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Project Euler:Problem 43 Sub-string divisibility

2015-06-05 10:24 585 查看
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 1st digit, d2 be the 2nd 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.

#include <iostream>
#include <iostream>
#include <string>
using namespace std;

unsigned long long res = 0;
int prime[7] = { 2, 3, 5, 7, 11, 13, 17 };

bool divis(string s)
{
	for (int i = 1; i <= 7; i++)
	{
		int d = (s[i] - '0') * 100 + (s[i + 1] - '0') * 10 + (s[i + 2] - '0');
		if (d%prime[i - 1] != 0)
			return false;
	}
	return true;
}
 
void perm(int list[], int n, int k)
{
	int temp1, temp2;
	if (n == 1)
	{		
		if (list[k] != 0)
		{
			string s = "";
			unsigned long long sum = 0;
			for (int i = 1; i <= k; i++)
			{
				char a = list[i] + '0';
				s = s + a;
				sum = sum * 10 + list[i];
			}
			if (divis(s))
				res += sum;
		}
	}
	else
	for (int i = 1; i <= n; i++)
	{
		temp1 = list[i];
		list[i] = list
;
		list
 = temp1;

		perm(list, n - 1, k);

		temp2 = list[i];
		list[i] = list
;
		list
 = temp2;
	}
}

int main()
{
	int list[11];
	for (int i = 1; i <= 10; i++)
		list[i] = i-1;
	perm(list, 10, 10);

	cout << res << endl;
	system("pause");

	return 0;
}
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