Catch That Cow--bfs 与优化

2019-11-14 12:30:14

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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 minuteTeleporting: 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?

Input

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

Output

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

Hint

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.

解题报告

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;}

对上面代码优化后

//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;}