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update 89 93 94 97, add pow_mod

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xw_y_am@rmbp 2017-08-29 22:26:21 +08:00
parent d19ee31562
commit 5198fce5b7
5 changed files with 103 additions and 133 deletions
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68
python/89.py
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@ -1,42 +1,40 @@
dic = {'I':1, 'V':5, 'X':10, 'L':50, 'C':100, 'D':500, 'M':1000}
rdic = {1:'I', 2:'II', 3:'III', 4:'IV', 5:'V', 6:'VI', 7:'VII', 8:'VIII', 9:'IX',
10:'X', 20:'XX', 30:'XXX', 40:'XL', 50:'L', 60:'LX', 70:'LXX', 80:'LXXX',
90:'XC', 100:'C', 200:'CC', 300:'CCC', 400:'CD', 500:'D', 600:'DC',
700:'DCC', 800:'DCCC', 900:'CM', 1000:'M'}
from functools import reduce
def rtoi(ss):
out = dic.get(ss[-1])
for i in xrange(len(ss) - 1):
if dic.get(ss[i]) < dic.get(ss[i + 1]):
out -= dic.get(ss[i])
else:
out += dic.get(ss[i])
return out
dct_n2r = {0: '', 1:'I', 2:'II', 3:'III', 4:'IV', 5:'V', 6:'VI', 7:'VII', 8:'VIII', 9:'IX',
10:'X', 20:'XX', 30:'XXX', 40:'XL', 50:'L', 60:'LX', 70:'LXX', 80:'LXXX', 90:'XC',
100:'C', 200:'CC', 300:'CCC', 400:'CD', 500:'D', 600:'DC', 700:'DCC', 800:'DCCC', 900:'CM',
1000:'M'}
dct_r2n = {'I':1, 'V':5, 'X':10, 'L':50, 'C':100, 'D':500, 'M':1000}
def itor(num):
out = ''
thousand = num - num % 1000
if num > 0:
out += rdic.get(1000) * (thousand / 1000)
def r2n(r_num):
last = 0
tale = 0
for digit in reversed(list(map(lambda x: dct_r2n[x], r_num))):
if digit < last:
tale -= digit
else:
tale += digit
last = digit
return tale
def n2r(num):
tale = dct_n2r[1000] * (num // 1000)
num %= 1000
hundred = num - num % 100
if hundred > 0:
out += rdic.get(hundred)
tale += dct_n2r[num - num % 100]
num %= 100
teen = num - num % 10
if teen > 0:
out += rdic.get(teen)
tale += dct_n2r[num - num % 10]
num %= 10
if num > 0:
out += rdic.get(num)
return out
return tale + dct_n2r[num]
ff = open('../roman.txt', 'r')
lis = ff.readlines()
ff.close()
def get_file(fn):
with open(fn, 'r') as f:
return list(map(lambda x: x.strip(), f.readlines()))
count = 0
for i in lis:
new = itor(rtoi(i.rstrip()))
count += abs(len(new) - len(i.rstrip()))
print count
def item_len(lst):
return reduce(lambda x, y: x + len(y), lst, 0)
def trans(fn):
lst = get_file(fn)
return item_len(lst) - item_len(map(lambda x: n2r(r2n(x)), lst))
print(trans('../resource/roman.txt'))

92
python/93.py
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@ -1,60 +1,50 @@
def two(a, b):
out = set([])
out.add(a + b)
out.add(a * b)
'''if a != b:
out.add(abs(a - b))'''
out.add(a - b)
out.add(b - a)
if a != 0:
out.add(b / float(a))
if b != 0:
out.add(a / float(b))
return out
out = set([a + b, a * b, a - b, b - a])
if a != 0:
out.add(b / a)
if b != 0:
out.add(a / b)
return out
def three(a, b, c):
out = set([])
for i in two(a, b):
out |= two(i, c)
for i in two(a, c):
out |= two(i, b)
for i in two(b, c):
out |= two(i, a)
return out
out = set([])
for i in two(a, b):
out |= two(i, c)
for i in two(a, c):
out |= two(i, b)
for i in two(b, c):
out |= two(i, a)
return out
def four(a, b, c, d):
first = two(a, b)
second = two(c, d)
out = set([])
for i in first:
out |= three(i, c, d)
for j in second:
out |= two(i, j)
for j in second:
out |= three(j, a, b)
return out
pair = two(c, d)
out = set([])
for i in two(a, b):
out |= three(i, c, d)
for j in pair:
out |= two(i, j)
for j in pair:
out |= three(j, a, b)
return out
def calc(a, b, c, d):
tmp = set([])
tmp |= four(a, b, c, d)
tmp |= four(a, c, b, d)
tmp |= four(a, d, b, c)
out = []
for i in tmp:
if i == int(i) > 0:
out.append(int(i))
return sorted(out)
out = list(sorted(list(filter(lambda x: x == int(x) > 0,
four(a, b, c, d) | four(a, c, b, d) | four(a, d, b, c)))))
for i in range(len(out)):
if i + 1 != out[i]:
return out[:i]
return out
maxx = [0, 0]
for m in xrange(1, 10):
for n in xrange(m + 1, 10):
for s in xrange(n + 1, 10):
for t in xrange(s + 1, 10):
tmp = calc(m, n, s, t)
for i in xrange(len(tmp)):
if i + 1 != tmp[i]:
break
if i > maxx[0]:
maxx = [i, (m, n, s, t)]
print maxx
def search():
maxi = [0, 0]
for m in range(1, 10):
for n in range(m + 1, 10):
for s in range(n + 1, 10):
for t in range(s + 1, 10):
count = len(calc(m, n, s, t))
if count > maxi[0]:
maxi = [count, (m, n, s, t)]
return maxi
print(search())

47
python/94.py
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@ -1,31 +1,20 @@
maxx = 1000000000
mul = 3 ** 0.5
n = 0
C = 0
total = 0
while 1:
n += 1
m = int((mul + 2) * n)
m += 1 - (m + n) % 2
C = 2 * (m + n) ** 2
if C > maxx: break
if abs((m - n) ** 2 - 2 * m * n) == 1:
print 4 * m * n, m ** 2 + n ** 2
total += C
def calc(limit):
return sum(map(lambda x:
sum(map(x[0], filter(x[1], map(x[2], range(1, x[3]))))),
[
(
lambda x: 2 * sum(x) ** 2,
lambda x: 2 * x[0] * x[1] + 1 == (x[0] - x[1]) ** 2,
lambda x: (int((2 + 3 ** 0.5) * x) + 1, x),
int((limit / (2 + 3 ** 0.5) / 12) ** 0.5)
),
(
lambda x: 4 * x[0],
lambda x: 3 * x[1] + 1 == x[0],
lambda x: (int((3 ** 0.5) * x + 1) ** 2, x ** 2),
int((limit / 12) ** 0.5)
)
]))
n = 0
C = 0
while 1:
n += 1
m = int(mul * n)
m += 1 - (m + n) % 2
xx = m ** 2
yy = n ** 2
C = 4 * xx
if C > maxx: break
if abs(xx - 3 * yy) == 1:
print 2 * (xx - yy), xx + yy
total += C
print total
print(calc(1000000000))

20
python/97.py
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@ -1,19 +1,3 @@
def powmod(x, y, z):
ybi = []
while y != 0:
ybi.append(y % 2)
y /= 2
out = 1
ybi.reverse()
for i in ybi:
out = out * out % z
if i == 1:
out = out * x % z
return out
from tools import number_theory
a = powmod(2, 7830457, 100000000000)
b = a * 28433 + 1
b %= 10000000000
print b
print(str(number_theory.pow_mod(2, 7830457, 10000000000) * 28433 + 1)[-10:])

9
python/tools/number_theory.py
View File

@ -10,6 +10,15 @@ def lcm(x, y):
return x * y // gcd(x, y)
def pow_mod(base, exp, mod):
result = 1
for digit in bin(exp)[2:]:
result = result ** 2 % mod
if '1' == digit:
result = result * base % mod
return result
def make_prime(limit):
if limit < 5:
if limit < 2: return