POJ 1326  对数位的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

题意：求从一个四位数素数到另一个四位数素数所需的最短步数，每一步只能改变一位数字，且改变过程中的数必须是四位数这是一道典型的数位搜索题，求最短路所以用bfs，难点在于模拟数的转化，另外注意边界控制

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

using namespace std;

const int maxn=10000;

int n,m;
bool vis[maxn];
int ans;
struct node
{
    int num,step;
};

int mypow(int n,int k)
{
    int res=1;
    while(k--) res*=n;
    return res;
}

bool isprime(int n) //判断素数，由于数据不大，懒得打印素数表了
{
    for(int i=2;i*i<=n;i++){
        if(n%i==0) return false;
    }
    return true;
}

int change(int n,int i,int j) //模拟数的转化，有很多技巧方法，一定要细心
{
    int f=n/mypow(10,i+1)*mypow(10,i+1);//保留前缀
    int r=n%mypow(10,i);//保留后缀
    int mid=j*mypow(10,i); //改变中间的数
    return f+mid+r;
}

bool bfs()
{
    memset(vis,0,sizeof(vis));
    queue<node> q;
    q.push({n,0});
    vis[n]=1;
    while(!q.empty()){
        node now=q.front();
        q.pop();
        if(now.num==m){
            ans=now.step;
            return true;
        }
        for(int i=0;i<4;i++){  //从第1位到第四位
            for(int j=0;j<=9;j++){  //把所在位数字改为j
                int nextnum=change(now.num,i,j);
                if(nextnum<1000||nextnum>=maxn) continue;//边界控制
                if(vis[nextnum]||!isprime(nextnum)) continue;
                vis[nextnum]=1;
                q.push({nextnum,now.step+1});
            }
        }
    }
    return false;
}

int main()
{
    int T;cin>>T;
    while(T--){
        cin>>n>>m;
        if(bfs()) cout<<ans<<endl;
        else cout<<"Impossible"<<endl;
    }
    return 0;
}

poj3126_bfs