Pandigital prime

Problem 41

We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime.

What is the largest n-digit pandigital prime that exists?

Answer:

7652413

Completed on Thu, 30 Jul 2015, 08:32

Go to the thread for problem 41 in the forum.

首先发现3k和3k-1位的ppandigital肯定能被3整除。所以就剩下1，4，7，10。13。。。推測题意应该是9以内的所以就试试7咯，代码是前面代码扩展，就出结果了

http://blog.csdn.net/zhangzhengyi03539/article/details/43501225

http://blog.csdn.net/zhangzhengyi03539/article/details/47057049

__author__ = 'zhengyi'

import math

from functools import reduce

def IsPrime(x):

    if x==1:

        return False

    k=int(math.sqrt(x))+1

    for i in range(2,k):

        if x%i==0:

            return False

    return True

def reducefunc(x,y):

    return 10*x+y

def func1(x):

    i=1

    val=1

    while val<x:

        i+=1

        val*=i

    if val==x:

        return (1,i,0)

    else:

        step=val//i

        k=x//step

        return (k,i-1,x%(k*step))

def func2(x):

    lst=[]

    result=func1(x)

    while result[2]!=0:

        lst.append(result[0:2])

        result=func1(result[2])

    lst.append(result[0:2])

    return lst

def func3(x,clst):

    result=[]

    count=len(clst)

    lst=func2(x)

    length=len(lst)

    for i in range(0,length):

        if i<length-1:

            delta=lst[i][0]

            position=lst[i][1]+1

            while count>position:

                result.append(clst[-count])

                del clst[-count]

                count-=1

            result.append(clst[-position+delta])

            del clst[-position+delta]

            count-=1

        else:

            delta=lst[i][0]-1

            position=lst[i][1]+1

            while count>position:

                result.append(clst[-count])

                del clst[-count]

                count-=1

            result.append(clst[-position+delta])

            del clst[-position+delta]

            count-=1

            while count>0:

                result.append(clst[-1])

                del clst[-1]

                count-=1

    return result

charlist=[i for i in range(7,0,-1)]

k=0

while True:

    k+=1

    temp=func3(k,charlist.copy())

    data=reduce(reducefunc,temp)

    if IsPrime(data):

        print(data)

        break

print("Get it")