Problem 57 - Project Euler

30分プログラム、その335。Problem 57 - Project Euler。
昨日(id:mzp:20080706:euler)の修正版。冷静に見直すと動的計画法がうまくできてなかった。それを直したら、再帰に関する例外も消えたし、速くもなった。

使い方

$ python problem57.py
...
951
956
964
972
977
985
990
998
answer: 153

ソースコード

#! /usr/bin/python
# -*- mode:python; coding:utf-8 -*-
#
# problem57.py -
#
# Copyright(C) 2008 by mzp
# Author: MIZUNO Hiroki / mzpppp at gmail dot com
# http://howdyworld.org
#
# Timestamp: 2008/07/06 22:51:36
#
# This program is free software; you can redistribute it and/or
# modify it under MIT Lincence.
#
from math import log10 

def gcd(n,m):
    if m == 0:
        return n
    else:
        return gcd(m,n % m)

class Ratio():
    def __init__(self,num,denom=1):
        n = gcd(num,denom)
        self.num = num/n
        self.denom = denom/n

    def __add__(self,other):
        return Ratio(self.num*other.denom+other.num*self.denom,
                        self.denom * other.denom)

    def __div__(self,other):
        return Ratio(self.num*other.denom,
                     self.denom*other.num)

    def __repr__(self):
        return "%s/%s" % (self.num,self.denom)


memo = {}
def makeFrac(n):
    if not (n in memo):
        if n == 0:
            memo[0] = Ratio(0)
        else:
            memo[n] =  Ratio(1) / (Ratio(2,1)+makeFrac(n-1))
    return memo[n]

def makeNum(n):
    return Ratio(1)+makeFrac(n)

def isSatisfy(r):
    return int(log10(r.num)) > int(log10(r.denom))

count = 0
for n in xrange(0,1001):
    if isSatisfy(makeNum(n)):
        count += 1
        print n
print "answer:",count

参考

• 過去の30分プログラム
• Problem 57 - PukiWiki