POJ 3126 Prime Path （BFS）

2019-11-11 03:03:52

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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.

1033173337333739377987798179

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

31033 81791373 80171033 1033

Sample Output

670

题意

给你n,m分别是素数，求由n到m变化的步骤数，规定每一步只能改变个十百千一位的数（千位不能为零），且变化得到的每一个数也为素数。

思路

首先进行素数打表，打出10000以内的所有素数（或者1000-10000），然后bfs。

对n变化个十百千的每一位，变化后检测是否为素数，若是，加入队列，同时标记已访问，然后对队列中的数进行同样的操作，直到某一次变化产生m，输出最少的变换次数。

若不可能达到m，则会在遍历完[1000-9999]之间所有素数后退出。

AC 代码

#include<iostream>#include<algorithm>#include<stdio.h>#include<string.h>#include<math.h>#include<iostream>using namespace std;#include<vector>#include<queue>#define Max 10000int prime[Max];bool isvis[Max]; //已经访问过的数字不需要重新加入队列void IsPrime() //素数打表{ prime[0]=prime[1]=0; prime[2]=1; for(int i=3; i<Max; i++) prime[i]=i%2==0?0:1; int t=(int)sqrt(Max*1.0); for(int i=3; i<=t; i++) if(prime[i]) for(int j=i*i; j<Max; j+=2*i) //优化 prime[j]=0;}struct point{ int data; int time; //当前进行到第几步 point(int data,int time) { this->data=data; this->time=time; }};int solve(point a,int b){ memset(isvis,false,sizeof(isvis)); queue<point>sk; sk.push(a); while(!sk.empty()) { point p=sk.front(); sk.pop(); if(p.data==b)return p.time; isvis[p.data]=true; for(int i=10; i<=10000; i*=10) //从低到高枚举 { for(int j=(i==10000)?1:0; j<=9; j++) //最高位不能是0 { int num=p.data/i*i+i/10*j+p.data%(i/10); //计算当前的数字 if(!isvis[num]&&prime[num]) sk.push(point(num,p.time+1)); } } } return -1;}int main(){ IsPrime(); int n; while(~scanf("%d",&n)) { int a,b; for(int i=0; i<n; i++) { scanf("%d%d",&a,&b); int ans=solve(point(a,0),b); printf(ans==-1?"Impossible/n":"%d/n",ans); } } return 0;}

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