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 = ; i*i <= n; i++)
           if(n%i==)return false;
     return true;
 }

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

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

     return ;
 }