No_43Sub-string divisibility

题目：

The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9 in some order, but it also has a rather interesting sub-string divisibility property.

Let d₁ be the 1^st digit, d₂ be the 2^nd digit, and so on. In this way, we note the following:

• d₂d₃d₄=406 is divisible by 2
• d₃d₄d₅=063 is divisible by 3
• d₄d₅d₆=635 is divisible by 5
• d₅d₆d₇=357 is divisible by 7
• d₆d₇d₈=572 is divisible by 11
• d₇d₈d₉=728 is divisible by 13
• d₈d₉d₁₀=289 is divisible by 17

Find the sum of all 0 to 9 pandigital numbers with this property.

代码为：

__author__ = 'Administrator'
import itertools,math,time
t=time.time()


soucestr='0123456789'
re_list=[]
totalsum=0
divlist=[2,3,5,7,11,13,17]
matched=0
for numstrlist in itertools.permutations(soucestr):
    numstr=''.join(numstrlist)
    matched=0
    for indexnum in xrange(7,0,-1):
        if not int(numstr[indexnum:indexnum+3])%divlist[indexnum-1]:
            matched+=1
        else:
            break
    if matched==7:
        totalsum+=int(numstr)
        #re_list.append(numstr)
"""
for numstr,templist in re_list:
    print numstr,templist
"""
#print sum([int(numstr) for numstr in re_list])
print time.time()-t

运行结果为：
16695334890
6.16100001335

不过运行结果太慢了，要6 秒钟。太长了。真的。
自己花了差不多一个小时改了下：

这种方法的思路是。把0-1000里能被2，3，5，7，11，14，17整除的数都列出来，然后组合出最终结果。
代码为：

import time
#coding=utf-8
starttime = time.time()
def getlist(sourcestr,numdict,index,divlist,outlist):
    if index==-1:
        print sourcestr
        if len(sourcestr)==9:
            outlist.append(sourcestr)
    else:
        notmatchedset=numdict[divlist[index]]
        if sourcestr:
            notmatchedset={numstr  for numstr in notmatchedset if numstr[0] not in sourcestr and  numstr[-2:]==sourcestr[0:2] }
        if not notmatchedset:
            return
        for numstr in notmatchedset:
            if index==len(divlist)-1:#如果第一次迭代
                getlist(numstr+sourcestr,numdict,index-1,divlist,outlist)

            else:
                getlist(numstr[0]+sourcestr,numdict,index-1,divlist,outlist)

divlist=[2,3,5,7,11,13,17]
soucedict=dict()
for num in divlist:
    soucedict.setdefault(num,set())
for num in range(0,1000):
    numstr='{0:03d}'.format(num)
    if len(str(numstr))>len(set(str(numstr))):
        continue
    else:
        for divnum in divlist:
            if not num%divnum:
                soucedict[divnum].add(numstr)
count=0
outlist=[]
getlist("",soucedict,len(divlist)-1,divlist,outlist)
print sum([int(item) for item in outlist])
print time.time()-starttime
#print '{0:02d}'.format(0)

运行结果为：
406357289
106357289
160357289
460357289
130952867
430952867
1695334890

0.00500011444092

生活就是一个不断发现自己是一个SB的过程。。。。。

这个题目就是一个迭代啊。很简单的东西啊我居然想了这么久。。。
牛人的代码为：

import time
#coding=utf-8
starttime = time.time()
def checkStrNum(str1):
    '''str1: string of length 3 or greater'''
    return not(str1[0] in str1[1:]) and str1[1] != str1[2]

pandigital = [];
for num in range(1,1000):
    if num % 17 == 0:
        strnum = str(num)
        if len(strnum) == 2:
            strnum = '0' + strnum
        if checkStrNum(strnum):
            pandigital.append(strnum)

divisors = [13,11,7,5,3,2,1]

for div in divisors:
    auxpandigital = []
    for addNum in range(0,10):
        for numPan in pandigital:
            newPan = str(addNum) + numPan
            if checkStrNum(newPan) and int(newPan[0:3]) % div == 0:
                auxpandigital.append(newPan)
    pandigital = auxpandigital

total = 0
for finalPan in pandigital:
    total += int(finalPan)

print(total)
print time.time()-starttime
#print '{0:02d}'.format(0)

16695334890
0.000999927520752