POJ3126(KB1-F BFS)

Prime Path

 

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

Source

Northwestern Europe 2006

 

//2017-02-23
#include <iostream>
#include <cstdio>
#include <cstring>
#include <queue>

using namespace std;

struct node
{
    int num, step;
};

bool isPrime(int n)
{
    for(int i = 2; i*i <= n; i++)
          if(n%i==0)return false;
    return true;
}

int pow(int a, int n)
{
    int ans = 1;
    for(int i = 0; i < n; i++)
        ans *= a;
    return ans;
}

int main()
{
    int n, x, y;
    bool book[10005];
    cin>>n;
    while(n--)
    {
        cin>>x>>y;
        queue<node> q;
        node tmp;
        tmp.num = x;
        tmp.step = 0;
        q.push(tmp);
        int num, step;
        bool ok = false;
        memset(book, 0, sizeof(book));
        book[x] = 1;
        while(!q.empty()){
            num = q.front().num;
            step = q.front().step;
            q.pop();
            if(num == y){
                ok = true;
                cout<<step<<endl;
                break;
            }
            for(int i = 0; i < 4; i++){
                for(int p = 0; p < 10; p++){
                    if(i==3 && p==0)continue;
                    int nowNum = num-((num/pow(10, i))%10)*pow(10, i)+p*pow(10, i);
                    if(!book[nowNum] && isPrime(nowNum)){
                        tmp.num = nowNum;
                        tmp.step = step+1;
                        q.push(tmp);
                        book[nowNum] = 1;
                    }
                }
            }
            if(ok)break;
        }
    }

    return 0;
}