Prime Path

水深无声 2022-08-07 09:51 189阅读 0赞

Prime Path  
Time Limit:1000MS Memory Limit:65536KB 64bit IO Format:%I64d & %I64u  
Submit  
  
Status  
  
Practice  
  
POJ 3126  
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

#include <cstdio>
    #include <cstring>
    #include <queue>
    #include <cmath>
    using namespace std;
    
    typedef struct pos{
        int x, num;
    }pos;
    int m, n;
    bool p[10000];
    bool rot[10000];
    
    void find_p()
    {
        memset(p, true, sizeof(p));
        for(int i=2; i<10000; i++){
            if( p[i] ){
                for(int j=i+i; j<10000; j+=i)
                    p[j] = false;
            }
        }
    }
    bool judge( pos x )
    {
        if( !p[x.x] || rot[x.x] )   return false;
        return true;
    }
    int get_num(int n, int k, int flag)
    {
        int w, m=n;
        w= (int) (pow(10,flag)+0.1);
        if(flag==3 && k==0) return n;
        m = m - m/w%10*w + k*w;
        return m;
    }
    int bfs()
    {
        pos now, next;
        queue<pos>Q;
        now.x=m;    now.num=0;
        rot[now.x]=true;
        Q.push(now);
        while( !Q.empty() ){
            now=Q.front();  Q.pop();
            if(now.x==n){ return now.num; }
            for(int w=0; w<=3; w++){
                for(int g=0; g<=9; g++){
                    next.x=get_num(now.x, g, w);
                    next.num = now.num+1;
                    if( judge(next) ){
                        rot[next.x]=true;
                        Q.push(next);
                    }
                }
            }
        }
        return -1;
    }
    
    int main()
    {
        int t;
        find_p();
        scanf("%d", &t);
        while(t--){
            scanf("%d%d", &m, &n);
            memset(rot, false, sizeof(rot));
            printf("%d\n", bfs());
        }
    
        return 0;
    }