Prime Path （POJ - 3126 ）（BFS）

转载请注明出处：https://blog.csdn.net/Mercury_Lc/article/details/82697622     作者：Mercury_Lc

题目链接

题意：就是给你一个n，让你每次可以改变n的位数上的一个数，每次操作完必须是素数，要求最小次数的改变到达m。

题解：对n每一位都进行判断，找到通过最小操作次数得到m。分别要从个位、十位、百位、千位判断，在个位的时候每次只能是1、3、5、7、9，其他的改变之后都不是素数，十位、百位、千位都从0开始遍历到9，每次只要符合是素数就放到队列中，开个结构体记录步数和当前的数就可以了。

#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <queue>
#include <iostream>

using namespace std;
const int maxn = 1e6;
int n,m;
int vis[maxn];
struct node
{
    int data,step;
} w,l;
bool prime(int x)
{
    if(x==1||x==0)
        return 0;
    for(int i = 2; i <= sqrt(x); i ++)
    {
        if(x % i == 0)
            return 0;
    }
    return 1;
}

void bfs()
{
    queue<node>q;
    memset(vis,0,sizeof(vis));
    vis[n] = 1;
    w.data = n;
    w.step = 0;
    q.push(w);
    while(!q.empty())
    {
        w = q.front();
        q.pop();
        if(w.data == m)
        {
            printf("%d\n",w.step);
            return ;
        }
        for(int i = 1; i <= 9; i += 2)  // ge
        {
            int s = w.data / 10 * 10 + i;
            if(!vis[s] && prime(s))
            {
                vis[s] = 1;
                l.data = s;
                l.step = w.step + 1;
                q.push(l);
            }
        }
        for(int i = 0; i <= 9; i++)  // shi
        {
            int s = w.data / 100 * 100 + i * 10 + w.data % 10;
            if(!vis[s] && prime(s))
            {
                vis[s] = 1;
                l.data = s;
                l.step = w.step + 1;
                q.push(l);
            }
        }
        for(int i = 0; i <= 9; i++)  // bai
        {
            int s = w.data / 1000 * 1000 + i * 100 + w.data % 100;
            if(!vis[s] && prime(s))
            {
                vis[s] = 1;
                l.data = s;
                l.step = w.step + 1;
                q.push(l);
            }
        }
        for(int i = 1; i <= 9; i++)  // qian
        {
            int s = i * 1000 + w.data % 1000;
            if(!vis[s] && prime(s))
            {
                vis[s] = 1;
                l.data = s;
                l.step = w.step + 1;
                q.push(l);
            }
        }
    }
    return ;
}
int main()
{
    int t;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%d%d",&n,&m);
        bfs();
    }
    return 0;
}

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