Project Euler

12>求數列,形式爲

 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

即每列的最後數字爲1+2+...,其他的數字爲其因子

要求第一個有超過100個因子的數

import math def getNumber(index): return sum(range(1,index+1)) def getFactors(number): begin=1 result=[] while begin<=math.sqrt(number): if number%begin==0: result.append(begin) result.append(number/begin) begin+=1 return result lastIndex=2 while 1: number=getNumber(lastIndex) factors=getFactors(number) l_factors=len(factors) if l_factors>499: print lastIndex,factors,l_factors break print lastIndex,l_factors lastIndex+=1

14>按照如下方式操作數字,例如

n->n/2    當n爲偶數時

n->3n+1 當n爲奇數時

對13而言,其對應的數列爲13 40 20 10 5 16 8 4 2 1

其長度爲10.

求出1000000以下的數字中哪個數字產生的數列長度最長.

def getNextNumber(number): if number%2==0: return number/2 else: return number*3+1 def getArray(number): result=[] while 1: result.append(number) number=getNextNumber(number) if number==1: result.append(number) break return result lastNumber=2 maxLength=(lastNumber,0) while lastNumber<1000000: array=getArray(lastNumber) if len(array)>maxLength[1]: maxLength=(lastNumber,len(array)) lastNumber+=1 print lastNumber,maxLength