poj 3126 prime path(bfs)
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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,每次只能换一个数字,而且要保证每一步得出的结果都是素数,先打个表,再bfs,水题。
#include <iostream>#include <cstdio>#include <cstring>#include <algorithm>#include <queue>using namespace std;int n1,n2;struct node{ int num,step; bool operator <(const node&rhs) const { return step>rhs.step; }};int prime[20050];priority_queue <node> que;int vis[11][11][11][11];int bfs(){ while(!que.empty()) { node head; head=que.top(); int x=head.num; int ss=head.step; que.pop(); // printf("%d\n",x ); int xx=0; for(int i=1;i<=9;i++) { xx=x%1000+i*1000; // printf("%d\n",xx ); getchar(); if(!vis[xx/1000][xx/100%10][xx/10%10][xx%10]&&!prime[xx]) { que.push(node{xx,ss+1}); vis[xx/1000][xx/100%10][xx/10%10][xx%10]=1; if(xx==n2) return ss+1; } } for(int i=0;i<=9;i++) { xx=x/1000*1000+i*100+x%100; // printf("%d\n",xx ); getchar(); if(!vis[xx/1000][xx/100%10][xx/10%10][xx%10]&&!prime[xx]) { que.push(node{xx,ss+1}); vis[xx/1000][xx/100%10][xx/10%10][xx%10]=1; if(xx==n2) return ss+1; } } for(int i=0;i<=9;i++) { xx=x/100*100+i*10+x%10; // printf("%d\n",xx ); getchar(); if(!vis[xx/1000][xx/100%10][xx/10%10][xx%10]&&!prime[xx]) { que.push(node{xx,ss+1}); vis[xx/1000][xx/100%10][xx/10%10][xx%10]=1; if(xx==n2) return ss+1; } } for(int i=0;i<=9;i++) { if(i%2) { xx=x/10*10+i; // printf("%d\n",xx ); getchar(); if(!vis[xx/1000][xx/100%10][xx/10%10][xx%10]&&!prime[xx]) { que.push(node{xx,ss+1}); vis[xx/1000][xx/100%10][xx/10%10][xx%10]=1; if(xx==n2) return ss+1; } } } }}int main(){ memset(prime,0,sizeof(prime)); for(int i=2;i<=20000;i++) { if(!prime[i]) for(int j=i*2;j<=20000;j+=i) { prime[j]=1; } } int t; cin>>t; while(t--) { cin>>n1>>n2; while(!que.empty()) que.pop(); memset(vis,0,sizeof(vis)); if(n1==n2) printf("0\n"); else { vis[n1/1000][n1/100%10][n1/10%10][n1%10]=1; que.push(node{n1,0}); printf("%d\n",bfs()); } }}
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