Catch That Cow--bfs 与 优化


Farmer John has been informed of the location of a fugitive cow and wants to catch her immediately. He starts at a point N (0 ≤ N ≤ 100,000) on a number line and the cow is at a point K (0 ≤ K ≤ 100,000) on the same number line. Farmer John has two modes of transportation: walking and teleporting.

Walking: FJ can move from any point X to the points X - 1 or X + 1 in a single minute Teleporting: FJ can move from any point X to the point 2 × X in a single minute.

If the cow, unaware of its pursuit, does not move at all, how long does it take for Farmer John to retrieve it?


Line 1: Two space-separated integers: N and K


Line 1: The least amount of time, in minutes, it takes for Farmer John to catch the fugitive cow.

Sample Input

5 17

Sample Output



The fastest way for Farmer John to reach the fugitive cow is to move along the following path: 5-10-9-18-17, which takes 4 minutes.


最小操作问题,典型用bfs,只是bfs 数据量指数增长会超内存,所以我们要想办法优化。

这个题的有效数据其实就是在[0,2 * K]内,最多2 * K个,所以去除重复数据后的有效数据也就2 * K个,如何去除重复,用bool vis[]记录是否访问,后访问的都是无效的数据,没必要加入队列,那么复杂度就是O(K)了

//BFS Memory Limit Exceeded #include<stdio.h> #include<queue> using namespace std; int N,K,ans; int main() { queue<pair<int,int> > que; while(~scanf("%d%d",&N,&K)){ que.push(make_pair(N,0)); while(true){ int s=que.front().first,t=que.front().second;que.pop(); if(s==K){ PRintf("%d\n",t); break; }t++; que.push(make_pair(s*2,t)); que.push(make_pair(s+1,t)); que.push(make_pair(s-1,t)); } while(!que.empty()) que.pop(); } return 0; }


//Accepted 1028kb 32ms #include<stdio.h> #include<string.h> #include<queue> using namespace std; int N,K,ans; queue<pair<int,int> > que; bool vis[200010]; int main() { while(~scanf("%d%d",&N,&K)){ que.push(make_pair(N,0)); memset(vis,0,sizeof(vis)); while(true){ int s=que.front().first,t=que.front().second;que.pop(); if(s==K){ printf("%d\n",t); break; }t++; if(s<K){ if(!vis[s*2]){ que.push(make_pair(s*2,t)); vis[s*2]=true; } if(!vis[s+1]){ que.push(make_pair(s+1,t)); vis[s+1]=true; } } if(s>0&&!vis[s-1]){ que.push(make_pair(s-1,t)); vis[s-1]=true; } } while(!que.empty()) que.pop(); } return 0; }

某神dfs 解法