D-POJ-3126 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

BFS，将素数打表可以缩短运行时间。

#include<iostream>#include<cstdio>#include<cmath>#include<queue>#include<cstring>using namespace std;#define maxn 10005bool vis[maxn];          //标记是否访问bool IsPrime[maxn];      //标记素数void Prime(){   //素数筛法    IsPrime[0]=IsPrime[1]=false;IsPrime[2]=true;    for(int i=3;i<maxn;i++){        if(i%2)            IsPrime[i]=true;        else            IsPrime[i]=false;    }    int m=sqrt(maxn*1.0);    for(int i=3;i<m;i++){        if(IsPrime[i]){            for(int j=i;j<maxn;j+=i)                IsPrime[j]=false;        }    }}struct Node{    int p[4];    int step;};void BFS(int a,int b){    memset(vis, false, sizeof(vis));    Node now,next;    int x;    queue<Node>Q;    now.p[0]=a/1000;now.p[1]=a%1000/100;now.p[2]=a%100/10;now.p[3]=a%10;    now.step=0;    Q.push(now);    while(!Q.empty()){        now=Q.front();        Q.pop();        if(now.p[0]*1000+now.p[1]*100+now.p[2]*10+now.p[3]==b){            printf("%d\n",now.step);            return;        }        for(int i=0;i<=3;i++){            for(int j=0;j<=9;j++){                if(i==0&&j==0)                    continue;                if(now.p[i]==j)                    continue;                next.p[0]=now.p[0];                next.p[1]=now.p[1];                next.p[2]=now.p[2];                next.p[3]=now.p[3];                next.p[i]=j;                x=next.p[0]*1000+next.p[1]*100+next.p[2]*10+next.p[3];                if(!vis[x]&&IsPrime[x]){                    next.step=now.step+1;                    vis[x]=true;                    Q.push(next);                }            }        }    }    printf("Impossible\n");}int main(){    Prime();    int n,a,b;    scanf("%d",&n);    while(n--){        scanf("%d%d",&a,&b);        BFS(a,b);    }    return 0;}

开始不管怎么运行都是输出Impossible，后来发现Prim函数没运行，蠢哭~