update 89 93 94 97, add pow_mod
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python/89.py
66
python/89.py
@ -1,42 +1,40 @@
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dic = {'I':1, 'V':5, 'X':10, 'L':50, 'C':100, 'D':500, 'M':1000}
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rdic = {1:'I', 2:'II', 3:'III', 4:'IV', 5:'V', 6:'VI', 7:'VII', 8:'VIII', 9:'IX',
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10:'X', 20:'XX', 30:'XXX', 40:'XL', 50:'L', 60:'LX', 70:'LXX', 80:'LXXX',
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90:'XC', 100:'C', 200:'CC', 300:'CCC', 400:'CD', 500:'D', 600:'DC',
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700:'DCC', 800:'DCCC', 900:'CM', 1000:'M'}
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from functools import reduce
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def rtoi(ss):
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out = dic.get(ss[-1])
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for i in xrange(len(ss) - 1):
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if dic.get(ss[i]) < dic.get(ss[i + 1]):
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out -= dic.get(ss[i])
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dct_n2r = {0: '', 1:'I', 2:'II', 3:'III', 4:'IV', 5:'V', 6:'VI', 7:'VII', 8:'VIII', 9:'IX',
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10:'X', 20:'XX', 30:'XXX', 40:'XL', 50:'L', 60:'LX', 70:'LXX', 80:'LXXX', 90:'XC',
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100:'C', 200:'CC', 300:'CCC', 400:'CD', 500:'D', 600:'DC', 700:'DCC', 800:'DCCC', 900:'CM',
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1000:'M'}
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dct_r2n = {'I':1, 'V':5, 'X':10, 'L':50, 'C':100, 'D':500, 'M':1000}
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def r2n(r_num):
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last = 0
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tale = 0
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for digit in reversed(list(map(lambda x: dct_r2n[x], r_num))):
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if digit < last:
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tale -= digit
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else:
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out += dic.get(ss[i])
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return out
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tale += digit
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last = digit
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return tale
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def itor(num):
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out = ''
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thousand = num - num % 1000
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if num > 0:
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out += rdic.get(1000) * (thousand / 1000)
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def n2r(num):
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tale = dct_n2r[1000] * (num // 1000)
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num %= 1000
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hundred = num - num % 100
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if hundred > 0:
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out += rdic.get(hundred)
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tale += dct_n2r[num - num % 100]
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num %= 100
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teen = num - num % 10
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if teen > 0:
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out += rdic.get(teen)
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tale += dct_n2r[num - num % 10]
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num %= 10
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if num > 0:
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out += rdic.get(num)
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return out
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return tale + dct_n2r[num]
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ff = open('../roman.txt', 'r')
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lis = ff.readlines()
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ff.close()
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def get_file(fn):
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with open(fn, 'r') as f:
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return list(map(lambda x: x.strip(), f.readlines()))
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count = 0
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for i in lis:
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new = itor(rtoi(i.rstrip()))
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count += abs(len(new) - len(i.rstrip()))
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print count
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def item_len(lst):
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return reduce(lambda x, y: x + len(y), lst, 0)
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def trans(fn):
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lst = get_file(fn)
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return item_len(lst) - item_len(map(lambda x: n2r(r2n(x)), lst))
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print(trans('../resource/roman.txt'))
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60
python/93.py
60
python/93.py
@ -1,15 +1,9 @@
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def two(a, b):
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out = set([])
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out.add(a + b)
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out.add(a * b)
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'''if a != b:
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out.add(abs(a - b))'''
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out.add(a - b)
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out.add(b - a)
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out = set([a + b, a * b, a - b, b - a])
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if a != 0:
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out.add(b / float(a))
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out.add(b / a)
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if b != 0:
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out.add(a / float(b))
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out.add(a / b)
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return out
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def three(a, b, c):
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@ -23,38 +17,34 @@ def three(a, b, c):
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return out
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def four(a, b, c, d):
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first = two(a, b)
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second = two(c, d)
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pair = two(c, d)
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out = set([])
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for i in first:
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for i in two(a, b):
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out |= three(i, c, d)
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for j in second:
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for j in pair:
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out |= two(i, j)
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for j in second:
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for j in pair:
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out |= three(j, a, b)
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return out
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def calc(a, b, c, d):
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tmp = set([])
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tmp |= four(a, b, c, d)
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tmp |= four(a, c, b, d)
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tmp |= four(a, d, b, c)
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out = []
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for i in tmp:
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if i == int(i) > 0:
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out.append(int(i))
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return sorted(out)
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out = list(sorted(list(filter(lambda x: x == int(x) > 0,
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four(a, b, c, d) | four(a, c, b, d) | four(a, d, b, c)))))
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for i in range(len(out)):
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if i + 1 != out[i]:
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return out[:i]
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return out
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maxx = [0, 0]
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for m in xrange(1, 10):
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for n in xrange(m + 1, 10):
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for s in xrange(n + 1, 10):
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for t in xrange(s + 1, 10):
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tmp = calc(m, n, s, t)
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for i in xrange(len(tmp)):
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if i + 1 != tmp[i]:
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break
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if i > maxx[0]:
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maxx = [i, (m, n, s, t)]
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print maxx
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def search():
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maxi = [0, 0]
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for m in range(1, 10):
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for n in range(m + 1, 10):
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for s in range(n + 1, 10):
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for t in range(s + 1, 10):
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count = len(calc(m, n, s, t))
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if count > maxi[0]:
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maxi = [count, (m, n, s, t)]
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return maxi
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print(search())
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47
python/94.py
47
python/94.py
@ -1,31 +1,20 @@
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maxx = 1000000000
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mul = 3 ** 0.5
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n = 0
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C = 0
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total = 0
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while 1:
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n += 1
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m = int((mul + 2) * n)
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m += 1 - (m + n) % 2
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C = 2 * (m + n) ** 2
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if C > maxx: break
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if abs((m - n) ** 2 - 2 * m * n) == 1:
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print 4 * m * n, m ** 2 + n ** 2
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total += C
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def calc(limit):
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return sum(map(lambda x:
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sum(map(x[0], filter(x[1], map(x[2], range(1, x[3]))))),
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[
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(
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lambda x: 2 * sum(x) ** 2,
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lambda x: 2 * x[0] * x[1] + 1 == (x[0] - x[1]) ** 2,
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lambda x: (int((2 + 3 ** 0.5) * x) + 1, x),
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int((limit / (2 + 3 ** 0.5) / 12) ** 0.5)
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),
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(
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lambda x: 4 * x[0],
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lambda x: 3 * x[1] + 1 == x[0],
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lambda x: (int((3 ** 0.5) * x + 1) ** 2, x ** 2),
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int((limit / 12) ** 0.5)
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)
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]))
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n = 0
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C = 0
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while 1:
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n += 1
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m = int(mul * n)
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m += 1 - (m + n) % 2
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xx = m ** 2
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yy = n ** 2
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C = 4 * xx
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if C > maxx: break
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if abs(xx - 3 * yy) == 1:
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print 2 * (xx - yy), xx + yy
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total += C
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print total
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print(calc(1000000000))
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20
python/97.py
20
python/97.py
@ -1,19 +1,3 @@
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def powmod(x, y, z):
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ybi = []
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while y != 0:
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ybi.append(y % 2)
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y /= 2
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out = 1
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ybi.reverse()
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for i in ybi:
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out = out * out % z
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if i == 1:
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out = out * x % z
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return out
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from tools import number_theory
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a = powmod(2, 7830457, 100000000000)
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b = a * 28433 + 1
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b %= 10000000000
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print b
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print(str(number_theory.pow_mod(2, 7830457, 10000000000) * 28433 + 1)[-10:])
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@ -10,6 +10,15 @@ def lcm(x, y):
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return x * y // gcd(x, y)
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def pow_mod(base, exp, mod):
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result = 1
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for digit in bin(exp)[2:]:
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result = result ** 2 % mod
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if '1' == digit:
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result = result * base % mod
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return result
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def make_prime(limit):
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if limit < 5:
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if limit < 2: return
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