return absa - abs;
}
} else {
vuint sumint(1);
vuint sumshort(1);
if(len >= opnum.getlen()) {
sumint.resize(len);
sumint = getvec();
sumshort = opnum.getvec();
} else {
sumint.resize(opnum.getlen());
sumint = opnum.getvec();
sumshort = getvec();
}
sumint.resize(sumint.size() + 1);
sumint[sumint.size()] = 0;
uint temp;
for(uint i = 0; i < sumshort.size(); i++) {
temp = sumint[i] + sumshort[i];
sumint[i] = temp % cunit;
sumint[i + 1] += temp / cunit;
}
for(uint i = sumshort.size(); i < sumint.size() - 1; i++) {
temp = sumint[i];
sumint[i] = temp % cunit;
sumint[i + 1] += temp / cunit;
}
if(sign == -1) return "-" + vtos(sumint);
else return vtos(sumint);
}
}
string lint::operator -(lint opnum)
{
if(sign * opnum.getsign() == -1) {
if(sign == 1) return operator +(opnum);
else return "-" + operator +(opnum);
} else {
vuint difint(len >= opnum.getlen() ? len : opnum.getlen());
vuint small(len >= opnum.getlen() ? opnum.getlen() : len);
if(compare(opnum) >= 0) {
difint = num;
small = opnum.getvec();
} else {
difint = opnum.getvec();
small = num;
}
for(uint i = small.size() - 1; i >= 0; i--) {
if(i > small.size()) break;
if(difint[i] < small[i]) {
uint temp = i + 1;
while(difint[temp] == 0) {
difint[temp] = cunit - 1;
temp++;
if(temp >= difint.size()) break;
}
if(temp < difint.size()) difint[temp]--;
difint[i] += cunit;
}
difint[i] -= small[i];
}
if(sign * compare(opnum) == 1) return vtos(difint);
else return "-" + vtos(difint);
}
}
/* 定义乘法，用 FFT 实现 */
string lint::operator *(lint opnum)
{
uint a_size = len, b_size = opnum.getlen();
vector< complex<long double> > a(a_size), b(b_size);
for(uint i = 0; i < a_size; i++) a[i].real() = num[i];
for(uint i = 0; i < b_size; i++) b[i].real() = (opnum[i]);
uint n;
a_size += b_size;
for (n = a_size; n != (n&-n); n += (n&-n));
a.resize(n);
b.resize(n);
FFT(a, n);
FFT(b, n);
for (uint i = 0; i < n; i++)
a[i] *= b[i];
IFFT(a, n);
for (uint i = 0; i < a_size-1; i++) {
a[i + 1] += a[i].real() / 1000.;
a[i] = fmodl(a[i].real(), 1000.L);
a[i].real() += eps;
}
vuint mulout(n);
for(uint i = 0; i < a.size(); i++) mulout[i] = a[i].real();
if(sign * opnum.getsign() == -1) return "-" + vtos(mulout);
else return vtos(mulout);
}
int lint::operator ==(lint opnum)
{
if(sign * opnum.getsign() > 0) {
if(sign == 1) return compare(opnum);
if(sign == -1) return -(compare(opnum));
else return 0;
} else {
if(sign == 1) return 1;
else return -1;
}
}
int lint::compare(lint opnum)
{
if(length > opnum.getlength()) return 1;
if(length < opnum.getlength()) return -1;
else {
for(uint i = len - 1; i >= 0; i--) {
if(i > len - 1) break;
if(num[i] > (opnum[i])) return 1;
if(num[i] < (opnum[i])) return -1;
}
return 0;
}
}
/* 定义除法 */
string lint::operator /(lint opnum)
{
if(compare(opnum) == -1) return "0";
if(compare(opnum) == 0) return "1";
else {
uint move = len - opnum.getlen();
vuint devint(move + 1);
vuint open = getvec();
open.resize(len + 1);
open[len] = 0;
for(uint i = move; i >= 0; i--) {
if(i > move) break;
uint high = i + opnum.getlen() - 1;
if(open.capacity() <= high) {
open.resize(high + 2);
open[high + 1] = 0;
}
uint temp = (open[high] + open[high + 1] * cunit) / opnum.getvec().back() + 2;
vuint tryvec;
int count = 1;
do {
if(--temp > cunit * cunit) temp = 1;
tryvec = vmul(opnum.getvec(), temp, i);
count++;
} while(vless(open, tryvec) && count < 20);
devint[i] = temp;
open = vdif(open, tryvec);
open[open.size()] = 0;
tryvec.clear();
}
if(sign * opnum.getsign() == 1) return vtos(devint);
else return "-" + vtos(devint);
}
}
string lint::operator %(lint opnum)
{
if(sign == 1 && compare(opnum) == -1) return getd();
else {
lint div = getd();
lint q = (div / opnum);
lint mod = (div - (q * opnum));
if(sign == 1) return mod.getd();
else return (opnum - mod);
}
}
vuint lint::getbit()
{
vuint out(len * 3);
lint opnum = getd();
lint bit("2");
uint i;
for(i = 0; i < len * 3; i++) {
if(opnum % bit == "1") out[i] = 1;
else out[i] = 0;
opnum = opnum / bit;
}
while(opnum.getd() != "0") {
out.resize(i + 2);
if(opnum % bit == "1") out[i] = 1;
else out[i] = 0;
opnum = opnum / bit;
i++;
}
return del(out);
}
string lint::operator ^(lint opnum)
{
lint power("1");
lint base = getd();
for(uint i = opnum.getbit().size() - 1; i >= 0; i--) {
if(i > opnum.getbit().size()) break;
power = (power * power);
if(opnum.getbit()[i] == 1) power = (power * base);
}
return del(power.getd());
}
/* 消去首位0 */
string del(string undel)
{
uint flag = 0;
while(undel.substr(0, 2) == "--") undel = undel.substr(2, undel.size() - 2);
if(undel[0] == '-') {
undel = undel.substr(1, undel.size() - 1);
flag = 1;
}
while(undel.size() > 1 && undel[0] == '0')
undel = undel.substr(1, undel.size() - 1);
if(undel.size() == 1 && undel[0] == '0') return "0";
if(flag) return "-" + undel;
return undel;
}
vuint del(vuint undel)
{
while(undel[undel.size() - 1] == 0) undel.pop_back();
vuint out(undel.size());
for(uint i = 0; i < undel.size(); i++) out[i] = undel[i];
return out;
}
/* 整数到字符串的转换 */
string itos(uint intin)
{
string strout = "";
if(intin == 0) return "0";
while(intin > 0) {
char temp = intin % carry + '0';
strout = temp + strout;
intin /= carry;
}
return strout;
}
/* 向量到字符串的转换 */
string vtos(vuint vin)
{
string strout = "";
string temp = "";
for(uint i = vin.size() - 1; i >= 0; i--) {
if(i > vin.size() - 1) break;
temp = itos(vin[i] % cunit);
while(temp.size() < unit) temp = "0" + temp;
strout += temp;
}
return del(strout);
}
/**
向量转比特流
string vtobit(vuint vin)
{
string strout = "";
for(uint i = vin.size() - 1; i >= 0; i--) {
if(i > vin.size()) break;
if(vin[i]) strout += "1";
else strout += "0";
}
return del(strout);
}*/
/* 向量和整数的乘法 */
vuint vmul(vuint op, uint opnum, uint power = 0)
{
if(power) {
op.resize(op.size() + power);
for(uint i = op.size() - 1; i >= power; i--) {
if(i > op.size()) break;
op[i] = op[i - power];
}
for(uint i = power - 1; i >= 0; i--) {
if(i > op.size()) break;
op[i] = 0;
}
}
lint big(vtos(op));
lint small(itos(opnum));
lint out(big * small);
return out.getvec();
}
/* 向量减法 */
vuint vdif(vuint big, vuint small)
{
lint bigint(vtos(big));
lint smallint(vtos(small));
if(bigint.compare(smallint) == -1) return big;
else {
lint out(bigint - smallint);
return out.getvec();
}
}
/* 比较大小 */
uint vless(vuint big, vuint small)
{
lint bigint(vtos(big));
lint smallint(vtos(small));
if(bigint.compare(smallint) == -1) return 1;
else return 0;
}
/* 快速傅立叶变换 */
void FFT(vector< complex<long double> > &x, uint n)
{
uint i,j,k,t;
for (i = 0; i < n; ++i) {
j = 0;
for (t = i, k = n; k /= 2; t /= 2)
j = j*2+t%2;
if (j > i) swap(x[j], x[i]);
}
for (k = 2; k <= n; k *= 2) {
const complex<long double> omega_unit(cosl(2*PI/k), sinl(2*PI/k));
for (i = 0; i < n; i += k) {
complex<long double> omega(1, 0);
for (j = 0; j < k/2; ++j) {
complex<long double> t = omega*x[i+j+k/2];
x[i+j+k/2] = x[i+j]-t;
x[i+j] += t;
omega *= omega_unit;
}
}
}
}
void IFFT(vector< complex<long double> > &x, uint n)
{ uint i,j,k,t;
for (i = 0; i < n; ++i) {
j = 0;
for (t = i, k = n; k /= 2; t /= 2)
j = j*2+t%2;
if (j > i) swap(x[j], x[i]);
}
for (k = 2; k <= n; k *= 2) {
const complex<long double> omega_unit(cosl(-2*PI/k), sinl(-2*PI/k));
for (i = 0; i < n; i += k) {
complex<long double> omega(1, 0);
for (j = 0; j < k/2; ++j) {
complex<long double> t = omega*x[i+j+k/2];
x[i+j+k/2] = x[i+j]-t;
x[i+j] += t;
omega *= omega_unit;
}
}
}
for (i = 0; i < n; ++i)
x[i] /= n;
}
/* 求两数最大公约数 */
string gcd(lint a, lint b)
{
if(b.getd() == "0") return a.getd();
else {
lint newb = a % b;
return gcd(b, newb);
}
}

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#include <stdlib.h>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <string.h>
#include <string>
#include <vector>
using namespace std;
#define unit 3
#define carry 10
#define cunit 1000
#define eps 0.00001
typedef unsigned int uint;
typedef vector<uint> vuint;
const long double PI = 3.1415926535897932384626433832795L;
string del(string);//除去字符串前位多余负号和0
vuint del(vuint);//除去向量前位多余0
string itos(uint);//整数转字符串
string vtos(vuint);//向量转字符串
//string vtobit(vuint);//向量转比特流
uint vless(vuint, vuint);//前者是否小于后者
vuint vmul(vuint, uint, uint);//向量与整数乘法
vuint vdif(vuint, vuint);//向量做差
void FFT(vector< complex<long double> > &, uint);
void IFFT(vector< complex<long double> > &, uint);
/* class */
class lint {
public:
lint();
lint(string);
~lint();
string getd();//获得十进制无符号整数
vuint getvec();//获得整数向量
vuint getbit();//获得二进制向量
uint operator [](uint);//获得整数向量中的元素
uint getlen();//获得向量长度
uint getlength();//获得无符号整数长度
int getsign();//获得符号
int compare(lint);//比较无符号整数大小
int operator ==(lint);//比较有符号整数大小
/*以下返回的都是有符号整数*/
void operator =(string);
string operator +(lint);
string operator *(lint);
string operator -(lint);
string operator /(lint);
string operator ^(lint);
/*以下返回无符号整数*/
string operator %(lint);
private:
uint len;//向量长度
uint length;//数字部分长度
vuint num;//整数组向量
int sign;//符号
};
string gcd(lint, lint);//求两数最大公约数

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#include <stdlib.h>
#include <time.h>
#include <math.h>
int random(int a_random, int b_random);
double random(double c_random, double d_random, int accu);
int random(int a_random, int b_random)
{
if(a_random >= b_random) return 0;
int temp_int_random;
int int_random = 0;
int accu = b_random - a_random;
if(accu < 10000) accu = 10000;
temp_int_random = time(NULL) % (accu - 1) + 1;
for(int i_int_random = 1; i_int_random <= temp_int_random; i_int_random++)
int_random = (int_random + rand()) % accu;
int_random = int_random % (b_random - a_random) + a_random;
return int_random;
}
double random(double a_random, double b_random, int accu = 4)
{
if(a_random >= b_random) return 0;
double temp = 0.0;
for(int i = 1; i <= accu; i++) {
temp += double(random(0, 10)) * pow(0.1, double(i));
}
return temp * (b_random - a_random) + a_random;
}

23
c++/lib/try.cpp Normal file
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@ -0,0 +1,23 @@
#include <iostream>
#include "lint.cpp"
#include <sys/timeb.h>
using namespace std;
const uint x = 10000 - 1;
int main()
{
lint a[3];
a[0] = "1";
a[1] = "1";
a[2] = "0";
timeb start, end;
ftime(&start);
for(uint i = 1; i <= x; i++) {
a[(i + 1) % 2] = a[i % 2] + a[(i - 1) % 2];
}
ftime(&end);
cout << a[x % 2].getd() << endl;
cout << (end.time - start.time) * 1000 + end.millitm - start.millitm << endl;
return 0;
}

1
cipher1.txt Normal file
View File

@ -0,0 +1 @@
79,59,12,2,79,35,8,28,20,2,3,68,8,9,68,45,0,12,9,67,68,4,7,5,23,27,1,21,79,85,78,79,85,71,38,10,71,27,12,2,79,6,2,8,13,9,1,13,9,8,68,19,7,1,71,56,11,21,11,68,6,3,22,2,14,0,30,79,1,31,6,23,19,10,0,73,79,44,2,79,19,6,28,68,16,6,16,15,79,35,8,11,72,71,14,10,3,79,12,2,79,19,6,28,68,32,0,0,73,79,86,71,39,1,71,24,5,20,79,13,9,79,16,15,10,68,5,10,3,14,1,10,14,1,3,71,24,13,19,7,68,32,0,0,73,79,87,71,39,1,71,12,22,2,14,16,2,11,68,2,25,1,21,22,16,15,6,10,0,79,16,15,10,22,2,79,13,20,65,68,41,0,16,15,6,10,0,79,1,31,6,23,19,28,68,19,7,5,19,79,12,2,79,0,14,11,10,64,27,68,10,14,15,2,65,68,83,79,40,14,9,1,71,6,16,20,10,8,1,79,19,6,28,68,14,1,68,15,6,9,75,79,5,9,11,68,19,7,13,20,79,8,14,9,1,71,8,13,17,10,23,71,3,13,0,7,16,71,27,11,71,10,18,2,29,29,8,1,1,73,79,81,71,59,12,2,79,8,14,8,12,19,79,23,15,6,10,2,28,68,19,7,22,8,26,3,15,79,16,15,10,68,3,14,22,12,1,1,20,28,72,71,14,10,3,79,16,15,10,68,3,14,22,12,1,1,20,28,68,4,14,10,71,1,1,17,10,22,71,10,28,19,6,10,0,26,13,20,7,68,14,27,74,71,89,68,32,0,0,71,28,1,9,27,68,45,0,12,9,79,16,15,10,68,37,14,20,19,6,23,19,79,83,71,27,11,71,27,1,11,3,68,2,25,1,21,22,11,9,10,68,6,13,11,18,27,68,19,7,1,71,3,13,0,7,16,71,28,11,71,27,12,6,27,68,2,25,1,21,22,11,9,10,68,10,6,3,15,27,68,5,10,8,14,10,18,2,79,6,2,12,5,18,28,1,71,0,2,71,7,13,20,79,16,2,28,16,14,2,11,9,22,74,71,87,68,45,0,12,9,79,12,14,2,23,2,3,2,71,24,5,20,79,10,8,27,68,19,7,1,71,3,13,0,7,16,92,79,12,2,79,19,6,28,68,8,1,8,30,79,5,71,24,13,19,1,1,20,28,68,19,0,68,19,7,1,71,3,13,0,7,16,73,79,93,71,59,12,2,79,11,9,10,68,16,7,11,71,6,23,71,27,12,2,79,16,21,26,1,71,3,13,0,7,16,75,79,19,15,0,68,0,6,18,2,28,68,11,6,3,15,27,68,19,0,68,2,25,1,21,22,11,9,10,72,71,24,5,20,79,3,8,6,10,0,79,16,8,79,7,8,2,1,71,6,10,19,0,68,19,7,1,71,24,11,21,3,0,73,79,85,87,79,38,18,27,68,6,3,16,15,0,17,0,7,68,19,7,1,71,24,11,21,3,0,71,24,5,20,79,9,6,11,1,71,27,12,21,0,17,0,7,68,15,6,9,75,79,16,15,10,68,16,0,22,11,11,68,3,6,0,9,72,16,71,29,1,4,0,3,9,6,30,2,79,12,14,2,68,16,7,1,9,79,12,2,79,7,6,2,1,73,79,85,86,79,33,17,10,10,71,6,10,71,7,13,20,79,11,16,1,68,11,14,10,3,79,5,9,11,68,6,2,11,9,8,68,15,6,23,71,0,19,9,79,20,2,0,20,11,10,72,71,7,1,71,24,5,20,79,10,8,27,68,6,12,7,2,31,16,2,11,74,71,94,86,71,45,17,19,79,16,8,79,5,11,3,68,16,7,11,71,13,1,11,6,1,17,10,0,71,7,13,10,79,5,9,11,68,6,12,7,2,31,16,2,11,68,15,6,9,75,79,12,2,79,3,6,25,1,71,27,12,2,79,22,14,8,12,19,79,16,8,79,6,2,12,11,10,10,68,4,7,13,11,11,22,2,1,68,8,9,68,32,0,0,73,79,85,84,79,48,15,10,29,71,14,22,2,79,22,2,13,11,21,1,69,71,59,12,14,28,68,14,28,68,9,0,16,71,14,68,23,7,29,20,6,7,6,3,68,5,6,22,19,7,68,21,10,23,18,3,16,14,1,3,71,9,22,8,2,68,15,26,9,6,1,68,23,14,23,20,6,11,9,79,11,21,79,20,11,14,10,75,79,16,15,6,23,71,29,1,5,6,22,19,7,68,4,0,9,2,28,68,1,29,11,10,79,35,8,11,74,86,91,68,52,0,68,19,7,1,71,56,11,21,11,68,5,10,7,6,2,1,71,7,17,10,14,10,71,14,10,3,79,8,14,25,1,3,79,12,2,29,1,71,0,10,71,10,5,21,27,12,71,14,9,8,1,3,71,26,23,73,79,44,2,79,19,6,28,68,1,26,8,11,79,11,1,79,17,9,9,5,14,3,13,9,8,68,11,0,18,2,79,5,9,11,68,1,14,13,19,7,2,18,3,10,2,28,23,73,79,37,9,11,68,16,10,68,15,14,18,2,79,23,2,10,10,71,7,13,20,79,3,11,0,22,30,67,68,19,7,1,71,8,8,8,29,29,71,0,2,71,27,12,2,79,11,9,3,29,71,60,11,9,79,11,1,79,16,15,10,68,33,14,16,15,10,22,73

50
keylog.txt Normal file
View File

@ -0,0 +1,50 @@
319
680
180
690
129
620
762
689
762
318
368
710
720
710
629
168
160
689
716
731
736
729
316
729
729
710
769
290
719
680
318
389
162
289
162
718
729
319
790
680
890
362
319
760
316
729
380
319
728
716

80
matrix.txt Normal file
View File

@ -0,0 +1,80 @@
4445,2697,5115,718,2209,2212,654,4348,3079,6821,7668,3276,8874,4190,3785,2752,9473,7817,9137,496,7338,3434,7152,4355,4552,7917,7827,2460,2350,691,3514,5880,3145,7633,7199,3783,5066,7487,3285,1084,8985,760,872,8609,8051,1134,9536,5750,9716,9371,7619,5617,275,9721,2997,2698,1887,8825,6372,3014,2113,7122,7050,6775,5948,2758,1219,3539,348,7989,2735,9862,1263,8089,6401,9462,3168,2758,3748,5870
1096,20,1318,7586,5167,2642,1443,5741,7621,7030,5526,4244,2348,4641,9827,2448,6918,5883,3737,300,7116,6531,567,5997,3971,6623,820,6148,3287,1874,7981,8424,7672,7575,6797,6717,1078,5008,4051,8795,5820,346,1851,6463,2117,6058,3407,8211,117,4822,1317,4377,4434,5925,8341,4800,1175,4173,690,8978,7470,1295,3799,8724,3509,9849,618,3320,7068,9633,2384,7175,544,6583,1908,9983,481,4187,9353,9377
9607,7385,521,6084,1364,8983,7623,1585,6935,8551,2574,8267,4781,3834,2764,2084,2669,4656,9343,7709,2203,9328,8004,6192,5856,3555,2260,5118,6504,1839,9227,1259,9451,1388,7909,5733,6968,8519,9973,1663,5315,7571,3035,4325,4283,2304,6438,3815,9213,9806,9536,196,5542,6907,2475,1159,5820,9075,9470,2179,9248,1828,4592,9167,3713,4640,47,3637,309,7344,6955,346,378,9044,8635,7466,5036,9515,6385,9230
7206,3114,7760,1094,6150,5182,7358,7387,4497,955,101,1478,7777,6966,7010,8417,6453,4955,3496,107,449,8271,131,2948,6185,784,5937,8001,6104,8282,4165,3642,710,2390,575,715,3089,6964,4217,192,5949,7006,715,3328,1152,66,8044,4319,1735,146,4818,5456,6451,4113,1063,4781,6799,602,1504,6245,6550,1417,1343,2363,3785,5448,4545,9371,5420,5068,4613,4882,4241,5043,7873,8042,8434,3939,9256,2187
3620,8024,577,9997,7377,7682,1314,1158,6282,6310,1896,2509,5436,1732,9480,706,496,101,6232,7375,2207,2306,110,6772,3433,2878,8140,5933,8688,1399,2210,7332,6172,6403,7333,4044,2291,1790,2446,7390,8698,5723,3678,7104,1825,2040,140,3982,4905,4160,2200,5041,2512,1488,2268,1175,7588,8321,8078,7312,977,5257,8465,5068,3453,3096,1651,7906,253,9250,6021,8791,8109,6651,3412,345,4778,5152,4883,7505
1074,5438,9008,2679,5397,5429,2652,3403,770,9188,4248,2493,4361,8327,9587,707,9525,5913,93,1899,328,2876,3604,673,8576,6908,7659,2544,3359,3883,5273,6587,3065,1749,3223,604,9925,6941,2823,8767,7039,3290,3214,1787,7904,3421,7137,9560,8451,2669,9219,6332,1576,5477,6755,8348,4164,4307,2984,4012,6629,1044,2874,6541,4942,903,1404,9125,5160,8836,4345,2581,460,8438,1538,5507,668,3352,2678,6942
4295,1176,5596,1521,3061,9868,7037,7129,8933,6659,5947,5063,3653,9447,9245,2679,767,714,116,8558,163,3927,8779,158,5093,2447,5782,3967,1716,931,7772,8164,1117,9244,5783,7776,3846,8862,6014,2330,6947,1777,3112,6008,3491,1906,5952,314,4602,8994,5919,9214,3995,5026,7688,6809,5003,3128,2509,7477,110,8971,3982,8539,2980,4689,6343,5411,2992,5270,5247,9260,2269,7474,1042,7162,5206,1232,4556,4757
510,3556,5377,1406,5721,4946,2635,7847,4251,8293,8281,6351,4912,287,2870,3380,3948,5322,3840,4738,9563,1906,6298,3234,8959,1562,6297,8835,7861,239,6618,1322,2553,2213,5053,5446,4402,6500,5182,8585,6900,5756,9661,903,5186,7687,5998,7997,8081,8955,4835,6069,2621,1581,732,9564,1082,1853,5442,1342,520,1737,3703,5321,4793,2776,1508,1647,9101,2499,6891,4336,7012,3329,3212,1442,9993,3988,4930,7706
9444,3401,5891,9716,1228,7107,109,3563,2700,6161,5039,4992,2242,8541,7372,2067,1294,3058,1306,320,8881,5756,9326,411,8650,8824,5495,8282,8397,2000,1228,7817,2099,6473,3571,5994,4447,1299,5991,543,7874,2297,1651,101,2093,3463,9189,6872,6118,872,1008,1779,2805,9084,4048,2123,5877,55,3075,1737,9459,4535,6453,3644,108,5982,4437,5213,1340,6967,9943,5815,669,8074,1838,6979,9132,9315,715,5048
3327,4030,7177,6336,9933,5296,2621,4785,2755,4832,2512,2118,2244,4407,2170,499,7532,9742,5051,7687,970,6924,3527,4694,5145,1306,2165,5940,2425,8910,3513,1909,6983,346,6377,4304,9330,7203,6605,3709,3346,970,369,9737,5811,4427,9939,3693,8436,5566,1977,3728,2399,3985,8303,2492,5366,9802,9193,7296,1033,5060,9144,2766,1151,7629,5169,5995,58,7619,7565,4208,1713,6279,3209,4908,9224,7409,1325,8540
6882,1265,1775,3648,4690,959,5837,4520,5394,1378,9485,1360,4018,578,9174,2932,9890,3696,116,1723,1178,9355,7063,1594,1918,8574,7594,7942,1547,6166,7888,354,6932,4651,1010,7759,6905,661,7689,6092,9292,3845,9605,8443,443,8275,5163,7720,7265,6356,7779,1798,1754,5225,6661,1180,8024,5666,88,9153,1840,3508,1193,4445,2648,3538,6243,6375,8107,5902,5423,2520,1122,5015,6113,8859,9370,966,8673,2442
7338,3423,4723,6533,848,8041,7921,8277,4094,5368,7252,8852,9166,2250,2801,6125,8093,5738,4038,9808,7359,9494,601,9116,4946,2702,5573,2921,9862,1462,1269,2410,4171,2709,7508,6241,7522,615,2407,8200,4189,5492,5649,7353,2590,5203,4274,710,7329,9063,956,8371,3722,4253,4785,1194,4828,4717,4548,940,983,2575,4511,2938,1827,2027,2700,1236,841,5760,1680,6260,2373,3851,1841,4968,1172,5179,7175,3509
4420,1327,3560,2376,6260,2988,9537,4064,4829,8872,9598,3228,1792,7118,9962,9336,4368,9189,6857,1829,9863,6287,7303,7769,2707,8257,2391,2009,3975,4993,3068,9835,3427,341,8412,2134,4034,8511,6421,3041,9012,2983,7289,100,1355,7904,9186,6920,5856,2008,6545,8331,3655,5011,839,8041,9255,6524,3862,8788,62,7455,3513,5003,8413,3918,2076,7960,6108,3638,6999,3436,1441,4858,4181,1866,8731,7745,3744,1000
356,8296,8325,1058,1277,4743,3850,2388,6079,6462,2815,5620,8495,5378,75,4324,3441,9870,1113,165,1544,1179,2834,562,6176,2313,6836,8839,2986,9454,5199,6888,1927,5866,8760,320,1792,8296,7898,6121,7241,5886,5814,2815,8336,1576,4314,3109,2572,6011,2086,9061,9403,3947,5487,9731,7281,3159,1819,1334,3181,5844,5114,9898,4634,2531,4412,6430,4262,8482,4546,4555,6804,2607,9421,686,8649,8860,7794,6672
9870,152,1558,4963,8750,4754,6521,6256,8818,5208,5691,9659,8377,9725,5050,5343,2539,6101,1844,9700,7750,8114,5357,3001,8830,4438,199,9545,8496,43,2078,327,9397,106,6090,8181,8646,6414,7499,5450,4850,6273,5014,4131,7639,3913,6571,8534,9703,4391,7618,445,1320,5,1894,6771,7383,9191,4708,9706,6939,7937,8726,9382,5216,3685,2247,9029,8154,1738,9984,2626,9438,4167,6351,5060,29,1218,1239,4785
192,5213,8297,8974,4032,6966,5717,1179,6523,4679,9513,1481,3041,5355,9303,9154,1389,8702,6589,7818,6336,3539,5538,3094,6646,6702,6266,2759,4608,4452,617,9406,8064,6379,444,5602,4950,1810,8391,1536,316,8714,1178,5182,5863,5110,5372,4954,1978,2971,5680,4863,2255,4630,5723,2168,538,1692,1319,7540,440,6430,6266,7712,7385,5702,620,641,3136,7350,1478,3155,2820,9109,6261,1122,4470,14,8493,2095
1046,4301,6082,474,4974,7822,2102,5161,5172,6946,8074,9716,6586,9962,9749,5015,2217,995,5388,4402,7652,6399,6539,1349,8101,3677,1328,9612,7922,2879,231,5887,2655,508,4357,4964,3554,5930,6236,7384,4614,280,3093,9600,2110,7863,2631,6626,6620,68,1311,7198,7561,1768,5139,1431,221,230,2940,968,5283,6517,2146,1646,869,9402,7068,8645,7058,1765,9690,4152,2926,9504,2939,7504,6074,2944,6470,7859
4659,736,4951,9344,1927,6271,8837,8711,3241,6579,7660,5499,5616,3743,5801,4682,9748,8796,779,1833,4549,8138,4026,775,4170,2432,4174,3741,7540,8017,2833,4027,396,811,2871,1150,9809,2719,9199,8504,1224,540,2051,3519,7982,7367,2761,308,3358,6505,2050,4836,5090,7864,805,2566,2409,6876,3361,8622,5572,5895,3280,441,7893,8105,1634,2929,274,3926,7786,6123,8233,9921,2674,5340,1445,203,4585,3837
5759,338,7444,7968,7742,3755,1591,4839,1705,650,7061,2461,9230,9391,9373,2413,1213,431,7801,4994,2380,2703,6161,6878,8331,2538,6093,1275,5065,5062,2839,582,1014,8109,3525,1544,1569,8622,7944,2905,6120,1564,1839,5570,7579,1318,2677,5257,4418,5601,7935,7656,5192,1864,5886,6083,5580,6202,8869,1636,7907,4759,9082,5854,3185,7631,6854,5872,5632,5280,1431,2077,9717,7431,4256,8261,9680,4487,4752,4286
1571,1428,8599,1230,7772,4221,8523,9049,4042,8726,7567,6736,9033,2104,4879,4967,6334,6716,3994,1269,8995,6539,3610,7667,6560,6065,874,848,4597,1711,7161,4811,6734,5723,6356,6026,9183,2586,5636,1092,7779,7923,8747,6887,7505,9909,1792,3233,4526,3176,1508,8043,720,5212,6046,4988,709,5277,8256,3642,1391,5803,1468,2145,3970,6301,7767,2359,8487,9771,8785,7520,856,1605,8972,2402,2386,991,1383,5963
1822,4824,5957,6511,9868,4113,301,9353,6228,2881,2966,6956,9124,9574,9233,1601,7340,973,9396,540,4747,8590,9535,3650,7333,7583,4806,3593,2738,8157,5215,8472,2284,9473,3906,6982,5505,6053,7936,6074,7179,6688,1564,1103,6860,5839,2022,8490,910,7551,7805,881,7024,1855,9448,4790,1274,3672,2810,774,7623,4223,4850,6071,9975,4935,1915,9771,6690,3846,517,463,7624,4511,614,6394,3661,7409,1395,8127
8738,3850,9555,3695,4383,2378,87,6256,6740,7682,9546,4255,6105,2000,1851,4073,8957,9022,6547,5189,2487,303,9602,7833,1628,4163,6678,3144,8589,7096,8913,5823,4890,7679,1212,9294,5884,2972,3012,3359,7794,7428,1579,4350,7246,4301,7779,7790,3294,9547,4367,3549,1958,8237,6758,3497,3250,3456,6318,1663,708,7714,6143,6890,3428,6853,9334,7992,591,6449,9786,1412,8500,722,5468,1371,108,3939,4199,2535
7047,4323,1934,5163,4166,461,3544,2767,6554,203,6098,2265,9078,2075,4644,6641,8412,9183,487,101,7566,5622,1975,5726,2920,5374,7779,5631,3753,3725,2672,3621,4280,1162,5812,345,8173,9785,1525,955,5603,2215,2580,5261,2765,2990,5979,389,3907,2484,1232,5933,5871,3304,1138,1616,5114,9199,5072,7442,7245,6472,4760,6359,9053,7876,2564,9404,3043,9026,2261,3374,4460,7306,2326,966,828,3274,1712,3446
3975,4565,8131,5800,4570,2306,8838,4392,9147,11,3911,7118,9645,4994,2028,6062,5431,2279,8752,2658,7836,994,7316,5336,7185,3289,1898,9689,2331,5737,3403,1124,2679,3241,7748,16,2724,5441,6640,9368,9081,5618,858,4969,17,2103,6035,8043,7475,2181,939,415,1617,8500,8253,2155,7843,7974,7859,1746,6336,3193,2617,8736,4079,6324,6645,8891,9396,5522,6103,1857,8979,3835,2475,1310,7422,610,8345,7615
9248,5397,5686,2988,3446,4359,6634,9141,497,9176,6773,7448,1907,8454,916,1596,2241,1626,1384,2741,3649,5362,8791,7170,2903,2475,5325,6451,924,3328,522,90,4813,9737,9557,691,2388,1383,4021,1609,9206,4707,5200,7107,8104,4333,9860,5013,1224,6959,8527,1877,4545,7772,6268,621,4915,9349,5970,706,9583,3071,4127,780,8231,3017,9114,3836,7503,2383,1977,4870,8035,2379,9704,1037,3992,3642,1016,4303
5093,138,4639,6609,1146,5565,95,7521,9077,2272,974,4388,2465,2650,722,4998,3567,3047,921,2736,7855,173,2065,4238,1048,5,6847,9548,8632,9194,5942,4777,7910,8971,6279,7253,2516,1555,1833,3184,9453,9053,6897,7808,8629,4877,1871,8055,4881,7639,1537,7701,2508,7564,5845,5023,2304,5396,3193,2955,1088,3801,6203,1748,3737,1276,13,4120,7715,8552,3047,2921,106,7508,304,1280,7140,2567,9135,5266
6237,4607,7527,9047,522,7371,4883,2540,5867,6366,5301,1570,421,276,3361,527,6637,4861,2401,7522,5808,9371,5298,2045,5096,5447,7755,5115,7060,8529,4078,1943,1697,1764,5453,7085,960,2405,739,2100,5800,728,9737,5704,5693,1431,8979,6428,673,7540,6,7773,5857,6823,150,5869,8486,684,5816,9626,7451,5579,8260,3397,5322,6920,1879,2127,2884,5478,4977,9016,6165,6292,3062,5671,5968,78,4619,4763
9905,7127,9390,5185,6923,3721,9164,9705,4341,1031,1046,5127,7376,6528,3248,4941,1178,7889,3364,4486,5358,9402,9158,8600,1025,874,1839,1783,309,9030,1843,845,8398,1433,7118,70,8071,2877,3904,8866,6722,4299,10,1929,5897,4188,600,1889,3325,2485,6473,4474,7444,6992,4846,6166,4441,2283,2629,4352,7775,1101,2214,9985,215,8270,9750,2740,8361,7103,5930,8664,9690,8302,9267,344,2077,1372,1880,9550
5825,8517,7769,2405,8204,1060,3603,7025,478,8334,1997,3692,7433,9101,7294,7498,9415,5452,3850,3508,6857,9213,6807,4412,7310,854,5384,686,4978,892,8651,3241,2743,3801,3813,8588,6701,4416,6990,6490,3197,6838,6503,114,8343,5844,8646,8694,65,791,5979,2687,2621,2019,8097,1423,3644,9764,4921,3266,3662,5561,2476,8271,8138,6147,1168,3340,1998,9874,6572,9873,6659,5609,2711,3931,9567,4143,7833,8887
6223,2099,2700,589,4716,8333,1362,5007,2753,2848,4441,8397,7192,8191,4916,9955,6076,3370,6396,6971,3156,248,3911,2488,4930,2458,7183,5455,170,6809,6417,3390,1956,7188,577,7526,2203,968,8164,479,8699,7915,507,6393,4632,1597,7534,3604,618,3280,6061,9793,9238,8347,568,9645,2070,5198,6482,5000,9212,6655,5961,7513,1323,3872,6170,3812,4146,2736,67,3151,5548,2781,9679,7564,5043,8587,1893,4531
5826,3690,6724,2121,9308,6986,8106,6659,2142,1642,7170,2877,5757,6494,8026,6571,8387,9961,6043,9758,9607,6450,8631,8334,7359,5256,8523,2225,7487,1977,9555,8048,5763,2414,4948,4265,2427,8978,8088,8841,9208,9601,5810,9398,8866,9138,4176,5875,7212,3272,6759,5678,7649,4922,5422,1343,8197,3154,3600,687,1028,4579,2084,9467,4492,7262,7296,6538,7657,7134,2077,1505,7332,6890,8964,4879,7603,7400,5973,739
1861,1613,4879,1884,7334,966,2000,7489,2123,4287,1472,3263,4726,9203,1040,4103,6075,6049,330,9253,4062,4268,1635,9960,577,1320,3195,9628,1030,4092,4979,6474,6393,2799,6967,8687,7724,7392,9927,2085,3200,6466,8702,265,7646,8665,7986,7266,4574,6587,612,2724,704,3191,8323,9523,3002,704,5064,3960,8209,2027,2758,8393,4875,4641,9584,6401,7883,7014,768,443,5490,7506,1852,2005,8850,5776,4487,4269
4052,6687,4705,7260,6645,6715,3706,5504,8672,2853,1136,8187,8203,4016,871,1809,1366,4952,9294,5339,6872,2645,6083,7874,3056,5218,7485,8796,7401,3348,2103,426,8572,4163,9171,3176,948,7654,9344,3217,1650,5580,7971,2622,76,2874,880,2034,9929,1546,2659,5811,3754,7096,7436,9694,9960,7415,2164,953,2360,4194,2397,1047,2196,6827,575,784,2675,8821,6802,7972,5996,6699,2134,7577,2887,1412,4349,4380
4629,2234,6240,8132,7592,3181,6389,1214,266,1910,2451,8784,2790,1127,6932,1447,8986,2492,5476,397,889,3027,7641,5083,5776,4022,185,3364,5701,2442,2840,4160,9525,4828,6602,2614,7447,3711,4505,7745,8034,6514,4907,2605,7753,6958,7270,6936,3006,8968,439,2326,4652,3085,3425,9863,5049,5361,8688,297,7580,8777,7916,6687,8683,7141,306,9569,2384,1500,3346,4601,7329,9040,6097,2727,6314,4501,4974,2829
8316,4072,2025,6884,3027,1808,5714,7624,7880,8528,4205,8686,7587,3230,1139,7273,6163,6986,3914,9309,1464,9359,4474,7095,2212,7302,2583,9462,7532,6567,1606,4436,8981,5612,6796,4385,5076,2007,6072,3678,8331,1338,3299,8845,4783,8613,4071,1232,6028,2176,3990,2148,3748,103,9453,538,6745,9110,926,3125,473,5970,8728,7072,9062,1404,1317,5139,9862,6496,6062,3338,464,1600,2532,1088,8232,7739,8274,3873
2341,523,7096,8397,8301,6541,9844,244,4993,2280,7689,4025,4196,5522,7904,6048,2623,9258,2149,9461,6448,8087,7245,1917,8340,7127,8466,5725,6996,3421,5313,512,9164,9837,9794,8369,4185,1488,7210,1524,1016,4620,9435,2478,7765,8035,697,6677,3724,6988,5853,7662,3895,9593,1185,4727,6025,5734,7665,3070,138,8469,6748,6459,561,7935,8646,2378,462,7755,3115,9690,8877,3946,2728,8793,244,6323,8666,4271
6430,2406,8994,56,1267,3826,9443,7079,7579,5232,6691,3435,6718,5698,4144,7028,592,2627,217,734,6194,8156,9118,58,2640,8069,4127,3285,694,3197,3377,4143,4802,3324,8134,6953,7625,3598,3584,4289,7065,3434,2106,7132,5802,7920,9060,7531,3321,1725,1067,3751,444,5503,6785,7937,6365,4803,198,6266,8177,1470,6390,1606,2904,7555,9834,8667,2033,1723,5167,1666,8546,8152,473,4475,6451,7947,3062,3281
2810,3042,7759,1741,2275,2609,7676,8640,4117,1958,7500,8048,1757,3954,9270,1971,4796,2912,660,5511,3553,1012,5757,4525,6084,7198,8352,5775,7726,8591,7710,9589,3122,4392,6856,5016,749,2285,3356,7482,9956,7348,2599,8944,495,3462,3578,551,4543,7207,7169,7796,1247,4278,6916,8176,3742,8385,2310,1345,8692,2667,4568,1770,8319,3585,4920,3890,4928,7343,5385,9772,7947,8786,2056,9266,3454,2807,877,2660
6206,8252,5928,5837,4177,4333,207,7934,5581,9526,8906,1498,8411,2984,5198,5134,2464,8435,8514,8674,3876,599,5327,826,2152,4084,2433,9327,9697,4800,2728,3608,3849,3861,3498,9943,1407,3991,7191,9110,5666,8434,4704,6545,5944,2357,1163,4995,9619,6754,4200,9682,6654,4862,4744,5953,6632,1054,293,9439,8286,2255,696,8709,1533,1844,6441,430,1999,6063,9431,7018,8057,2920,6266,6799,356,3597,4024,6665
3847,6356,8541,7225,2325,2946,5199,469,5450,7508,2197,9915,8284,7983,6341,3276,3321,16,1321,7608,5015,3362,8491,6968,6818,797,156,2575,706,9516,5344,5457,9210,5051,8099,1617,9951,7663,8253,9683,2670,1261,4710,1068,8753,4799,1228,2621,3275,6188,4699,1791,9518,8701,5932,4275,6011,9877,2933,4182,6059,2930,6687,6682,9771,654,9437,3169,8596,1827,5471,8909,2352,123,4394,3208,8756,5513,6917,2056
5458,8173,3138,3290,4570,4892,3317,4251,9699,7973,1163,1935,5477,6648,9614,5655,9592,975,9118,2194,7322,8248,8413,3462,8560,1907,7810,6650,7355,2939,4973,6894,3933,3784,3200,2419,9234,4747,2208,2207,1945,2899,1407,6145,8023,3484,5688,7686,2737,3828,3704,9004,5190,9740,8643,8650,5358,4426,1522,1707,3613,9887,6956,2447,2762,833,1449,9489,2573,1080,4167,3456,6809,2466,227,7125,2759,6250,6472,8089
3266,7025,9756,3914,1265,9116,7723,9788,6805,5493,2092,8688,6592,9173,4431,4028,6007,7131,4446,4815,3648,6701,759,3312,8355,4485,4187,5188,8746,7759,3528,2177,5243,8379,3838,7233,4607,9187,7216,2190,6967,2920,6082,7910,5354,3609,8958,6949,7731,494,8753,8707,1523,4426,3543,7085,647,6771,9847,646,5049,824,8417,5260,2730,5702,2513,9275,4279,2767,8684,1165,9903,4518,55,9682,8963,6005,2102,6523
1998,8731,936,1479,5259,7064,4085,91,7745,7136,3773,3810,730,8255,2705,2653,9790,6807,2342,355,9344,2668,3690,2028,9679,8102,574,4318,6481,9175,5423,8062,2867,9657,7553,3442,3920,7430,3945,7639,3714,3392,2525,4995,4850,2867,7951,9667,486,9506,9888,781,8866,1702,3795,90,356,1483,4200,2131,6969,5931,486,6880,4404,1084,5169,4910,6567,8335,4686,5043,2614,3352,2667,4513,6472,7471,5720,1616
8878,1613,1716,868,1906,2681,564,665,5995,2474,7496,3432,9491,9087,8850,8287,669,823,347,6194,2264,2592,7871,7616,8508,4827,760,2676,4660,4881,7572,3811,9032,939,4384,929,7525,8419,5556,9063,662,8887,7026,8534,3111,1454,2082,7598,5726,6687,9647,7608,73,3014,5063,670,5461,5631,3367,9796,8475,7908,5073,1565,5008,5295,4457,1274,4788,1728,338,600,8415,8535,9351,7750,6887,5845,1741,125
3637,6489,9634,9464,9055,2413,7824,9517,7532,3577,7050,6186,6980,9365,9782,191,870,2497,8498,2218,2757,5420,6468,586,3320,9230,1034,1393,9886,5072,9391,1178,8464,8042,6869,2075,8275,3601,7715,9470,8786,6475,8373,2159,9237,2066,3264,5000,679,355,3069,4073,494,2308,5512,4334,9438,8786,8637,9774,1169,1949,6594,6072,4270,9158,7916,5752,6794,9391,6301,5842,3285,2141,3898,8027,4310,8821,7079,1307
8497,6681,4732,7151,7060,5204,9030,7157,833,5014,8723,3207,9796,9286,4913,119,5118,7650,9335,809,3675,2597,5144,3945,5090,8384,187,4102,1260,2445,2792,4422,8389,9290,50,1765,1521,6921,8586,4368,1565,5727,7855,2003,4834,9897,5911,8630,5070,1330,7692,7557,7980,6028,5805,9090,8265,3019,3802,698,9149,5748,1965,9658,4417,5994,5584,8226,2937,272,5743,1278,5698,8736,2595,6475,5342,6596,1149,6920
8188,8009,9546,6310,8772,2500,9846,6592,6872,3857,1307,8125,7042,1544,6159,2330,643,4604,7899,6848,371,8067,2062,3200,7295,1857,9505,6936,384,2193,2190,301,8535,5503,1462,7380,5114,4824,8833,1763,4974,8711,9262,6698,3999,2645,6937,7747,1128,2933,3556,7943,2885,3122,9105,5447,418,2899,5148,3699,9021,9501,597,4084,175,1621,1,1079,6067,5812,4326,9914,6633,5394,4233,6728,9084,1864,5863,1225
9935,8793,9117,1825,9542,8246,8437,3331,9128,9675,6086,7075,319,1334,7932,3583,7167,4178,1726,7720,695,8277,7887,6359,5912,1719,2780,8529,1359,2013,4498,8072,1129,9998,1147,8804,9405,6255,1619,2165,7491,1,8882,7378,3337,503,5758,4109,3577,985,3200,7615,8058,5032,1080,6410,6873,5496,1466,2412,9885,5904,4406,3605,8770,4361,6205,9193,1537,9959,214,7260,9566,1685,100,4920,7138,9819,5637,976
3466,9854,985,1078,7222,8888,5466,5379,3578,4540,6853,8690,3728,6351,7147,3134,6921,9692,857,3307,4998,2172,5783,3931,9417,2541,6299,13,787,2099,9131,9494,896,8600,1643,8419,7248,2660,2609,8579,91,6663,5506,7675,1947,6165,4286,1972,9645,3805,1663,1456,8853,5705,9889,7489,1107,383,4044,2969,3343,152,7805,4980,9929,5033,1737,9953,7197,9158,4071,1324,473,9676,3984,9680,3606,8160,7384,5432
1005,4512,5186,3953,2164,3372,4097,3247,8697,3022,9896,4101,3871,6791,3219,2742,4630,6967,7829,5991,6134,1197,1414,8923,8787,1394,8852,5019,7768,5147,8004,8825,5062,9625,7988,1110,3992,7984,9966,6516,6251,8270,421,3723,1432,4830,6935,8095,9059,2214,6483,6846,3120,1587,6201,6691,9096,9627,6671,4002,3495,9939,7708,7465,5879,6959,6634,3241,3401,2355,9061,2611,7830,3941,2177,2146,5089,7079,519,6351
7280,8586,4261,2831,7217,3141,9994,9940,5462,2189,4005,6942,9848,5350,8060,6665,7519,4324,7684,657,9453,9296,2944,6843,7499,7847,1728,9681,3906,6353,5529,2822,3355,3897,7724,4257,7489,8672,4356,3983,1948,6892,7415,4153,5893,4190,621,1736,4045,9532,7701,3671,1211,1622,3176,4524,9317,7800,5638,6644,6943,5463,3531,2821,1347,5958,3436,1438,2999,994,850,4131,2616,1549,3465,5946,690,9273,6954,7991
9517,399,3249,2596,7736,2142,1322,968,7350,1614,468,3346,3265,7222,6086,1661,5317,2582,7959,4685,2807,2917,1037,5698,1529,3972,8716,2634,3301,3412,8621,743,8001,4734,888,7744,8092,3671,8941,1487,5658,7099,2781,99,1932,4443,4756,4652,9328,1581,7855,4312,5976,7255,6480,3996,2748,1973,9731,4530,2790,9417,7186,5303,3557,351,7182,9428,1342,9020,7599,1392,8304,2070,9138,7215,2008,9937,1106,7110
7444,769,9688,632,1571,6820,8743,4338,337,3366,3073,1946,8219,104,4210,6986,249,5061,8693,7960,6546,1004,8857,5997,9352,4338,6105,5008,2556,6518,6694,4345,3727,7956,20,3954,8652,4424,9387,2035,8358,5962,5304,5194,8650,8282,1256,1103,2138,6679,1985,3653,2770,2433,4278,615,2863,1715,242,3790,2636,6998,3088,1671,2239,957,5411,4595,6282,2881,9974,2401,875,7574,2987,4587,3147,6766,9885,2965
3287,3016,3619,6818,9073,6120,5423,557,2900,2015,8111,3873,1314,4189,1846,4399,7041,7583,2427,2864,3525,5002,2069,748,1948,6015,2684,438,770,8367,1663,7887,7759,1885,157,7770,4520,4878,3857,1137,3525,3050,6276,5569,7649,904,4533,7843,2199,5648,7628,9075,9441,3600,7231,2388,5640,9096,958,3058,584,5899,8150,1181,9616,1098,8162,6819,8171,1519,1140,7665,8801,2632,1299,9192,707,9955,2710,7314
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-,573,-,311,351,66,-,79,574,463,-,609,829,-,142,585,500,941,627,553,-,202,388,-,164,829,-,620,523,639,936,-,-,490,-,695,-,505,109,-
856,531,-,404,969,-,-,-,53,733,-,-,-,-,379,-,-,707,817,304,-,-,939,164,-,-,616,716,728,-,889,349,-,963,150,447,-,292,586,264
221,539,-,-,925,27,-,712,793,665,-,270,234,128,885,-,968,156,282,703,-,-,-,829,-,-,-,822,-,-,-,736,576,-,697,946,443,-,205,194
514,667,108,-,987,-,-,613,-,494,966,861,198,437,89,321,-,757,-,455,267,-,959,-,616,-,-,-,349,156,339,-,102,790,359,-,439,938,809,260
-,607,-,588,328,-,449,312,-,644,-,-,145,-,-,398,291,258,698,857,407,-,-,620,716,822,-,-,293,486,943,-,779,-,6,880,116,775,-,947
591,-,727,680,282,290,120,452,777,863,-,-,409,383,848,-,-,251,398,260,27,867,83,523,728,-,349,293,-,212,684,505,341,384,9,992,507,48,-,-
762,920,225,875,589,-,797,-,330,25,406,165,68,364,258,-,-,-,222,-,651,140,463,639,-,-,156,486,212,-,-,349,723,-,-,186,-,36,240,752
182,-,578,-,-,786,358,978,936,385,989,-,359,966,112,950,765,807,-,991,80,403,361,936,889,-,339,943,684,-,-,965,302,676,725,-,327,134,-,147
56,-,699,615,873,-,232,900,883,-,772,675,-,227,-,68,196,-,649,182,927,962,-,-,349,736,-,-,505,349,965,-,474,178,833,-,-,555,853,-
-,315,-,-,477,554,550,-,286,342,932,250,814,-,900,193,504,-,-,351,-,785,-,-,-,576,102,779,341,723,302,474,-,689,-,-,-,451,-,-
884,649,898,409,-,817,-,901,-,470,7,686,218,-,-,-,757,-,-,477,974,-,512,490,963,-,790,-,384,-,676,178,689,-,245,596,445,-,-,343
412,937,294,758,-,33,305,-,174,-,-,995,186,807,-,697,-,461,-,867,977,511,931,-,150,697,359,6,9,-,725,833,-,245,-,949,-,270,-,112
273,-,-,221,19,-,997,-,-,-,823,366,-,993,818,-,542,501,-,-,-,-,-,695,447,946,-,880,992,186,-,-,-,596,949,-,91,-,768,273
636,185,575,-,450,54,662,225,-,-,391,191,-,-,639,390,-,-,-,-,-,1,224,-,-,443,439,116,507,-,327,-,-,445,-,91,-,248,-,344
-,102,168,-,-,506,744,533,-,730,-,-,929,-,268,588,395,-,654,889,457,-,690,505,292,-,938,775,48,36,134,555,451,-,270,-,248,-,371,680
-,636,432,76,-,386,686,770,828,582,-,433,203,526,600,848,227,616,-,217,117,707,369,109,586,205,809,-,-,240,-,853,-,-,-,768,-,371,-,540
774,289,833,257,-,381,239,722,711,468,933,-,-,17,-,-,148,-,-,853,-,-,-,-,264,194,260,947,-,752,147,-,-,343,112,273,344,680,540,-

1000
poker.txt Normal file
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25
python/1.py Normal file
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# coding=utf-8
''' If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below 1000. '''
def calc(n, a):
tmp = n / a
return (tmp + 1) * tmp * a / 2
x = 3
y = 5
maxx = 1000
out = calc(maxx, x) + calc(maxx, y) - calc(maxx, x * y)
print out
'''
total = 0
for i in range(1000):
if i % 3 == 0 or i % 5 == 0: # 条件为能被 3 或 5 整除
total += i # 足条件的数字加入到 total 中
print total
'''

42
python/10.py Normal file
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''' The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
Find the sum of all the primes below two million. '''
def makeP(x):
P = [3]
p = [3]
n = 5
while n < x:
for i in p:
if n % i == 0:
break
else:
P.append(n)
n += 2
while p[-1] ** 2 < n:
p.append(P[len(p)])
return P
maxx = 2000000
maxxx = int(maxx ** 0.5)
prime = makeP(maxxx)
total = 2 + 3 + 5 + 7
for i in xrange(len(prime) - 1):
for x in xrange(prime[i] ** 2 + 2, prime[i + 1] ** 2, 2):
for p in prime[:i + 1]:
if x % p == 0:
break
else:
total += x
for x in xrange(prime[-1] ** 2 + 2, maxx, 2):
for p in prime:
if x % p == 0:
break
else:
total += x
print total

6
python/100.py Normal file
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a, b = 1, 1
n = (a + 1) // 2
while n < 10 ** 12:
a, b = 3 * a + 4 * b, 2 * a + 3 * b
n = (a + 1) // 2
print (b + 1) // 2

30
python/101.py Normal file
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def poly(x, coef):
out = 0
for i in coef:
out = out * x + i
return out
un = (1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1)
a = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
for i in xrange(len(a)):
a[i] = poly(a[i], un)
total = 0
for length in xrange(2, len(a) + 1):
y = a[:length]
n = len(y)
L = 0
for k in xrange(n):
l = 1
for xi in xrange(n):
if xi != k:
l *= (n - xi)
for xi in xrange(n):
if xi != k:
l /= (k - xi)
L += (l * y[k])
total += L
print total + 1

26
python/102.py Normal file
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def pl(p1, p2):
return p1[0] * p2[1] - p1[1] * p2[0]
def isit(lis):
if pl(lis[1], lis[0]) * pl(lis[2], lis[0]) > 0:
return False
if pl(lis[0], lis[1]) * pl(lis[2], lis[1]) > 0:
return False
if pl(lis[0], lis[2]) * pl(lis[1], lis[2]) > 0:
return False
return True
def breaknum(lis):
return [[int(lis[0]), int(lis[1])], [int(lis[2]), int(lis[3])], [int(lis[4]), int(lis[5])]]
ff = open('../triangles.txt', 'r')
points = ff.readlines()
ff.close()
count = 0
for i in points:
if isit(breaknum(i.split(','))):
count += 1
print count

48
python/104.py Normal file
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unit = 1000000000
bigunit = 1.0e+100
def musq(a, b):
bi = []
while b != 0:
bi.append(b % 2)
b /= 2
bi.reverse()
out = 1
for p in bi:
out = out * out
if out > bigunit:
out /= bigunit
if p == 1:
out *= a
if out > bigunit:
out /= bigunit
return out
def fib(x):
sq5 = 5 ** 0.5
oa = musq((1 + sq5) / 2, n)
return oa / sq5
n = 0
a, b = 0, 1
while 1:
a, b = b, a + b
a %= unit
b %= unit
n += 1
bit = set('#'.join(str(a)).split('#'))
if len(bit) == 9 and (not '0' in bit):
try:
pre = str(fib(n))
if pre == 'inf':
break
except OverflowError:
print n
break
pre = pre[0] + pre[2:]
bitend = set('#'.join(pre[:9]).split('#'))
if len(bitend) == 9 and (not '0' in bitend):
print n, a, pre[:9]
break

45
python/107.py Normal file
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ff = open('../network.txt', 'r')
nnn = ff.readlines()
ff.close()
inf = 10 ** 10
def stolis(s):
mid = s.split(',')
out = []
for i in mid:
if i.isdigit():
out.append(int(i))
else:
out.append(inf)
return out
hole = 0
net = []
for i in nnn:
tmp = stolis(i.strip())
for j in tmp:
if j < inf:
hole += j
net.append(tmp)
#print net
have = [0]
nothave = range(1, len(net))
total = 0
while len(nothave) > 0:
choose = [inf, 0]
node = 0
it = 0
for node in nothave:
for it in have:
if net[node][it] < choose[0]:
choose = [net[node][it], node]
if choose[0] < inf:
have.append(choose[1])
nothave.remove(choose[1])
total += choose[0]
print hole / 2 - total

49
python/108.py Normal file
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def mkp(n):
P = [2]
p = [2]
x = 3
while len(P) < n:
for i in p:
if x % i == 0:
break
else:
P.append(x)
while x > p[-1]**2:
p.append(P[len(p)])
x += 2
return P
primes = mkp(1000)
def factor(x):
out = []
for p in primes:
if p * p > x:
break
if x % p == 0:
count = 0
while x % p == 0:
x /= p
count += 1
out.append(count)
if x > 1:
out.append(1)
return out
def sum(x):
pre = factor(x)
out = 1
for i in pre:
out *= i * 2 + 1
return (out + 1) / 2
def maxx(x):
n = 4
while sum(n) < x:
n += 1
return n
print maxx(1000)

30
python/109.py Normal file
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from sys import argv
limit = int(argv[1])
kind = range(1, 21)
kind.extend(range(2, 41, 2))
kind.extend(range(3, 61, 3))
kind.extend([25, 50])
doub = range(2, 41, 2)
doub.extend([50])
count = 0
for i in doub:
if i <= limit:
count += 1
for j in kind:
if i + j <= limit:
count += 1
tmp = 0
for i in doub:
for j in xrange(len(kind)):
for k in xrange(j, len(kind)):
if i + kind[j] + kind[k] <= limit:
tmp += 1
print count + tmp

45
python/11.py Normal file
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a = [[8, 2, 22, 97, 38, 15, 0, 40, 0, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8],
[49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 4, 56, 62, 0],
[81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 3, 49, 13, 36, 65],
[52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 36, 91],
[22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80],
[24, 47, 32, 60, 99, 3, 45, 2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50],
[32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70],
[67, 26, 20, 68, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21],
[24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72],
[21, 36, 23, 9, 75, 0, 76, 44, 20, 45, 35, 14, 0, 61, 33, 97, 34, 31, 33, 95],
[78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92],
[16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 0, 17, 54, 24, 36, 29, 85, 57],
[86, 56, 0, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58],
[19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40],
[04, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66],
[88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69],
[4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36],
[20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16],
[20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54],
[1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48]]
def summ(x, y, flag):
vector = ((1, 0), (0, 1), (1, 1), (1, -1))
total = 1
for i in xrange(4):
total *= a[x][y]
x += vector[flag][0]
y += vector[flag][1]
return total
maxx = [0,]
for i in xrange(20 - 4):
for j in xrange(20 - 4):
for k in xrange(3):
tmp = summ(i, j, k)
if tmp > maxx[0]:
maxx = [tmp, i, j, k]
for j in xrange(3, 20):
tmp = summ(i, j, 3)
if tmp > maxx[0]:
maxx = [tmp, i, j, 3]
print maxx

49
python/110.py Normal file
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def mkp(n):
P = [2]
p = [2]
x = 3
while len(P) < n:
for i in p:
if x % i == 0:
break
else:
P.append(x)
while x > p[-1]**2:
p.append(P[len(p)])
x += 2
return P
primes = mkp(1000)
def factor(x):
out = []
for p in primes:
if p * p > x:
break
if x % p == 0:
count = 0
while x % p == 0:
x /= p
count += 1
out.append(count)
if x > 1:
out.append(1)
return out
def sum(x):
pre = factor(x)
out = 1
for i in pre:
out *= i * 2 + 1
return (out + 1) / 2
def maxx(x):
n = 4
while sum(n) < x:
n += 1
return n
print maxx(100000)

68
python/111.py Normal file
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maxx = 10
def mkp(x):
P = [2]
p = [2]
n = 3
while n < x:
for i in p:
if n % i == 0:
break
else:
P.append(n)
n += 2
while n > p[-1] ** 2:
p.append(P[len(p)])
return P
prime = mkp(100000)
def isp(x, lis = prime):
for i in lis:
if i ** 2 > x:
break
if x % i == 0:
return False
return True
maxx = 10
total = 0
for i in xrange(1, 10):
for j in xrange(1, 10):
num = ['0'] * maxx
num[0] = str(i)
num[-1] = str(j)
tmp = int(''.join(num))
if isp(tmp) and (tmp > 10 ** (maxx - 1)):
#print tmp
total += tmp
for same in xrange(1, 10):
for new in xrange(10):
for local in xrange(maxx):
num = [str(same)] * maxx
num[local] = str(new)
tmp = int(''.join(num))
if isp(tmp) and (tmp > 10 ** (maxx - 1)):
#print tmp
total += tmp
sp = set([])
no = set(range(10))
for special in [2, 8]:
for new1 in no - set([special]):
for new2 in no - set([special]):
for local1 in xrange(maxx):
for local2 in xrange(maxx):
num = [str(special)] * maxx
num[local1] = str(new1)
num[local2] = str(new2)
tmp = int(''.join(num))
if isp(tmp) and (tmp > 10 ** (maxx - 1)):
sp.add(tmp)
#print tmp
print total + sum(list(sp))

27
python/112.py Normal file
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def ala(x):
out = []
while x != 0:
out.append(x % 10)
x /= 10
b = sorted(out)
if out == b:
return False
b.reverse()
if out == b:
return False
return True
nis = 0
nnot = 100
n = 100
while nis != nnot * 99:
n += 1
if ala(n):
nis += 1
else:
nnot += 1
print n

24
python/113.py Normal file
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@ -0,0 +1,24 @@
n = 2
maxx = 100
path1 = range(1,10)
path_1 = range(1,11)
total = sum(path1) + sum(path_1) - 1
while n < maxx:
new1 = []
new_1 = []
tmp1 = 0
tmp_1 = 0
for i in xrange(9):
tmp1 += path1[i]
new1.append(tmp1)
path1 = new1
for i in xrange(10):
tmp_1 += path_1[i]
new_1.append(tmp_1)
path_1 = new_1
# print path1, path_1
total += sum(path1) + sum(path_1) - 9 - 1
n += 1
print total

29
python/119.py Normal file
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@ -0,0 +1,29 @@
def ala(x):
tmp = 0
while x != 0:
tmp += x % 10
x /= 10
return tmp
def ist(x, i):
if i == 1:
return False
if x < 10:
return False
while x != 1:
if x % i != 0:
return False
x /= i
return True
n = 2
count = []
while n < 100:
for i in xrange(100):
tmp = n ** i
if ist(tmp, ala(tmp)):
if count.count(tmp) == 0:
count.append(tmp)
count.sort()
n += 1
print count[29]

30
python/12.py Normal file
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@ -0,0 +1,30 @@
''' The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
Let us list the factors of the first seven triangle numbers:
1: 1
3: 1,3
6: 1,2,3,6
10: 1,2,5,10
15: 1,3,5,15
21: 1,3,7,21
28: 1,2,4,7,14,28
We can see that 28 is the first triangle number to have over five divisors.
What is the value of the first triangle number to have over five hundred divisors? '''
def play(stop):
num = 3
while 1:
num += 1
n = num * (num + 1) / 2
sqr = int(n ** 0.5)
count = 0
if sqr * sqr == n: count = 1
for tmp in xrange(2, sqr):
if n % tmp == 0:
count += 1
if count >= stop // 2:
print n
return 1
if __name__ == '__main__':
play(500)

108
python/13.py Normal file
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@ -0,0 +1,108 @@
num = [
37107287533902102798797998220837590246510135740250,
46376937677490009712648124896970078050417018260538,
74324986199524741059474233309513058123726617309629,
91942213363574161572522430563301811072406154908250,
23067588207539346171171980310421047513778063246676,
89261670696623633820136378418383684178734361726757,
28112879812849979408065481931592621691275889832738,
44274228917432520321923589422876796487670272189318,
47451445736001306439091167216856844588711603153276,
70386486105843025439939619828917593665686757934951,
62176457141856560629502157223196586755079324193331,
64906352462741904929101432445813822663347944758178,
92575867718337217661963751590579239728245598838407,
58203565325359399008402633568948830189458628227828,
80181199384826282014278194139940567587151170094390,
35398664372827112653829987240784473053190104293586,
86515506006295864861532075273371959191420517255829,
71693888707715466499115593487603532921714970056938,
54370070576826684624621495650076471787294438377604,
53282654108756828443191190634694037855217779295145,
36123272525000296071075082563815656710885258350721,
45876576172410976447339110607218265236877223636045,
17423706905851860660448207621209813287860733969412,
81142660418086830619328460811191061556940512689692,
51934325451728388641918047049293215058642563049483,
62467221648435076201727918039944693004732956340691,
15732444386908125794514089057706229429197107928209,
55037687525678773091862540744969844508330393682126,
18336384825330154686196124348767681297534375946515,
80386287592878490201521685554828717201219257766954,
78182833757993103614740356856449095527097864797581,
16726320100436897842553539920931837441497806860984,
48403098129077791799088218795327364475675590848030,
87086987551392711854517078544161852424320693150332,
59959406895756536782107074926966537676326235447210,
69793950679652694742597709739166693763042633987085,
41052684708299085211399427365734116182760315001271,
65378607361501080857009149939512557028198746004375,
35829035317434717326932123578154982629742552737307,
94953759765105305946966067683156574377167401875275,
88902802571733229619176668713819931811048770190271,
25267680276078003013678680992525463401061632866526,
36270218540497705585629946580636237993140746255962,
24074486908231174977792365466257246923322810917141,
91430288197103288597806669760892938638285025333403,
34413065578016127815921815005561868836468420090470,
23053081172816430487623791969842487255036638784583,
11487696932154902810424020138335124462181441773470,
63783299490636259666498587618221225225512486764533,
67720186971698544312419572409913959008952310058822,
95548255300263520781532296796249481641953868218774,
76085327132285723110424803456124867697064507995236,
37774242535411291684276865538926205024910326572967,
23701913275725675285653248258265463092207058596522,
29798860272258331913126375147341994889534765745501,
18495701454879288984856827726077713721403798879715,
38298203783031473527721580348144513491373226651381,
34829543829199918180278916522431027392251122869539,
40957953066405232632538044100059654939159879593635,
29746152185502371307642255121183693803580388584903,
41698116222072977186158236678424689157993532961922,
62467957194401269043877107275048102390895523597457,
23189706772547915061505504953922979530901129967519,
86188088225875314529584099251203829009407770775672,
11306739708304724483816533873502340845647058077308,
82959174767140363198008187129011875491310547126581,
97623331044818386269515456334926366572897563400500,
42846280183517070527831839425882145521227251250327,
55121603546981200581762165212827652751691296897789,
32238195734329339946437501907836945765883352399886,
75506164965184775180738168837861091527357929701337,
62177842752192623401942399639168044983993173312731,
32924185707147349566916674687634660915035914677504,
99518671430235219628894890102423325116913619626622,
73267460800591547471830798392868535206946944540724,
76841822524674417161514036427982273348055556214818,
97142617910342598647204516893989422179826088076852,
87783646182799346313767754307809363333018982642090,
10848802521674670883215120185883543223812876952786,
71329612474782464538636993009049310363619763878039,
62184073572399794223406235393808339651327408011116,
66627891981488087797941876876144230030984490851411,
60661826293682836764744779239180335110989069790714,
85786944089552990653640447425576083659976645795096,
66024396409905389607120198219976047599490197230297,
64913982680032973156037120041377903785566085089252,
16730939319872750275468906903707539413042652315011,
94809377245048795150954100921645863754710598436791,
78639167021187492431995700641917969777599028300699,
15368713711936614952811305876380278410754449733078,
40789923115535562561142322423255033685442488917353,
44889911501440648020369068063960672322193204149535,
41503128880339536053299340368006977710650566631954,
81234880673210146739058568557934581403627822703280,
82616570773948327592232845941706525094512325230608,
22918802058777319719839450180888072429661980811197,
77158542502016545090413245809786882778948721859617,
72107838435069186155435662884062257473692284509516,
20849603980134001723930671666823555245252804609722,
53503534226472524250874054075591789781264330331690,]
total = 0
for i in num:
total += i
#print total
print str(total)[:10]

32
python/130.py Normal file
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def A(x):
if x % 2 == 0 or x % 5 == 0:
return -1
n = 0
num = 0
while 1:
n = (n * 10 + 1) % x
num += 1
if n == 0:
return num
P = [2]
p = [2]
n = 3
out = []
while len(out) < 25:
for i in p:
if n % i == 0:
tmp = A(n)
if tmp > 0:
if (n - 1) % A(n) == 0:
out.append(n)
break
else:
P.append(n)
n += 2
while n > p[-1] ** 2:
p.append(P[len(p)])
print sum(out)

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python/132.py Normal file
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def A(x):
if x % 2 == 0 or x % 5 == 0:
return -1
n = 0
num = 0
while 1:
n = (n * 10 + 1) % x
num += 1
if n == 0:
return num
maxx = 10 ** 9
P = [2]
p = [2]
n = 3
out = []
while len(out) < 40:
for i in p:
if n % i == 0:
break
else:
P.append(n)
tmp = A(n)
if tmp > 0:
if maxx % tmp == 0:
out.append(n)
n += 2
while n > p[-1] ** 2:
p.append(P[len(p)])
print sum(out), out

41
python/134.py Normal file
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def mkp(x):
P = [2]
p = [2]
n = 3
while n < x:
for i in p:
if n % i == 0:
break
else:
P.append(n)
n += 2
while n > p[-1] ** 2:
p.append(P[len(p)])
return P
def re(x, p):
za = [0, 1, 1]
zb = [1, 1, 0]
a = p
b = x
n = 3
while b != 0:
n += 1
q = a / b
za[n % 3] = za[(n - 2) % 3] - q * za[(n - 1) % 3]
zb[n % 3] = zb[(n - 2) % 3] - q * zb[(n - 1) % 3]
a, b = b, a % b
return (zb[(n - 1) % 3] + p) % p
def S(p1, p2):
tmp = 10 ** (len(str(p1)))
return (p2 - p1) * re(tmp, p2) % p2
p = mkp(1000004)
print p[-1]
total = 0
for i in xrange(3, len(p)):
total += int(str(S(p[i - 1], p[i])) + str(p[i - 1]))
print total

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python/138.py Normal file
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k = 2 + 5 ** 0.5
out = []
maxx = 12
m = 4
n = 1
def test(x, y):
b2 = 4 * x * y
h = x ** 2 - y ** 2
if abs(h - b2) == 1:
#print b2, h, x, y
out.append(x ** 2 + y ** 2)
return True
return False
while len(out) < maxx:
m = int(k * n) - 1
for i in [0,1,2]:
if test(m + i, n):
#print out[-1]
n = m
n += 1
print sum(out)

49
python/14.py Normal file
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def sq(x):
out = 0
while x != 1:
out += 1
if x % 2 == 1:
x = x * 3 + 1
else:
x /= 2
return out
maxx = [0, 0]
limit = 1000000
for i in xrange(1, limit + 1):
if i % 100000 == 0:
print i
tmp = sq(i)
if tmp > maxx[1]:
maxx[1] = tmp
maxx[0] = i
print maxx
'''
limit = 1000000
num = {1:1}
maxx = [0, 0]
tmp = []
for i in xrange(2, limit + 1):
x = i
while 1:
if num.has_key(x):
tmp.reverse()
bak = x
while len(tmp) > 0:
num.update({tmp[0]: num.get(bak) + 1})
bak = tmp[0]
tmp.pop(0)
break
else:
tmp.append(x)
if x % 2 == 0:
x /= 2
else:
x = 3 * x + 1
if num.get(i) > maxx[1]:
maxx = [i, num.get(i)]
print maxx
'''

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''' Starting in the top left corner of a 2*2 grid, there are 6 routes (without backtracking) to the bottom right corner.
How many routes are there through a 20*20 grid? '''
total = 1
for i in xrange(40, 20, -1):
total *= i
for i in xrange(1, 21):
total /= i
print total

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python/16.py Normal file
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''' What is the sum of the digits of the number 2^1000 ? '''
stri = str(2 ** 1000)
total = 0
for i in xrange(len(stri)):
total += ord(stri[i]) - ord('0')
print total

25
python/162.py Normal file
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def frag(x):
out = []
for i in xrange(1, x - 1):
for j in xrange(1, x - i):
out.append((i, j, x - i - j))
return out
def C(n, m):
total = 1
for i in xrange(n, n - m, -1):
total *= i
for i in xrange(m, 1, -1):
total /= i
return total
total = 0
for length in xrange(3, 17):
for same in xrange(3, length + 1):
for (x,y,z) in frag(same):
total += C(length - 1, x) * C(length - x, y) * C(length
- x - y, z) * 13 ** (length - same)
print '%X' % total

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python/17.py Normal file
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dic = {
0:'',
1:'one',
2:'two',
3:'three',
4:'four',
5:'five',
6:'six',
7:'seven',
8:'eight',
9:'nine',
10:'ten',
11:'eleven',
12:'twelve',
13:'thirteen',
14:'fourteen',
15:'fifteen',
16:'sixteen',
17:'seventeen',
18:'eighteen',
19:'nineteen',
20:'twenty',
30:'thirty',
40:'forty',
50:'fifty',
60:'sixty',
70:'seventy',
80:'eighty',
90:'nithty',
100:'hundred',
1000:'thousand'
}
def analyse(x, p = 0):
if p: print x,
if x == 1000:
if p: print dic.get(x)
return len(dic.get(x))
out = 0
tmp = x / 100
if tmp:
out += len(dic.get(tmp))
if p: print dic.get(tmp),
out += len(dic.get(100))
if p: print dic.get(100),
if x % 100 == 0:
if p: print
return out
out += 3
if p: print 'and',
tmp = x % 100
if tmp < 20:
out += len(dic.get(tmp))
if p: print dic.get(tmp)
return out
out += len(dic.get(tmp / 10 * 10))
if p: print dic.get(tmp / 10 * 10),
out += len(dic.get(tmp % 10))
if p: print dic.get(tmp % 10)
return out
total = 0
for i in xrange(1, 1001):
total += analyse(i)
print total

50
python/18.py Normal file
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a = [[75],
[95, 64],
[17, 47, 82],
[18, 35, 87, 10],
[20, 4, 82, 47, 65],
[19, 1, 23, 75, 3, 34],
[88, 2, 77, 73, 7, 63, 67],
[99, 65, 4, 28, 6, 16, 70, 92],
[41, 41, 26, 56, 83, 40, 80, 70, 33],
[41, 48, 72, 33, 47, 32, 37, 16, 94, 29],
[53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14],
[70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57],
[91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48],
[63, 66, 4, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31],
[4, 62, 98, 27, 23, 9, 70, 98, 73, 93, 38, 53, 60, 4, 23]]
path = a[-1][:]
for i in xrange(len(a) - 2, 0, -1):
newpath = []
for j in xrange(i + 1):
better = max(path[j], path[j + 1])
newpath.append(a[i][j] + better)
path = newpath
print max(path) + a[0][0]
'''
path = [[a[0][0], [a[0][0]]]]
for i in xrange(1, len(a)):
newpath = []
tmp = path[0][1][:]
tmp.append(a[i][0])
newpath.append([path[0][0] + a[i][0], tmp])
for j in xrange(1, i):
flag = (path[j - 1][0] > path[j][0]) and -1 or 0
tmp = path[j + flag][1][:]
tmp.append(a[i][j])
newpath.append([path[j + flag][0] + a[i][j], tmp])
tmp = path[i - 1][1][:]
tmp.append(a[i][i])
newpath.append([path[i - 1][0] + a[i][i], tmp])
path = newpath
maxx = [0, 0]
for i in path:
if i[0] > maxx[0]:
maxx = i
print maxx
'''

33
python/19.py Normal file
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month = (0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31)
def testyear(x):
if x % 400 == 0:
return True
if x % 100 != 0 and x % 4 == 0:
return True
return False
pair = [[1900, 1], 1]
def next():
pair[1] += month[pair[0][1]]
if testyear(pair[0][0]) and pair[0][1] == 2:
pair[1] += 1
pair[1] %= 7
pair[0][1] += 1
if pair[0][1] > 12:
pair[0][1] = 1
pair[0][0] += 1
total = 0
for i in xrange(12):
next()
while pair[0][0] < 2001:
if pair[1] == 0:
total += 1
next()
print total

24
python/2.py Normal file
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# coding=utf-8
''' Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms. '''
fib = [1, 1, 0] # 设置 fib 数列循环的数组
i = 1 # fib 数列的项计数器
total = 0 # 满足条件的数的和
while fib[i] <= 4000000: # fib 数列小于要求值时不断循环
if fib[i] % 2 == 0:
print fib[i]
total += fib[i] # 满足条件的项计入总和
i = (i + 1) % 3 # 项计数器
fib[i] = fib[(i + 1) % 3] + fib[(i + 2) % 3] #
print total #
a, b = 2, 8
total = 0
while a < 4000000:
total += a
a, b = b, a + b * 4
print total

13
python/20.py Normal file
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''' n! means n * (n - 1) * ... * 3 * 2 * 1
For example, 10! = 10 * 9 * ... * 3 * 2 * 1 = 3628800,
and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27.
Find the sum of the digits in the number 100! '''
a = 1
sum = 0
for i in xrange(1, 101):
a *= i
while a > 0:
sum += a % 10
a /= 10
print sum

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python/21.py Normal file
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''' Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).
If d(a) = b and d(b) = a, where a b, then a and b are an amicable pair and each of a and b are called amicable numbers.
For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.
Evaluate the sum of all the amicable numbers under 10000. '''
import math
def ami(x):
test = 1
sqr = int(math.ceil(math.sqrt(x)))
if sqr * sqr == x: test += sqr
for i in xrange(2, sqr + 1):
if x % i == 0: test += i + x / i
return test
for j in xrange(2, 10000):
tmp = ami(j)
if j == ami(tmp) and j != tmp:
print j, '\t', tmp

21
python/22.py Normal file
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''' Using names.txt (right click and 'Save Link/Target As...'), a 46K text file containing over five-thousand first names, begin by sorting it into alphabetical order. Then working out the alphabetical value for each name, multiply this value by its alphabetical position in the list to obtain a name score.
For example, when the list is sorted into alphabetical order, COLIN, which is worth 3 + 15 + 12 + 9 + 14 = 53, is the 938th name in the list. So, COLIN would obtain a score of 938 * 53 = 49714.
What is the total of all the name scores in the file? '''
def namescore(nn):
mark = 0
for i in nn:
mark += ord(i) - ord('A') + 1
return mark
filein = open('names.txt', 'r')
names = filein.read().split(',')
names.sort()
test = names[:]
for xx in xrange(len(names)):
test[xx] = (xx + 1) * namescore(names[xx])
print sum(test)

49
python/23.py Normal file
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# coding=utf-8
''' A perfect number is a number for which the sum of its proper divisors is exactly equal to the number. For example, the sum of the proper divisors of 28 would be 1 + 2 + 4 + 7 + 14 = 28, which means that 28 is a perfect number.
A number n is called deficient if the sum of its proper divisors is less than n and it is called abundant if this sum exceeds n.
As 12 is the smallest abundant number, 1 + 2 + 3 + 4 + 6 = 16, the smallest number that can be written as the sum of two abundant numbers is 24. By mathematical analysis, it can be shown that all integers greater than 28123 can be written as the sum of two abundant numbers. However, this upper limit cannot be reduced any further by analysis even though it is known that the greatest number that cannot be expressed as the sum of two abundant numbers is less than this limit.
Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers. '''
_limit = 20161
def factor(n):
ll = [1]
i = 2
while i <= int(n ** 0.5):
if n % i == 0:
ll.append(i)
if n // i != i:
ll.append(n / i)
i += 1
return ll
def test(x):
sum = 0
for i in factor(x):
sum += i
if sum > x:
return 1
else: return 0
def ablist(max):
all = []
for i in xrange(10, max + 1):
if test(i):
all.append(i)
return all
abnum = ablist(_limit)
if __name__ == '__main__':
num = range(_limit + 1)
for xx in abnum:
for yy in abnum:
tmp = xx + yy
if tmp < _limit:
num[tmp] = 0
else:
break
sum = 0
for i in num:
sum += i
print sum

25
python/24.py Normal file
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_max = 10
_end = 1000000
_last = 3628800
locale = _end - 1
num = [1, 1]
count = [1,1,1,1,1,1,1,1,1,1]
ch = '0123456789'
out = ''
i = 2
while len(num) < 10:
num.append(num[-1] * i)
i += 1
for i in xrange(_max - 1, 0, -1):
count[i] = locale / num[i]
locale %= num[i]
out += ch[count[i]]
ch = ch[:count[i]] + ch[count[i] + 1:]
print out + ch

7
python/25.py Normal file
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fib = [1, 1, 0]
num = 2
while 1:
fib[num % 2] = fib[(num + 1) % 2] + fib[(num + 2) % 2]
if len(str(fib[num % 2])) == 1000: break
num += 1
print num + 1

39
python/26.py Normal file
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# coding=utf-8
def divnum(a):
mod = []
div = 1
while 1:
tmp = div % a
if tmp == 0:
return len(mod)
elif mod.count(tmp): break
else:
mod.append(tmp)
div *= 10
return len(mod) - mod.index(tmp)
def divnum1(a):
while a % 2 == 0:
a /= 2
while a % 5 == 0:
a /= 5
j = 1
while 1:
tmp = int('9' * j)
if tmp % a == 0:
return str(tmp / a)
j += 1
maxnum = [0, 0]
maxx = 1000
for i in xrange(1, maxx + 1):
temp = divnum(i)
#temp = len(divnum1(i))
if temp > maxnum[1]:
maxnum[0] = i
maxnum[1] = temp
print maxnum

33
python/27.py Normal file
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def isprime(x):
if x <= 0:
return False
if x == 2:
return True
temp = 3
while temp <= int(x ** 0.5) + 1:
if x % temp == 0: return False
else: temp += 2
return True
delta = lambda x, y: 2 * x + y + 1
a = [0, 0, 0]
for j in xrange(1001):
if isprime(j):
for i in xrange(-1000, 1001):
n = 0
tmp = j
while 1:
tmp += delta(n, i)
if isprime(tmp):
#print j, '\t', i, '\t', tmp
n += 1
else:
break
if n > a[0]:
a[0] = n
a[1] = i
a[2] = j
print a[1] * a[2], '=', a[1], '*', a[2]

8
python/28.py Normal file
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total = 0
for i in xrange(1, 1002):
tmp = i * i
total += tmp + (1 - i % 2)
total += tmp + i + 1
print total - 1001 * 1002 - 1

8
python/29.py Normal file
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lis = []
for i in xrange(2, 101):
for j in xrange(2, 101):
tmp = i ** j
if lis.count(tmp) == 0:
lis.append(tmp)
print len(lis)

20
python/3.py Normal file
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# coding=utf-8
''' The prime factors of 13195 are 5, 7, 13 and 29.
What is the largest prime factor of the number 600851475143 ? '''
'''分解因数，如果是素数返回'''
def factor(x, min = 2):
temp = min
while temp <= int(x ** 0.5) + 1: #从最小值到上界开始尝试
if x % temp == 0: return temp # 如果 a 能分解则返回最小因子
else: temp += 1
return 1 # 如果 a 是素数就返回 1，此处也可以设置为返回 x 本身
n = 600851475143
i = 2 # 尝试循环分解 n 的因子
while i <= int(math.sqrt(n)) + 1:
if n % i == 0 : # 如果满足 i 整除 n
if factor(n / i) == 1: break # 同时 n / i 是素数则返回
else: n /= i # 如果 n / i 不为素数，就缩小 n 以减小运算量
i += 1
print n / i # 输出结果

15
python/30.py Normal file
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def ala(x, n = 5):
ss = 0
while x != 0:
ss += (x % 10) ** n
x /= 10
return ss
total = 0
for i in xrange(1000000):
if i == ala(i):
print i
total += i
print '\n\n', total - 1

17
python/31.py Normal file
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cash = (200, 100, 50, 20, 10, 5, 2, 1)
#cash = (5, 2, 1)
total = []
def im(lis, x, n, a = 0):
if a == len(cash) - 1:
x.append(n)
lis.append(x[:])
x.pop()
return
for i in xrange(int(n / cash[a]) + 1):
x.append(i)
im(lis, x, n - i * cash[a], a + 1)
x.pop()
im(total, [], 200)
print len(total)

53
python/32.py Normal file
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from math import log10
def pick(x, lis, out, a = 0):
if x == 0:
out.append([a, lis])
return
a *= 10
for i in xrange(len(lis)):
tmp = lis[:]
tmpa = a + lis[i]
tmp.pop(i)
pick(x - 1, tmp, out, tmpa)
def test(x, n):
tmp = x[:]
while n > 0:
if tmp.count(n % 10):
tmp.remove(n % 10)
n /= 10
else:
return False
if len(tmp) > 0:
return False
return True
total = []
tt = []
pick(1, [1,2,3,4,5,6,7,8,9], tt)
for i in tt:
yy = []
pick(4, i[1], yy)
for j in yy:
if test(j[1], i[0] * j[0]):
tmp = i[0] * j[0]
if total.count(tmp) == 0:
total.append(tmp)
tt = []
pick(2, [1,2,3,4,5,6,7,8,9], tt)
for i in tt:
yy = []
pick(3, i[1], yy)
for j in yy:
if test(j[1], i[0] * j[0]):
tmp = i[0] * j[0]
if total.count(tmp) == 0:
total.append(tmp)
print sum(total)

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gcd = lambda x, y: y == 0 and x or gcd(y, x % y)
def common(x, y):
a = []
b = []
while x > 0:
a.append(x % 10)
x /= 10
while y > 0:
b.append(y % 10)
y /= 10
outa = 0
outb = 0
tmp = list(set(a) & set(b))
if tmp.count(0) != 0:
tmp.remove(0)
if len(tmp) > 0:
for i in tmp:
a.remove(i)
b.remove(i)
if len(a) == 0 or len(b) == 0:
return (False, 0)
a.reverse()
for j in a: outa = outa * 10 + j
b.reverse()
for j in b: outb = outb * 10 + j
return (True, outa, outb)
else:
return (False, 0)
for i in xrange(11, 100):
for j in xrange(i + 1, 100):
tmp = common(i, j)
if tmp[0]:
if tmp[1] * j == tmp[2] * i:
print i, j

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def mul(x):
out = 1
for i in xrange(2, x + 1):
out *= i
return out
def ala(x):
tt = x
xx = 0
while tt > 0:
xx += mul(tt % 10)
tt /= 10
if xx == x:
return True
else:
return False
total = 0
i = 3
while i < 100000:
if ala(i):
print i
total += i
i += 1
print total

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''' The number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime.
There are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97.
How many circular primes are there below one million? '''
from math import log10
pp = [2]
for i in xrange(3, 1000, 2):
for x in pp:
if i % x == 0:
break
else:
pp.append(i)
def isp(a):
for i in pp:
if a % i == 0:
if a == i:
return True
return False
return True
def loop(x):
length = int(log10(x))
return (x % 10) * 10 ** length + x / 10
def lote(n):
tt = n
while 1:
if not isp(tt):
return False
tt = loop(tt)
if tt == n:
return True
out = [2]
for ii in xrange(3, 1000000, 2):
if lote(ii):
out.append(ii)
print len(out)

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def rev(x):
out = ''
for i in xrange(len(x)):
out += x[-1 - i]
return out
def make(x):
if x == 1:
return [1,2,3,4,5,6,7,8,9]
lenn = 10 ** (x / 2)
out = []
for i in xrange(lenn / 10, lenn):
a = str(i)
b = rev(a)
if x % 2:
for i in xrange(10):
out.append(int(a + str(i) + b))
else:
out.append(int(a + b))
return out
def test(x):
bi = []
while x > 0:
bi.append(x % 2)
x /= 2
bb = bi[:]
bb.reverse()
if bi == bb:
#print bi,
return True
else:
return False
total = 0
for i in xrange(1, 7):
for j in make(i):
if test(j):
#print j
total += j
print total

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from math import sqrt, log10
def isp(x):
if x == 2:
return True
if x <= 1 or x & 1 == 0:
return False
for i in xrange(3, int(sqrt(x)) + 1, 2):
if x % i == 0:
return False
return True
def ananum(x):
if isp(x):
for i in xrange(1, int(log10(x)) + 1):
if isp(x / (10 ** i)) and isp(x % (10 ** i)):
continue
else:
return False
return True
return False
count = 0
total = []
n = 11
while count < 11:
if ananum(n):
count += 1
total.append(n)
n += 1
print count, sum(total)
print total

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def pick(x, lis, out, a = 0):
if x == 0:
out.append(a)
return
a *= 10
for i in xrange(len(lis)):
tmp = lis[:]
tmpa = a + lis[i]
tmp.pop(i)
pick(x - 1, tmp, out, tmpa)
def test(x):
mm = '932718654'
ss = ''
i = 0
while len(ss) < 9:
i += 1
ss += str(i * x)
tt = []
for j in xrange(len(ss)):
tt.append(ss[j])
if len(tt) == len(set(tt)) and ss >= mm:
if not tt.count('0'):
print ss
num = [1,2,3,4,5,6,7,8,9]
tt = []
pick(4, num, tt)
for i in tt:
test(i)

98
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from math import log
from sys import argv
fib = [1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,28657,46368,75025,121393,196418,317811,514229,832040,1346269,2178309,3524578,5702887,9227465,14930352,24157817,39088169,63245986,102334155,165580141,267914296,433494437,701408733,1134903170,1836311903]
def sqrs(x):
out = ''
while x > 0:
out += chr(ord('0') + x % 2)
x /= 2
if len(out) <= 1: return 1
outnum = 1
for i in xrange(1, len(out)):
if out[i] == out[i - 1] == '1':
outnum *= -1
return outnum
'''
def trace(x, n):
bale = 0
print '%12s' % bin(x)[2:],
for i in xrange(1, n + 1):
bale += sqrs(x + i)
if bale == 0:
print '%4d' % i,
break
for kk in xrange(10):
trace(2 ** kk + int(argv[1]), 1000)
print
'''
'''
a = 0
for i in xrange(10000):
a += sqrs(i)
print a,
'''
def listsr(x):
out = [1]
for i in xrange(x):
out.append(out[i] + sqrs(i + 1))
return out
def sqs(lis):
dic = {}
for i in xrange(len(lis)):
tmp = lis[i]
if dic.keys().count(tmp) == 0:
dic.update({tmp: [i]})
else:
dic.get(tmp).append(i)
return dic
def log2(x):
return int(log(x)/log(2))
def first(x):
if x == 0:
return 0
minus = 0
if x & 1 == 0:
tmp = 1
while x & tmp == 0:
tmp *= 2
else:
minus = ((4 ** log2(tmp) - 1) / 3 + 1) / 2
x += 1
length = log2(x)
value = 4 ** length / 2
can = 2 ** length + 1 # 1000...0001
for i in xrange(1, length):
bar = 2 ** i
if (bar & can) != (bar & x):
value += 4 ** i / 2
return value - minus
lis = listsr(50000)
#print lis
a = sqs(lis)
a.pop(1)
for item in a.keys():
tmp = a.get(item)[0]
for i in xrange(len(a.get(item))):
a.get(item)[i] -= tmp
#print item, '\t', '%8s' % bin(tmp)[2:], '\t', a.get(item)
print '%10s' % bin(item)[2:], '%6d' % first(item), '%7d' % a.get(item)[-1], '%8d' % ((first(item) + a.get(item)[-1]) / 2), a.get(item)[(item + 1) / 2]

50
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\documentclass[12pt,a4paper]{article}
\usepackage[top=2cm, bottom=2cm, left=2.5cm, right=2.5cm]{geometry}
\usepackage{indentfirst}%首行缩进
\XeTeXlinebreaklocale "zh"%中文换行
\XeTeXlinebreakskip = 0pt plus 1pt minus 0.1pt%放宽断行限制
\usepackage[cm-default, no-math, no-config]{fontspec}%字体包
\setmainfont[BoldFont=WenQuanYi Micro Hei]{SimSun}%设置字体
\title{问题 384}
\author{Project Euler}
\begin{document}
\maketitle
定义数列 $a(n)$ 是 $n$ 的二进制数字中成对出现的$1$的对数。例如：
$$
a(5)=a(101_2)=0,a(6)=a(110_2)=1,a(7)=a(111_2)=2
$$
定义数列 $b(n)=(-1)^{a(n)}$。此数列被称为 Rudin-Shapiro 数列。\\
考察数列 $b(n)$ 的前 $n$ 项和 $$s(n)=\sum^n_{i=0}b(i)$$
此三个数列的前几项为
\begin{center}
\begin{tabular}{lrrrrrrrr}
n & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\
a(n) & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 2 \\
b(n) & 1 & 1 & 1 & -1 & 1 & 1 & -1 & 1 \\
s(n) & 1 & 2 & 3 & 2 & 3 & 4 & 3 & 4 \\
\end{tabular}
\end{center}
数列 $s(n)$ 有如下性质，所有数字都为整数，且每个数字出现的次数与其本身数值相等。\\
定义 $g(t,c)$，其中 $1 \leq c \leq t$，表示 $t$ 第 $c$ 次出现时的下标 $n$。
例如 $g(3,3)=6, g(4,2)=7, g(54321, 12345)=1220847710$。\\
令 $F(n)$ 是 fibonacci 数列，其中 $F(0) = F(1) = 1$。\\
定义 $GF(t)=g(F(t),F(t-1))$，求
$$
\sum_{t=2}^{45}GF(t)
$$
\end{document}

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python/39.py Normal file
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a = {}
for i in xrange(1, 1000):
for j in xrange(i, 1000):
tmp = i * i + j * j
sqr = int(tmp ** 0.5)
if tmp == sqr * sqr and i + j + sqr <= 1000:
tt = i + j + sqr
if a.keys().count(tt):
a.update({tt: a.get(tt) + 1})
else:
a.update({tt: 1})
mm = [0, 0]
for i in a.keys():
if a.get(i) > mm[1]:
mm[0] = i
mm[1] = a.get(i)
print mm

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# coding=utf-8
''' A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 * 99.
Find the largest palindrome made from the product of two 3-digit numbers.. '''

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''' An irrational decimal fraction is created by concatenating the positive
integers:
0.123456789101112131415161718192021...
It can be seen that the 12th digit of the fractional part is 1.
If dn represents the nth digit of the fractional part, find the value of the following expression.
d1 * d10 * d100 * d1000 * d10000 * d100000 * d1000000 '''
from math import log10
def num(x, i):
if i > int(log10(x)):
raise IOError
else:
i = int(log10(x)) - i
while i > 0:
x /= 10
i -= 1
return x % 10
def d(x):
elem = [0, 9, 189, 2889, 38889, 488889, 5888889, 68888889]
for i in xrange(len(elem)):
if elem[i] >= x:
break
x -= elem[i - 1] + 1
return num(10 ** (i - 1) + x / i, x % i)
multi = 1
for i in xrange(7):
multi *= d(10 ** i)
#print d(10 ** i)
print multi

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def pick(x, lis, out, a = 0):
if x == 0:
out.append(a)
return
a *= 10
for i in xrange(len(lis)):
tmp = lis[:]
tmpa = a + lis[i]
tmp.pop(i)
pick(x - 1, tmp, out, tmpa)
def isprime(x):
if x == 2:
return True
if x % 2 == 0:
return False
temp = 3
while temp <= int(x ** 0.5) + 1:
if x % temp == 0: return False
else: temp += 2
return True
a = [1,2,3,4,5,6,7]
tt = []
pick(len(a), a, tt)
tt.reverse()
for i in tt:
if isprime(i):
print i
break

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def trinum(x):
if x == 1:
return True
x *= 2
sqr = int(x ** 0.5)
if x == sqr * (sqr + 1):
return True
else:
return False
filein = open('words.txt', 'r')
names = filein.read().split(',')
for ii in xrange(len(names)):
names[ii] = names[ii][1:-1]
def score(nn):
mark = 0
for i in nn:
mark += ord(i) - ord('A') + 1
return mark
count = 0
for i in names:
if trinum(score(i)):
#print '%3d\t' % score(i), i
count += 1
print count

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python/43.py Normal file
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def picksort(x, lis, out, a = 0):
if x == 0:
out.append(a)
return
a *= 10
for i in xrange(len(lis)):
tmp = lis[:]
tmpa = a + lis[i]
tmp.pop(i)
picksort(x - 1, tmp, out, tmpa)
a = [0,1,2,3,4,6,7,8,9]
tt = []
picksort(len(a), a, tt)
total = 0
for i in tt:
tttt = str(i)
if tttt[0] != '0' and int(tttt[3]) % 2 == 0:
if int(tttt[2:5]) % 3 == 0 and int(tttt[5:8]) % 13 == 0 and int(tttt[6:]) % 17 == 0:
tmp = i % 10000 + (i / 10000 * 10 + 5) * 10000
if int(str(tmp)[4:7]) % 7 == 0 and int(str(tmp)[5:8]) % 11 == 0:
print tmp
total += tmp
print total

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def test(x):
sq = 12 * x + 1
ss = int(sq ** 0.5)
if ss * ss != sq:
return False
if ss % 6 != 5:
return False
return True
def main():
max = 3000
for n in xrange(4, max):
for m in xrange(n + 1, max):
a = 3 * (m * m + n * n) - m - n
b = (m - n) * (3 * (m + n) - 1)
if test(a) and test(b):
print a / 2, b / 2, m, n
return
main()

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