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update with new python skill

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xw_y_am@rmbp 2017-08-15 21:18:39 +08:00
parent 0a01cc0ac8
commit 1b1c91e4e0
68 changed files with 1236 additions and 1537 deletions
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28
python/1.py
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@ -1,25 +1,9 @@
# 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 multi_in_num(limit, base):
count = limit // base
return (count + 1) * count * base // 2
def calc(n, a):
tmp = n / a
return (tmp + 1) * tmp * a / 2
def dual_multi_in_num(limit, a, b):
return multi_in_num(limit, a) + multi_in_num(limit, b) - multi_in_num(limit, a * b)
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
'''
print(dual_multi_in_num(1000 - 1, 3, 5))

43
python/10.py
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@ -1,42 +1,3 @@
''' 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
from tools import number_theory
print(sum(number_theory.make_prime(2000000)))

92
python/11.py
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@ -1,45 +1,51 @@
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],
from functools import reduce
def get_block(matrix, x, y, size):
block = []
for i in range(x, x + size):
block += matrix[i][y : y + size]
return block
def calc_max(cmpr, l):
return max(cmpr, reduce(lambda x, y: x * y, l, 1))
def block_max(block, size):
maxi = 0
for i in range(0, size * size, size):
maxi = calc_max(maxi, block[i : i + size])
for i in range(size):
maxi = calc_max(maxi, block[i : size * size : size])
maxi = calc_max(maxi, block[0 : size * size : size + 1])
maxi = calc_max(maxi, block[size - 1 : size * size - 1: size - 1])
return maxi
def seek_matrix(size, matrix):
maxi = 0
for x in range(len(matrix) - size):
for y in range(len(matrix[0]) - size):
maxi = max(maxi, block_max(get_block(matrix, x, y, size), size))
return maxi
print(seek_matrix(4, [
[ 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],
[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
[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]
]))

71
python/12.py
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@ -1,30 +1,45 @@
''' 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
from functools import reduce
from tools import number_theory
if __name__ == '__main__':
play(500)
g_prime = list(number_theory.make_prime(1000000))
def find_a_factor(num, prime):
while prime:
p = prime.pop(0)
if not (num % p):
return p, prime
return 0, []
def factor_num(num):
global g_prime
for i, value in enumerate(g_prime):
if value ** 2 > num:
break
prime = g_prime[:i]
factors = {}
while True:
factor, prime = find_a_factor(num, prime)
if factor:
count = 0
while not (num % factor):
num //= factor
count += 1
factors[factor] = count
else:
if 1 != num:
factors[num] = 1
return factors
def tri_num():
x = 2
while True:
yield x * (x + 1) // 2
x += 1
for x in tri_num():
factor_count = reduce(lambda x, y: x * (y + 1), factor_num(x).values(), 1)
if factor_count > 500:
print(x)
break

12
python/13.py
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@ -1,4 +1,5 @@
num = [
nums = [
37107287533902102798797998220837590246510135740250,
46376937677490009712648124896970078050417018260538,
74324986199524741059474233309513058123726617309629,
@ -98,11 +99,6 @@ num = [
77158542502016545090413245809786882778948721859617,
72107838435069186155435662884062257473692284509516,
20849603980134001723930671666823555245252804609722,
53503534226472524250874054075591789781264330331690,]
53503534226472524250874054075591789781264330331690]
total = 0
for i in num:
total += i
#print total
print str(total)[:10]
print(str(sum(nums))[:10])

95
python/14.py
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@ -1,49 +1,52 @@
def sq(x):
out = 0
while x != 1:
out += 1
if x % 2 == 1:
x = x * 3 + 1
class Step:
l = []
d = {}
limit = 0
def __init__(self, num):
self.limit = 5 * num
self.l = [0] * self.limit
self.l[0] = 1
def __getitem__(self, key):
if self.limit > key:
return self.l[key]
else:
return self.d.setdefault(key, 0)
def __setitem__(self, key, value):
if self.limit > key:
self.l[key] = value
else:
self.d[key] = value
def collatz_step(x, path):
global steps
if steps[x - 1]:
foot = steps[x - 1] + 1
while path:
steps[path.pop() - 1] = foot
foot += 1
return
else:
x /= 2
return out
path.append(x)
if x % 2:
collatz_step(3 * x + 1, path)
else:
collatz_step(x // 2, path)
def collatz_max(num):
global steps
for x in range(1, num + 1):
if steps[x - 1]:
continue
collatz_step(x, [])
return steps.l.index(max(steps.l[:num])) + 1
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
'''
steps = Step(limit)
print(collatz_max(limit))

13
python/15.py
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@ -1,9 +1,6 @@
''' 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
from functools import reduce
total = reduce(lambda x, y: x * y, range(40, 20, -1), 1)
total = reduce(lambda x, y: x // y, range(1, 21), total)
print(total)

9
python/16.py
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@ -1,7 +1,4 @@
''' 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
from functools import reduce
print(reduce(lambda x, y: x + int(y), str(2 ** 1000), 0))

66
python/17.py
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@ -1,66 +0,0 @@
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

58
python/18.py
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@ -1,50 +1,24 @@
a = [[75],
def trace(pick, triangle):
maxi = [0] * (len(triangle[-1]) + 1)
for line in reversed(triangle):
for i, value in enumerate(line):
maxi[i] = value + pick(maxi[i], maxi[i + 1])
return maxi[0]
print(trace(max,[
[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],
[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
'''
[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]]))

43
python/19.py
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@ -1,33 +1,18 @@
month = (0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31)
weekday = [5]
month = (31, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30)
def testyear(x):
if x % 400 == 0:
return True
if x % 100 != 0 and x % 4 == 0:
return True
return False
def leap_day(year):
if not (year % 400):
return 1
if (year % 100) and (not (year % 4)):
return 1
return 0
for y in range(1900, 2001):
for m in month:
weekday.append((weekday[-1] + m) % 7)
if 28 == m:
weekday[-1] = (weekday[-1] + leap_day(y)) % 7
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
print(weekday[13:].count(0))

35
python/2.py
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@ -1,24 +1,17 @@
# 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. '''
def fibonacci():
a, b = 1, 1
while True:
yield a
a, b = b, a + b
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
def target_sum(limit, match):
total = 0
for x in fibonacci():
if x >= limit:
break
if match(x):
total += x
return total
print(target_sum(4000000, lambda x: not (x & 1)))

20
python/20.py
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@ -1,13 +1,9 @@
''' 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
from functools import reduce
def factorial(n):
if 1 == n:
return 1
return n * factorial(n - 1)
print(reduce(lambda x, y: x + int(y), str(factorial(100)), 0))

36
python/21.py
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@ -1,19 +1,23 @@
''' 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 all_factor(num):
factors = [1]
sqrt = int(num ** 0.5)
if sqrt ** 2 == num:
factors.append(sqrt)
sqrt -= 1
for x in range(2, sqrt + 1):
if not (num % x):
factors += [x, num // x]
return factors
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
def count_amicable(begin, end):
total = 0
while begin < end:
factor_sum = sum(all_factor(begin))
if (sum(all_factor(factor_sum)) == begin) and (factor_sum != begin):
total += begin + factor_sum
begin = factor_sum
begin += 1
return total
for j in xrange(2, 10000):
tmp = ami(j)
if j == ami(tmp) and j != tmp:
print j, '\t', tmp
print(count_amicable(200, 10000))

24
python/22.py
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@ -1,21 +1,11 @@
''' 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
from functools import reduce
def get_file():
names = open('../resource/names.txt', 'r').read().split(',')
return sorted(names)
filein = open('names.txt', 'r')
names = filein.read().split(',')
names.sort()
test = names[:]
def name_score(name):
return reduce(lambda x, y: x + ord(y) - ord('A') + 1, name, 0)
for xx in xrange(len(names)):
test[xx] = (xx + 1) * namescore(names[xx])
print sum(test)
print(reduce(lambda x, y: x + (y[0] + 1) * y[1], enumerate(map(lambda x: name_score(x), get_file())), 0))

72
python/23.py
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@ -1,49 +1,31 @@
# 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 all_factor(num):
factors = [1]
sqrt = int(num ** 0.5)
if sqrt ** 2 == num:
factors.append(sqrt)
sqrt -= 1
for x in range(2, sqrt + 1):
if not (num % x):
factors += [x, num // x]
return factors
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 get_abundant(limit):
gets = [12]
for x in range(13, limit):
if sum(all_factor(x)) > x:
gets.append(x)
return gets
def test(x):
sum = 0
for i in factor(x):
sum += i
if sum > x:
return 1
else: return 0
def get_none_dule_abundant(limit):
factor = get_abundant(limit)
flags = [1] * (limit + 1)
for x in range(len(factor)):
for y in range(x, len(factor)):
s = factor[x] + factor[y]
if s > limit:
break
flags[s] = 0
return [x[0] for x in enumerate(flags) if x[1]]
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
print(sum(get_none_dule_abundant(28123)))

38
python/24.py
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@ -1,25 +1,19 @@
_max = 10
_end = 1000000
_last = 3628800
def make_permutation(n):
p = [1]
for i in range(2, n):
p = [p[0] * i] + p
return p
locale = _end - 1
def get_order(n, order):
permutation = make_permutation(n)
number = list(range(n))
sequence = []
order -= 1
for p in permutation:
q = order // p
sequence.append(number.pop(q))
order %= p
return sequence + number
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
print(''.join(map(lambda x: str(x), get_order(10, 1000000))))

20
python/25.py
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@ -1,7 +1,13 @@
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
def fibonacci():
a, b = 1, 1
while True:
yield a
a, b = b, a + b
def fib_digit(digit):
for i, value in enumerate(fibonacci()):
if len(str(value)) == digit:
return i + 1
print(fib_digit(1000))

56
python/26.py
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@ -1,39 +1,25 @@
# 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 sum_mod(m):
mod = 9 % m
while True:
yield mod
mod = ((mod * 10) + 9) % m
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
def exact_div(m):
if not m:
return 0
while not (m % 2):
m //= 2
while not (m % 5):
m //= 5
if 1 == m:
return 0
for i, value in enumerate(sum_mod(m)):
if not value:
return i + 1
def max_cycle(limit):
cycles = [exact_div(x) for x in range(limit + 1)]
return cycles.index(max(cycles))
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
print(max_cycle(1000))

62
python/27.py
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@ -1,33 +1,37 @@
def isprime(x):
if x <= 0:
from tools import number_theory
def test_prime(x, prime):
for p in prime:
if p ** 2 > x:
return True
if not (x % p):
return False
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
def gen_value(a, b):
n = 0
x = b
prime = list(number_theory.make_prime(10000))
while True:
if prime[-1] ** 2 < x:
prime = list(number_theory.make_prime(prime[-1] * 2 + 1))
if 0 > x:
return
if not test_prime(x, prime):
return
yield x
x += 2 * n + a + 1
n += 1
delta = lambda x, y: 2 * x + y + 1
def test_polynomial(limit):
maxi = [0, (0, 0)]
for b in number_theory.make_prime(limit):
for a in range(-b, 0, 2):
l = len(list(gen_value(a, b)))
if l > maxi[0]:
maxi = [l, (a, b)]
print(maxi)
return maxi[1][0] * maxi[1][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]
print(test_polynomial(1000))

9
python/28.py
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@ -1,8 +1 @@
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
print(sum([4 * (x ** 2 + x // 2 + 1) for x in range(0, 1001, 2)]) - 3)

15
python/29.py
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@ -1,8 +1,9 @@
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)
def mk_uniqe(limit):
s = set()
for i in range(2, limit + 1):
for j in range(2, limit + 1):
s.add(i ** j)
return s
print(len(mk_uniqe(100)))

41
python/3.py
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@ -1,20 +1,25 @@
# 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
from tools import number_theory
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
def find_a_factor(num, prime):
while prime:
p = prime.pop(0)
if not (num % p):
return p, prime
return 0, []
def factor_num(num):
prime = list(number_theory.make_prime(int(num ** 0.5)))
factors = []
while True:
factor, prime = find_a_factor(num, prime)
if factor:
factors.append(factor)
while not (num % factor):
num //= factor
else:
if 1 != num:
factors.append(num)
return factors
print(factor_num(600851475143))

30
python/30.py
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@ -1,15 +1,21 @@
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
def get_limit(num):
n = 1
while (10 ** n) < n * (9 ** num):
n += 1
return n
def eq(x, num):
ori_number = x
sum_power = 0
while x:
sum_power += (x % 10) ** num
x //= 10
return sum_power == ori_number
print '\n\n', total - 1
def get(num):
for x in range(2, 10 ** get_limit(num)):
if eq(x, num):
yield x
print(sum(get(5)))

27
python/31.py
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@ -1,17 +1,14 @@
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()
def count_money_iter(total, cash, count):
if not len(cash):
count[0] += 1
else:
for x in range(total // cash[0] + 1):
count_money_iter(total - x * cash[0], cash[1:], count)
im(total, [], 200)
print len(total)
def count_money(total, cash):
count = [0]
count_money_iter(total, cash, count)
return count[0]
print(count_money(200, [200, 100, 50, 20, 10, 5, 2]))

66
python/32.py
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@ -1,53 +1,23 @@
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
def make_permutation_iter(num, l, s, result):
if not num:
result.append((s, l))
else:
return False
if len(tmp) > 0:
return False
return True
for i in range(len(l)):
make_permutation_iter(num - 1, l[:i] + l[i + 1:], s + l[i], result)
total = []
def make_permutation(num, l):
result = []
make_permutation_iter(num, l, '', result)
return result
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)
def add_type(a, b):
s = set()
for x, left in make_permutation(a, '123456789'):
for y, cmpr in make_permutation(b, left):
multi = int(x) * int(y)
if str(sorted(cmpr)) == str(sorted(str(multi))):
s.add(multi)
return sum(s)
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)
print(add_type(1, 4) + add_type(2, 3))

48
python/33.py
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@ -1,39 +1,15 @@
gcd = lambda x, y: y == 0 and x or gcd(y, x % y)
from tools import number_theory
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
def multi():
numerator, denominator = 1, 1
for a in range(1, 10):
for b in range(1, 10):
if a != b:
if not ((10 * a * b) % (9 * a + b)):
c = 10 * a * b // (9 * a + b)
numerator *= 10 * a + b
denominator *= 10 * b + c
return denominator // number_theory.gcd(numerator, denominator)
print(multi())

42
python/34.py
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@ -1,25 +1,21 @@
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
from functools import reduce
total = 0
i = 3
while i < 100000:
if ala(i):
print i
total += i
i += 1
print total
def gen_fac(n):
base = 1
for n in range(1, n + 2):
yield base
base *= n
def find_sum():
s = set()
fac = list(gen_fac(9))
for value in fac:
if 3 > value:
continue
for x in range(value, value + 1000):
if reduce(lambda x, y: x + fac[y], list(map(lambda x: int(x), str(x))), 0) == x:
s.add(x)
return s
print(sum(find_sum()))

55
python/35.py
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@ -1,42 +1,21 @@
''' 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
from tools import number_theory
pp = [2]
for i in xrange(3, 1000, 2):
for x in pp:
if i % x == 0:
break
else:
pp.append(i)
def roll(num):
s = str(num)
for i in range(len(s)):
yield int(s[i:] + s[: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)
def find_roll_prime(limit):
count = 13
prime = list(number_theory.make_prime(limit))[25:]
prime = list(filter(lambda x: ('5' not in str(x)), prime))
for p in prime:
for x in roll(p):
if x not in prime:
break
else:
count += 1
return count
print(find_roll_prime(1000000))

62
python/36.py
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@ -1,45 +1,23 @@
def rev(x):
out = ''
for i in xrange(len(x)):
out += x[-1 - i]
return out
def gen_bit(bit_len):
for i in range(2 ** ((bit_len + 1) // 2)):
unit = bin(i)[2:]
half = '0' * ((bit_len + 1) // 2 - len(unit)) + unit
if bit_len % 2:
yield half + half[-2::-1]
else:
yield half + half[::-1]
def count_palindromic(limit):
bit_len = 1
result = []
while True:
for s in gen_bit(bit_len):
num = eval('0b1' + s + '1')
if num > limit:
return [1, 3] + result
if str(num) == str(num)[::-1]:
result.append(num)
bit_len += 1
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
print(sum(count_palindromic(1000000)))

66
python/37.py
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@ -1,35 +1,45 @@
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
from tools import number_theory
def shift(num):
left = str(num)[:-1]
while left:
yield int(left)
left = left[:-1]
right = str(num)[1:]
while right:
yield int(right)
right = right[1:]
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:
def check_prime(x):
x = str(x)
if ('9' == x[0]) or ('9' == x[-1]):
return False
if ('1' == x[0]) or ('1' == x[-1]):
return False
if '5' in x[1:]:
return False
if '2' in x[1:]:
return False
if '0' in x:
return False
if '4' in x:
return False
if '6' in x:
return False
if '8' in x:
return False
return True
return False
def search():
find = []
prime = list(number_theory.make_prime(1000000))
for p in filter(lambda x: check_prime(x), prime):
for s in shift(p):
if s not in prime:
break
else:
find.append(p)
return find[4:]
count = 0
total = []
n = 11
while count < 11:
if ananum(n):
count += 1
total.append(n)
n += 1
print count, sum(total)
print total
print(sum(search()))

43
python/38.py
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@ -1,31 +1,18 @@
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
def seek(prefix, l):
for a in l[::-1]:
for b in l[::-1]:
if a != b:
yield int(prefix + a + b)
num = [1,2,3,4,5,6,7,8,9]
tt = []
pick(4, num, tt)
def test():
for x in seek('93', '24567'):
num = str(x) + str(x * 2)
if '123456789' == ''.join(sorted(list(num))):
return num
for x in seek('92', '34567'):
num = str(x) + str(x * 2)
if '123456789' == ''.join(sorted(list(num))):
return num
for i in tt:
test(i)
print(test())

29
python/39.py
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@ -1,21 +1,12 @@
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})
def count(side):
sides = {}
for a in range(1, side // 3 + 1):
for b in range(a + 1, (side - a) // 2):
c = int((a ** 2 + b ** 2) ** 0.5)
if (a ** 2 + b ** 2) == c ** 2:
s = a + b + c
sides[s] = sides.setdefault(s, 0) + 1
return max(sides, key=lambda x: sides[x])
mm = [0, 0]
for i in a.keys():
if a.get(i) > mm[1]:
mm[0] = i
mm[1] = a.get(i)
print mm
print(count(1000))

21
python/4.py
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@ -1,4 +1,19 @@
# 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.. '''
def find_factor(num):
for x in range(999, 99, -1):
if not (num % x):
return x
else:
return 0
def make_palindrome():
for x in range(999, 99, -1):
s = str(x)
yield int(s + s[::-1])
for x in make_palindrome():
p = find_factor(x)
if p:
if 3 == len(str(x // p)):
print(x)
exit()

48
python/40.py
View File

@ -1,32 +1,22 @@
''' 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 get_digit(n):
n -= 1
i = 0
while True:
count_digit = (i + 1) * 9 * (10 ** i)
if n < count_digit:
break
n -= count_digit
i += 1
num, index = divmod(n, i + 1)
return int(str(num + 10 ** i)[index])
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 multi_digit(limit):
multi = 1
n = 1
while n < limit + 1:
multi *= get_digit(n)
n *= 10
return multi
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
print(multi_digit(1000000))

56
python/41.py
View File

@ -1,33 +1,33 @@
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)
from tools import number_theory
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
def is_prime(num, prime):
for p in prime:
if p ** 2 > num:
return True
if not (num % p):
return False
def gen_p(digit):
l = list(reversed(range(1, digit + 1)))
not_ordered = True
while not_ordered:
yield int(''.join(map(lambda x: str(x), l)))
for i in range(len(l) - 1, 0, -1):
if l[i - 1] > l[i]:
post = list(sorted(l[i - 1:]))
get = post.pop(post.index(l[i - 1]) - 1)
l = l[:i - 1] + [get] + list(reversed(post))
break
else:
not_ordered = False
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
def find():
prime = list(number_theory.make_prime(10000))
for digit in range(8, 3, -1):
if digit % 3:
for x in gen_p(digit):
if is_prime(x, prime):
return x
print(find())

37
python/42.py
View File

@ -1,29 +1,18 @@
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]
from functools import reduce
def score(nn):
mark = 0
for i in nn:
mark += ord(i) - ord('A') + 1
return mark
def word_num(word):
return reduce(lambda x, y: x + ord(y) - ord('A') + 1, word, 0)
def is_tri_num(num):
sqrt = int((2 * num) ** 0.5)
return not ((sqrt + 1) * sqrt // 2 - num)
count = 0
for i in names:
if trinum(score(i)):
#print '%3d\t' % score(i), i
count += 1
def file_get():
with open('../resource/words.txt', 'r') as f:
context = f.read().replace('"', '').split(',')
return list(filter(lambda x: is_tri_num(x), map(lambda x: word_num(x), context)))
print count
open('../resource/words')
print(len(file_get()))

60
python/43.py
View File

@ -1,31 +1,45 @@
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)
import time
time.clock()
def check_3(result, num, num_set):
for p in num_set:
if 0 == int(p + num[:2]) % 3:
last_num = ''.join(list(num_set - set(p)))
result.append(int(last_num + p + num))
result.append(int(last_num[::-1] + p + num))
def check_5(result, num, num_set):
for p in num_set:
if 0 == int(p) % 2:
check_3(result, p + num, num_set - set(p))
def check_7(result, num, num_set):
for p in num_set:
if 0 == int(p + num[:2]) % 7:
check_5(result, p + num, num_set - set(p))
a = [0,1,2,3,4,6,7,8,9]
tt = []
picksort(len(a), a, tt)
def check_11(result, num, num_set):
for p in '05':
if 0 == int(p + num[:2]) % 11:
check_7(result, p + num, num_set - set(p))
def check_13(result, num, num_set):
for p in num_set:
if '0' == p or '5' == p:
continue
if 0 == int(p + num[:2]) % 13:
check_11(result, p + num, num_set - set(p))
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
def check_17():
result = []
for n in range(136, 1000, 17):
num = str(n)
if '0' in num or '5' in num:
continue
if len(num) == len(set(num)):
check_13(result, num, set('1234567890') - set(num))
return result
print total
print(sum(check_17()))
print(time.clock())

13
python/44.py
View File

@ -7,15 +7,14 @@ def test(x):
return False
return True
def main():
max = 3000
for n in xrange(4, max):
for m in xrange(n + 1, max):
def main(limit):
for d in xrange(1, limit):
for n in xrange(5, limit):
m = n + d
a = 3 * (m * m + n * n) - m - n
b = (m - n) * (3 * (m + n) - 1)
b = d * (3 * (m + n) - 1)
if test(a) and test(b):
print a / 2, b / 2, m, n
return
main()
main(1300)

2
python/45.py
View File

@ -5,4 +5,4 @@ while 1:
if five == n * (n + 1) and n % 2 == 1:
break
m += 1
print m * (3 * m - 1) / 2
print m, (n + 1) / 2, m * (3 * m - 1) / 2

44
python/46.py
View File

@ -1,31 +1,21 @@
from math import sqrt, log10
def isp(x):
if x == 2:
return True
if x <= 1 or x & 1 == 0:
from tools import number_theory
import time
time.clock()
def match(x, prime):
for base in range(1, int(((x - 3) // 2) ** 0.5) + 1):
if x - 2 * base * base in prime:
return True
return False
for i in xrange(3, int(sqrt(x)) + 1, 2):
if x % i == 0:
return False
return True
def search(limit):
prime = list(number_theory.make_prime(limit))
for x in range(21, limit, 2):
if x in prime:
continue
if not match(x, prime):
return x
def test(x):
sqr = int(sqrt((x - 1) / 2))
for i in xrange(1, sqr + 1):
tt = x - 2 * i * i
if isp(tt):
return True
return False
n = 9
while 1:
if not isp(n):
if not test(n):
print n
break
n += 2
#kkkk = input('end')
print(search(10000))
print(time.clock())

69
python/47.py
View File

@ -1,37 +1,40 @@
def factor(x):
out = []
if x % 2 == 0:
out.append(2)
while x % 2 == 0:
x /= 2
i = 3
while 1:
if x % i == 0:
out.append(i)
while x % i == 0:
x /= i
i += 2
if i ** 2 > x:
out.append(x)
break
while out.count(1):
out.remove(1)
return out
from tools import number_theory
def main(same):
n = 6
num = 0
while num != same:
if len(factor(n)) == same:
num += 1
else:
num = 0
n += 1
return n
def num_factor(num):
factor = []
if not num % 2:
factor.append(2)
while not num % 2:
num //= 2
p = 3
while p * p < num:
if not num % p:
factor.append(p)
while not num % p:
num //= p
p += 2
if 1 < num:
factor.append(num)
return factor
def find(count, a, b):
seq = 0
a += 1
while b + seq >= count + a:
if len(num_factor(a)) == count:
seq += 1
else:
seq = 0
if seq == count:
return a - count + 1
a += 1
maxx = 4
a = main(maxx)
for i in xrange(1, maxx + 1):
print a - i, factor(a - i)
def search(count, limit):
prime = list(number_theory.make_prime(limit))
for i in range(len(prime) - 1):
get = find(count, prime[i], prime[i + 1])
if get:
return get
print(search(4, 200000))

7
python/48.py
View File

@ -1,6 +1,3 @@
total = 0
for i in xrange(1, 1001):
total += i ** i
print total % (10 ** 10)
from functools import reduce
print(str(reduce(lambda x, y: x + y ** y, range(1, 1001), 0))[-10:])

6
python/49.py
View File

@ -10,7 +10,7 @@ def pick(x, lis, out, a = 0):
out.append([a, lis])
return
a *= 10
for i in xrange(len(lis)):
for i in range(len(lis)):
tmp = lis[:]
tmpa = a + lis[i]
tmp.pop(i)
@ -21,7 +21,7 @@ def isp(x):
return True
if x <= 1 or x & 1 == 0:
return False
for i in xrange(3, int(x ** 0.5) + 1, 2):
for i in range(3, int(x ** 0.5) + 1, 2):
if x % i == 0:
return False
return True
@ -45,4 +45,4 @@ def main():
return str(n) + str(ii) + str(jj) #(n, ii, jj)
n += 1
print main()
print(main())

38
python/5.py
View File

@ -1,36 +1,8 @@
# coding=utf-8
''' 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? '''
from time import time
from functools import reduce
from tools import number_theory
gcd = lambda x, y: (y == 0) and x or gcd(y, x % y)
def multu_lcm(l):
return reduce(number_theory.lcm, l)
def p1(maxx = 20):
maxx += 1
num = []
for i in range(maxx): num.append(i)
for i in range(2, maxx):
if num[i] > 1:
for j in range(i + 1, maxx):
if num[j] % num[i] == 0: num[j] /= num[i]
total = 1
for i in num[1 : maxx]: total *= num[i]
#print num
print total
def p2(maxx = 20):
n = 2
for i in xrange(3, maxx + 1):
if n % i != 0:
n = n * i / gcd(n, i)
return n
#p1(20)
print p2(50000)
print(multu_lcm(list(range(1, 21))))

73
python/50.py
View File

@ -1,34 +1,49 @@
# coding=utf8
prime = []
total = 0
n = 2
from tools import number_theory
def factor(x):
x = int(x)
if x <= 1: return 0
else:
for i in xrange(2, int(x ** 0.5) + 1):
if x % i == 0: break
else: return x
return i
def is_prime(num):
if not num % 2:
return False
for p in range(3, int(num ** 0.5) + 1, 2):
if not num % p:
return False
return True
while total <= 1000000:
if factor(n) == n:
total += n
prime.append(n)
n += 1
def longest_slice(limit, prime):
for l in range(len(prime)):
if sum(prime[:l]) > limit:
return (l - 1, sum(prime[:l - 1]))
def search():
for length in xrange(len(prime) - 1, 2, -1):
for start in xrange(0, len(prime) - length + 1):
sump = 0
for tmp in prime[start: start + length]:
sump += tmp
if factor(sump) == sump:
print sump
print prime[start: start + length]
return 0
def reduce_slice(limit, prime, start, length, tale):
tale -= prime[start]
start += 1
t = tale
while True:
t = tale - prime[start] + prime[start + length]
if t > limit:
break
tale = t
return (start, tale)
if __name__ == '__main__':
search()
def shift_slice(limit, prime, start, length, tale):
for s in range(start - 1, -1, -1):
tale = tale + prime[s] - prime[s + length]
if is_prime(tale):
return (tale, length)
def search(limit):
prime = list(number_theory.make_prime(4000))
length, tale = longest_slice(limit, prime)
if is_prime(tale):
return (tale, length)
start = 0
while length > 1:
length -= 1
start, tale = reduce_slice(limit, prime, start, length, tale)
if is_prime(tale):
return (tale, length)
get = shift_slice(limit, prime, start, length, tale)
if get:
return get
print(search(1000000))

13
python/51.py
View File

@ -1,3 +1,4 @@
'''
from string import maketrans, translate
def numbreak(x):
@ -9,7 +10,7 @@ def numbreak(x):
def numloop(x, a, lis):
out = []
for i in xrange(10 - a):
for i in range(10 - a):
tt = maketrans(str(a), str(i + a))
tmp = int(translate(str(x), tt))
if isp(tmp, lis):
@ -45,13 +46,19 @@ def main():
xx = 56003
while 1:
ss = numbreak(xx)
for syn in xrange(3):
for syn in range(3):
if syn in ss:
tmp = numloop(xx, syn, prime)
if len(tmp) >= 8:
print xx, tmp
print(xx, tmp)
return
xx += 2
while not isp(xx, prime): xx += 2
main()
'''
from tools import number_theory
prime = list(number_theory.make_prime(1000))
print(prime)

33
python/52.py
View File

@ -1,24 +1,15 @@
def divnum(x):
out = []
while x > 0:
out.append(x % 10)
x /= 10
return out
def multi_same(num, multi):
s = set(str(num))
for m in range(multi, 1, -1):
if set(str(num * m)) != s:
return False
return True
def testnum(x, n):
a = divnum(x)
for i in xrange(2, n + 1):
b = divnum(x * i)
if set(a) != set(b):
return False
return True
def search(multi):
num = 124847
while not multi_same(num, multi):
num += 1
return num
n = 1
while n < 1000000:
if testnum(n, 6):
break
n += 1
for i in xrange(1, 7):
print n * i
print(search(6))

34
python/53.py
View File

@ -1,26 +1,14 @@
def C(x, y):
if x * 2 > y:
return C(y - x, y)
out = 1
for i in xrange(y, y - x, -1):
out *= i
for i in xrange(1, x + 1):
out /= i
return out
total = []
for i in xrange(1, 101):
j = 0
tmp = 0
for j in xrange(i + 1):
tmp = C(j, i)
if tmp < 1000000:
total.append((j, i, tmp))
else:
break
if 2 * j < i:
for j in xrange(j - 1, -1, -1):
total.append((i - j, i))
import time
time.clock()
def search(limit, count):
l = [1, 1]
tale = 0
while len(l) < count + 2:
tale += len(list(filter(lambda x: x > limit - 1, l)))
l = list(map(lambda x: x[0] + x[1], zip(l + [0], [0] + l)))
return tale
print 103 * 50 - len(total)
print(search(1000000, 100))
print(time.clock())

6
python/54.py
View File

@ -16,7 +16,7 @@ def calc(x):
step = 1
dic = {4:[], 3:[], 2:[], 1:[]}
same = 1
for i in xrange(1, len(num)):
for i in range(1, len(num)):
diff = num[i] - num[i - 1]
if diff == 0:
same += 1
@ -48,7 +48,7 @@ def calc(x):
return (flag, 0, dic.get(1))
def main():
ff = open('poker.txt', 'r')
ff = open('../resource/poker.txt', 'r')
out = 0
for line in ff.readlines():
strlis = line.split(' ')
@ -58,4 +58,4 @@ def main():
return out
#print calc(['7C','4C','4C','4C','7C'])
print main()
print(main())

69
python/55.py
View File

@ -1,39 +1,34 @@
def revnum(x):
out = 0
while x != 0:
out *= 10
out += x % 10
x /= 10
return out
def isL(x_ori):
x = x_ori
x += revnum(x)
n = 0
while n < 50:
x_ = revnum(x)
if x_ == x:
return False
x += x_
n += 1
return True
def test(x):
n = 0
while n < 50:
print x
x_ = revnum(x)
if x == x_: break
x += x_
n += 1
import time
a0 = time.clock()
be = []
for i in xrange(1, 10001):
if isL(i):
be.append(i)
a1 = time.clock()
print be
print a1 - a0
time.clock()
def is_sync(num):
s = str(num)
return s == s[::-1]
def is_lic(num, lic_set, non_set):
step = set([num])
for i in range(50):
num = num + int(str(num)[::-1])
step.add(num)
if num in lic_set:
return (True, step)
if num in non_set:
return (False, step)
if is_sync(num):
return (False, step)
return (True, step)
def search(limit):
lic_set = set()
non_set = set()
for x in range(1, limit + 1):
judge, step = is_lic(x, lic_set, non_set)
if judge:
lic_set |= set(filter(lambda x: x <= limit, step))
else:
non_set |= set(filter(lambda x: x <= limit, step))
return lic_set
print(len(search(10000)))
print(time.clock())

24
python/56.py
View File

@ -1,15 +1,13 @@
def numsum(x):
out = 0
while x > 0:
out += x % 10
x /= 10
return out
def search(limit):
maxi = [0, 0, 0]
for x in range(1, limit + 1):
num = 1
for y in range(limit):
num *= x
s = sum(map(lambda x: int(x), str(num)))
if s > maxi[0]:
maxi = [s, x, y + 1]
return maxi
mmax = [0, 0, 0]
for i in xrange(1, 101):
for j in xrange(1, 101):
tmp = numsum(i ** j)
if tmp > mmax[0]:
mmax = [tmp, i, j]
print mmax
print(search(100))

18
python/57.py
View File

@ -1,10 +1,8 @@
from math import log10
sq2 = [(1, 1)]
count = 0
for i in xrange(1, 1001):
last = sq2[len(sq2) - 1]
if int(log10(last[0])) > int(log10(last[1])):
print last
count += 1
sq2.append((last[0] + 2 * last[1], last[0] + last[1]))
print count
def iter_sqrt(limit):
a, b = 2, 1
for i in range(limit):
a, b = b + 2 * a, a
yield a - b, b
print(len(list(filter(lambda x: len(str(x[0])) > len(str(x[1])), iter_sqrt(1000)))))

40
python/58.py
View File

@ -1,28 +1,20 @@
laymax = lambda x: (2 * x + 1) ** 2
def isp(x):
if x == 2:
def is_prime(x):
for p in range(3, int(x ** 0.5) + 1, 2):
if x % p == 0:
return False
return True
if x <= 1 or x & 1 == 0:
return False
for i in xrange(3, int(x ** 0.5) + 1, 2):
if x % i == 0:
return False
return True
be = 3
non = 2
def search(percent):
n = 7
prime = 8
total = 13
while prime / total > percent:
n += 2
total += 4
for num in range((n - 3) * n + 3, n * n - 1, n - 1):
if is_prime(num):
prime += 1
return n
i = 2
while 9 * be >= non:
tmp = laymax(i)
for j in xrange(4):
#print float(be) / (be + non)
if isp(tmp):
be += 1
else:
non += 1
tmp -= 2 * i
i += 1
print 2 * i - 1
print(search(0.1))

28
python/6.py
View File

@ -1,16 +1,14 @@
# coding=utf-8
''' 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. '''
total = 0
num = []
for i in range(100): num.append(i + 1)
for i in range(100):
for j in range(i + 1, 100):
total += num[i] * num[j]
total *= 2
print total
from functools import reduce
def product(p, q):
multi = 0
while True:
q.pop(0)
if not q:
break
multi += reduce(lambda x, y: x + y[0] * y[1], zip(p, q), 0)
return multi
limit = 10000 + 1
print(2 * product(list(range(1, limit)), list(range(1, limit))))

42
python/68.py Normal file
View File

@ -0,0 +1,42 @@
m = 0
def eq(l):
if l[0] + l[1] - l[2] - l[5]:
return False
if l[2] + l[3] - l[4] - l[7]:
return False
if l[4] + l[5] - l[6] - l[9]:
return False
if l[6] + l[7] - l[8] - l[1]:
return False
return True
def ext(l):
o = l[1::2]
e = l[::2]
while e[0] != min(e):
o = o[1:] + o[0:1]
e = e[1:] + e[0:1]
o = list(map(lambda x: str(x), o))
e = list(map(lambda x: str(x), e))
s = o[1:] + o[0:1]
return ''.join([''.join(x) for x in zip(e, o, s)])
def num(l):
bn = ext(l)
if len(bn) != 16:
return 0
return int(bn)
def mksq(sq, pl):
if not pl:
if eq(sq):
n = num(sq)
global m
if n > m:
m = n
print(m)
for it in pl:
mksq(sq + [it], list(filter(lambda x: x != it, pl)))
mksq([], list(range(1, 11)))

29
python/7.py
View File

@ -1,23 +1,14 @@
# coding=utf-8
''' 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 10 001st prime number? '''
import math
from tools import number_theory
def countp(count):
if count == 1: return 2
prime = [2]
x = 1
while 1:
for i in xrange(x ** 2 + (x + 1) % 2, (x + 1) ** 2, 2):
for p in prime:
if i % p == 0: break
else: count -= 1
if count == 0: return i
x += 1
for p in prime:
if x % p == 0: break
else: prime.append(x)
def mkp(count):
limit = int(count / math.log(count))
limit = count * count // limit * 11 // 10
while True:
prime = list(number_theory.make_prime(limit))
if count < len(prime):
return prime[count - 1]
limit = limit * 11 // 10
if __name__ == '__main__':
print countp(10001)
print(mkp(10001))

25
python/71.py
View File

@ -1,15 +1,16 @@
f = lambda x: 3 * x / 7
gcd = lambda x, y: (y == 0) and x or gcd(y, x % y)
maxx = [1] * 3
def gcd(a, b):
return 0 == b and a or gcd(b, a % b)
for i in xrange(1, 1000001):
if i % 7 == 0:
continue
tmpi = f(i)
if gcd(i, tmpi) == 1:
tmp = 3.0 / 7 - float(tmpi) / i
if tmp < maxx[0]:
maxx = [tmp, tmpi, i]
def t(limit, a, b):
l = []
for m in range(limit + 1, 1, -1):
n, d = divmod(m * a, b)
if gcd(n, m) == 1:
l.append((d / m, n, m))
if 1 == d:
break
for x in sorted(l, key=lambda x: x[0]):
return x[1:]
print maxx
print(t(1000000, 3, 7))

25
python/8.py
View File

@ -1,19 +1,12 @@
# coding=utf-8
''' Discover the largest product of five consecutive digits in the 1000-digit number. '''
def va(string):
x = 1
for i in range(len(string)):
x *= ord(string[i]) - ord('0')
return x
from functools import reduce
ch = '731671765313306249192251196744265747423553491949349698352031277450632623957831801698480186947885184385861560789112949495459501737958331952853208805511125406987471585238630507156932909632952274430435576689664895044524452316173185640309871112172238311362229893423380308135336276614282806444486645238749303589072962904915604407723907138105158593079608667017242712188399879790879227492190169972088809377665727333001053367881220235421809751254540594752243258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450'
max = [0, 0, '']
for i in range(len(ch) - 5):
temp = va(ch[i : i + 5])
if temp > max[1]:
max[0] = i
max[1] = temp
max[2] = ch[i : i + 5]
def seek(maxi, length, context):
if length > len(context):
return maxi
multi = reduce(lambda x, y: x * int(y), context[:length], 1)
return seek(max(maxi, multi), length, context[1:])
print max
print(seek(0, 13,
'731671765313306249192251196744265747423553491949349698352031277450632623957831801698480186947885184385861560789112949495459501737958331952853208805511125406987471585238630507156932909632952274430435576689664895044524452316173185640309871112172238311362229893423380308135336276614282806444486645238749303589072962904915604407723907138105158593079608667017242712188399879790879227492190169972088809377665727333001053367881220235421809751254540594752243258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450'
))

50
python/80.py
View File

@ -1,37 +1,25 @@
from math import sqrt, log10
def fiter(a, finit, fcntn, ftrns):
x = finit(a)
while fcntn(a, x):
x = ftrns(a, x)
return x
def newton(a, n = 2):
x = 0
x_ = int(sqrt(a))
if x_ ** n == a:
return x_
while abs(x - x_) > 1:
x = x_
tmp = x ** (n - 1)
x_ = x - (tmp * x - a) / tmp / n
x_ = int(x_)
while x ** n > a:
x -= 1
return x
def newton_root(a):
return fiter(a,
lambda x: x // 2,
lambda p, x: not (0 < p - x ** 2 < 2 * x + 1),
lambda p, x: (x + p // x) // 2)
def numsum(x):
total = 0
while x != 0:
total += x % 10
x /= 10
return total
def main(maxx):
ss = 0
for i in xrange(maxx + 1):
if int(sqrt(i)) ** 2 == i:
continue
tmp = newton(i * 100 ** 99)
ss += numsum(tmp)
print ss
def all_root(limit, digit):
root_sum = []
digit -= 1
for x in range(2, limit + 1):
if int(x ** 0.5) ** 2 != x:
root_sum.append(sum(map(lambda x: int(x), str(newton_root(100 ** digit * x)))))
return root_sum
print(sum(all_root(100, 100)))

74
python/81.py
View File

@ -1,43 +1,39 @@
a = []
ff = open('matrix.txt.', 'r')
for i in ff.readlines():
tmp = i.split(',')
for j in xrange(len(tmp)):
tmp[j] = int(tmp[j])
a.append(tmp)
ff.close()
path = [[a[0][0], [a[0][0]]]]
n = len(a)
m = [
[131, 673, 234, 103, 18],
[201, 96, 342, 965, 150],
[630, 803, 746, 422, 111],
[537, 699, 497, 121, 956],
[805, 732, 524, 37, 331]
]
for k in xrange(1, n):
pathtmp = []
tmp = [a[k][0] + path[0][0], path[0][1][:]]
tmp[1].append(a[k][0])
pathtmp.append(tmp)
for i in xrange(1, k):
if path[i - 1][0] < path[i][0]:
flag = i - 1
else:
flag = i
tmp = [path[flag][0] + a[k - i][i], path[flag][1][:]]
tmp[1].append(a[k - i][i])
pathtmp.append(tmp)
tmp = [a[0][k] + path[k - 1][0], path[k - 1][1][:]]
tmp[1].append(a[0][k])
pathtmp.append(tmp)
path = pathtmp
def getm(file):
matrix = []
for line in open(file, 'r'):
matrix.append(list(map(lambda x: int(x), line.split(','))))
return matrix
for k in xrange(n, 2 * n - 1):
pathtmp = []
for i in xrange(2 * n - 1 - k):
if path[i][0] < path[i + 1][0]:
flag = i
else:
flag = i + 1
tmp = [path[flag][0] + a[n - 1 - i][k + i + 1 - n], path[flag][1][:]]
tmp[1].append(a[n - 1 - i][k + i + 1 - n])
pathtmp.append(tmp)
path = pathtmp
def calc_short(short, nl):
for i in range(len(nl)):
nl[i] += min(short[i], short[i + 1])
return nl
print path
def short_lu(matrix):
short = [0]
for x in range(len(matrix)):
nl = []
for i in range(x + 1):
nl.append(matrix[x - i][i])
short = calc_short(short[:1] + short + short[-1:], nl)
return short
def short_rd(matrix, short):
for x in range(len(matrix), (len(matrix) - 1) * 2 + 1):
nl = []
for i in range(x - len(matrix) + 1, len(matrix)):
nl.append(matrix[x - i][i])
short = calc_short(short, nl)
return short[0]
m = getm('../resource/matrix.txt')
print(short_rd(m, short_lu(m)))

123
python/82.py
View File

@ -1,88 +1,45 @@
a = []
ff = open('../matrix.txt', 'r')
for i in ff.readlines():
tmp = i.split(',')
for j in xrange(len(tmp)):
tmp[j] = int(tmp[j])
a.append(tmp)
ff.close()
n = len(a)
m = [
[131, 673, 234, 103, 18],
[201, 96, 342, 965, 150],
[630, 803, 746, 422, 111],
[537, 699, 497, 121, 956],
[805, 732, 524, 37, 331]
]
path = []
for i in xrange(n):
path.append([a[i][-1] + a[i][-2], []])
def getm(file):
matrix = []
for line in open(file, 'r'):
matrix.append(list(map(lambda x: int(x), line.split(','))))
return matrix
for j in xrange(n - 3, -1, -1):
#newpath = [a[0][j] + min(path[0][0], a[1][j] + path[1][0])]
if path[0][0] <= a[1][j] + path[1][0]:
tmp = path[0][1] + [(0, j)]
newpath.append([path[0][0] + a[0][j], tmp])
else:
tmp = path[1][1] + [(1, j), (0, j)]
newpath.append([path[1][0] + a[1][j] + a[0][j], tmp])
for i in xrange(1, n - 1):
better = min(a[i - 1][j] + path[i - 1][0], path[i][0], a[i + 1][j] + path[i + 1][0])
#newpath.append(a[i][j] + better)
if better == path[i][0]:
tmp = path[i][1] + [(i, j)]
newpath.append([path[i][0] + a[i][j], tmp])
elif better == a[i - 1][j] + path[i - 1][0]:
tmp = path[i - 1][1] + [(i - 1, j), (i, j)]
newpath.append([])
#newpath.append(a[-1][j] + min(path[-1], a[-2][j] + path[-2]))
if path[-1][0] <= a[-2][j] + path[-2][0]:
tmp = path[-1][1] + [(n - 1, j)]
newpath.append([a[-1][j] + path[-1][0], tmp])
else:
tmp = path[-1][1] + [(n - 2, j), (n - 1, j)]
newpath.append([a[-1][j] + a[-2][j] + path[-2][0], tmp])
path = newpath
def rev(matrix):
n = []
scale = len(matrix)
for j in range(scale):
line = []
for i in range(scale):
line.append(matrix[i][j])
n.append(line)
return n
def trace(matrix):
short = matrix.pop(0)
for line in matrix:
ns = []
for i in range(len(line)):
vs = 0
vl = [short[i]]
for k in range(i - 1, -1, -1):
vs += line[k]
vl.append(vs + short[k])
vs = 0
for k in range(i + 1, len(line)):
vs += line[k]
vl.append(vs + short[k])
ns.append(min(vl) + line[i])
short = ns
return short
print sorted(path)
'''
path = []
for i in xrange(n):
path.append([a[i][0], [[i, 0]]])
for y in xrange(1, n):
pathtmp = []
for x in xrange(n):
tmp = [[0, 0]]
#papapa = 0
if x - 1 >= 0:
if a[x - 1][y] < a[x][y - 1]:
tmp.append([a[x - 1][y], -1, [x - 1, y]])
path[x] =
else:
if not [x, y - 1] in path[x - 1][1]:
tmp.append([a[x][y - 1], -1, [x, y - 1]])
#else:
#papapa += 1
if x + 1 < n:
if a[x + 1][y] < a[x][y - 1]:
tmp.append([a[x + 1][y], 1, [x + 1, y]])
else:
if not [x, y - 1] in path[x + 1][1]:
tmp.append([a[x][y - 1], 1, [x, y - 1]])
#else:
#papapa += 2
for item in tmp:
item[0] += path[x + item[1]][0]
tmp.sort()
#if papapa != 0:
#print papapa, "**", tmp
if len(tmp[0]) > 2:
last = [tmp[0][-1], [x, y]]
else:
last = [[x, y]]
pathtmp.append([tmp[0][0] + a[x][y], path[x + tmp[0][1]][1] + last])
path = pathtmp
path.sort()
print path[0]
'''
#print(min(trace(rev(m))))
print(min(trace(rev(getm('../resource/matrix.txt')))))

47
python/85.py
View File

@ -1,24 +1,31 @@
def sum(m, n):
return m * n * (m + 1) * (n + 1) / 4
maxx = 2000000
x = int((8 * maxx + 1) ** 0.5 / 2)
while sum(x, 1) < maxx: x += 1
def gen_tri(limit):
tale = 1
base = 1
while tale < limit:
yield (base, tale)
base += 1
tale += base
orisub = abs(sum(x, 1) - maxx)
near = [orisub]
y = 1
def tri_pair(num):
seq = int(((8 * num - 1) ** 0.5 - 1) / 2)
return ((seq , (seq + 1) * seq // 2),
(seq + 1, (seq + 1) * (seq + 2) // 2))
while x > y:
tmp = maxx
y_lst = y
while tmp > maxx - orisub and y > 0:
tmp = sum(x, y)
if abs(tmp - maxx) < near[0]:
near = [abs(tmp - maxx), x, y]
y -= 1
x -= 1
y = y_lst
while sum(x, y) < maxx: y += 1
def renew(result, limit, t_n, t_o):
cmpr = t_n[1] * t_o[1]
new_result = [max(limit, cmpr) - min(limit, cmpr), t_n[0] * t_o[0]]
if new_result[0] < result[0]:
return new_result
else:
return result
print near[1] * near[2]
def search(limit):
result = [limit, 0]
for t_n in gen_tri(int(limit ** 0.5) + 1):
t_l, t_r = tri_pair(limit // t_n[1])
result = renew(result, limit, t_n, t_l)
result = renew(result, limit, t_n, t_r)
return result[1]
print(search(2000000))

51
python/86.py
View File

@ -1,31 +1,28 @@
def test_ori(a, b):
tmp = a ** 2 + b ** 2
sqr = int(tmp ** 0.5)
if tmp == sqr ** 2: return True
return False
def test(a, b, c):
if test_ori(b + c, a): return 1
return 0
import time
def test1(a, b):
if test_ori(b + b, a): return 1
return 0
def is_sqrt(x, y):
z = x ** 2 + y ** 2
if int(z ** 0.5) ** 2 == z:
if x > y:
return x // 2 - x + y + 1
else:
return x // 2
return 0
total = 1975
n = 100
while 1:
tmp = 0
for i in xrange(2, 2 * n + 1):
if test_ori(n, i):
#print i
tmp += i / 2
if i > n:
tmp -= i - n - 1
total += tmp
if total > 1000000:
break
#print n, tmp, total
n += 1
def count(m):
count = 0
for a in range(1, m * 2 + 1):
count += is_sqrt(a, m)
return count
print n
def gen(limit):
m = 1
tale = 0
while tale < limit:
tale += count(m)
m += 1
return m - 1, tale
print(gen(1000000))
print(time.process_time())

62
python/88.py
View File

@ -1,16 +1,50 @@
def log2(x):
out = 0
while x > 0:
x /= 2
out += 1
return out - 1
def break(x):
x -= 1
n = int(x ** 0.5)
while x % n != 0:
n -= 1
return (n, x / n)
from functools import reduce
def A(k):
dd
class Num:
n = 0
l = []
over = False
def __init__(self, limit):
if limit < 2:
self.over = True
self.num = limit
self.l = [1] * limit
self.l[:2] = [2, 2]
def multi(self):
return reduce(lambda x, y: x * y, self.l, 1)
def add(self):
return sum(self.l)
def is_overload(self):
return self.multi() > self.add()
def inc(self):
if self.over:
return
if not self.is_overload():
self.l[0] += 1
else:
for i in range(len(self.l)):
if self.l[i + 1] < self.l[i]:
self.l[i + 1] += 1
self.l[:i] = [self.l[i + 1]] * (i + 1)
if self.is_overload():
self.over = True
def eq(self):
return self.multi() == self.add()
def get_min(self):
while not self.eq():
self.inc()
if self.over:
return NULL
return self.add()
for x in range(3, 20):
f = Num(x)
print(x, f.get_min())

13
python/9.py
View File

@ -1,8 +1,7 @@
# coding=utf-8
''' 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. '''
import math
from math import sqrt
for x in range(int(5 * sqrt(10)) + 1, int(5 * sqrt(20)) + 1):
if not (500 % x):
y = 500 // x - x
print(2 * x * y * (x ** 4 - y ** 4))

47
python/tools/number_theory.py Normal file
View File

@ -0,0 +1,47 @@
def gcd(x, y):
if 0 == y:
return x
else:
return gcd(y, x % y)
def lcm(x, y):
return x * y // gcd(x, y)
def make_prime(limit):
if limit < 5:
if limit < 2: return
yield 2
if limit < 3: return
yield 3
return
n = (limit + 1) // 6
a = [True] * n
b = [True] * n
for i in range((int(limit ** 0.5) + 1) // 6 + 1):
if a[i]:
p = 6 * i + 7
f = 7 * i + 7
g = 5 * i + 5
a[f::p] = [False] * ((n - f - 1) // p + 1)
b[g::p] = [False] * ((n - g - 1) // p + 1)
if b[i]:
p = 6 * i + 5
f = 5 * i + 3
g = 7 * i + 5
a[f::p] = [False] * ((n - f - 1) // p + 1)
b[g::p] = [False] * ((n - g - 1) // p + 1)
yield 2
yield 3
for i in range(n):
if b[i]:
yield 6 * i + 5
if a[i]:
yield 6 * i + 7