POJ 3126 Prime Path(BFS 数字处理)

意甲冠军给你两个4位质数a, b 每次你可以改变a个位数，但仍然需要素数的变化乞讨a有多少次的能力，至少修改成b

基础的bfs 注意数的处理即可了出队一个数然后入队全部能够由这个素数经过一次改变而来的素数知道得到b

#include <cstdio>

#include <cstring>

using namespace std;

const int N = 10000;

int p[N], v[N], d[N], q[N], a, b;

void initPrime()

{

    memset(v, 0 , sizeof(v));

    for(int i = 2; i * i < N; ++i)

        if(!v[i]) for(int j = i; i * j < N; ++j)  v[i * j] = 1;

    for(int i = 2; i < N ; ++i) p[i] = !v[i];

}

int bfs()

{

    int c, t, le = 0, ri = 0;

    memset(v, 0, sizeof(v));

    q[ri++] = a, v[a] = 1, d[a] = 0;

    while(le < ri)

    {

        c = q[le++];

        if( c == b) return d[c];

        for(int i = 1; i < N; i *= 10)

        {

            for(int j = 0; j < 10; ++j)   //把c第i数量级的数改为j

            {

                if(i == 1000 && j == 0) continue;

                t = c / (i * 10) * i * 10 + i * j + c % i;

                if(p[t] && !v[t])

                    v[t] = 1, d[t] = d[c] + 1, q[ri++] = t;

            }

        }

    }

    return -1;

}

int main()

{

    int cas;

    scanf("%d", &cas);

    initPrime();

    while(cas--)

    {

        scanf("%d%d", &a, &b);

        if((a = bfs()) != -1) printf("%d\n", a);

        else puts("Impossible");

    }

    return 0;

}

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

Sample Output

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POJ 3126 Prime Path(BFS 数字处理)

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