POJ - 3126 Prime Path —— BFS

Prime Path

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 23030		Accepted: 12756

Description

The ministers of the cabinet were quite upset by the message from the Chief of Security stating that they would all have to change the four-digit room numbers on their offices. 
— It is a matter of security to change such things every now and then, to keep the enemy in the dark. 
— But look, I have chosen my number 1033 for good reasons. I am the Prime minister, you know! 
— I know, so therefore your new number 8179 is also a prime. You will just have to paste four new digits over the four old ones on your office door. 
— No, it’s not that simple. Suppose that I change the first digit to an 8, then the number will read 8033 which is not a prime! 
— I see, being the prime minister you cannot stand having a non-prime number on your door even for a few seconds. 
— Correct! So I must invent a scheme for going from 1033 to 8179 by a path of prime numbers where only one digit is changed from one prime to the next prime. 

Now, the minister of finance, who had been eavesdropping, intervened. 
— No unnecessary expenditure, please! I happen to know that the price of a digit is one pound. 
— Hmm, in that case I need a computer program to minimize the cost. You don't know some very cheap software gurus, do you? 
— In fact, I do. You see, there is this programming contest going on... Help the prime minister to find the cheapest prime path between any two given four-digit primes! The first digit must be nonzero, of course. Here is a solution in the case above. 

1033
1733
3733
3739
3779
8779
8179

The cost of this solution is 6 pounds. Note that the digit 1 which got pasted over in step 2 can not be reused in the last step – a new 1 must be purchased.

Input

One line with a positive number: the number of test cases (at most 100). Then for each test case, one line with two numbers separated by a blank. Both numbers are four-digit primes (without leading zeros).

Output

One line for each case, either with a number stating the minimal cost or containing the word Impossible.

Sample Input

3
1033 8179
1373 8017
1033 1033

Sample Output

6
7
0

题意：给出一个四位数 每次更换一个数字 最后更换成目标数字 要求更换过程中成的四位数字必须也是素数

#include <iostream>
#include <queue>
#include <cstring>
#include <cstdio>
#include <cmath>
#define max 10010
using namespace std;
bool prime[max];
queue<int>q;
int count=0,x,y,num[max],dir[4]={1,10,100,1000};
bool isprime()
{
	prime[0]=prime[1]=false;
	prime[2]=true;
	for(int i=2;i<max;i++)
	{
		if(prime[i]==true)
        {
            for(int j=i+i;j<max;j+=i)
            {
            	prime[j]=false;
			}
		}
	}
}
void bfs(int x)
{
	q.push(x);
	num[x]=1;
	while(q.size())
	{
		int u=q.front();
		q.pop();
		if(u==y)
		break;
		int i,k;
		for(i=-9;i<=9;i++)
		{
			for(k=0;k<4;k++)
			{
				int t=u+i*dir[k];
				if(t>=1000&&t<=9999)
				{
					if(num[t]==0&&prime[t])
					{
						int a=i*dir[k];
						int b=u%(dir[k]*10);
						if(a+b>=0&&a+b<dir[k]*10)
						{
							num[t]=num[u]+1;
							q.push(t);
						}
					}
				}
			}
		}
	}
}
int main()
{
	memset(prime,true,sizeof(prime));
	isprime();
	int t;
	cin>>t;
	while(t--)
	{
		memset(num,0,sizeof(num));
		while(q.size())
		q.pop();
		cin>>x>>y;
		bfs(x);
		cout<<num[y]-1<<endl;
	}
}