poj2594——Treasure Exploration（闭包+最小路径覆盖）-白红宇

poj2594——Treasure Exploration（闭包+最小路径覆盖）

阅读量：2344 次

发布时间：2019-05-10

本文共 2910 字，大约阅读时间需要 9 分钟。

Description

Have you ever read any book about treasure exploration? Have you ever see any film about treasure exploration? Have you ever explored treasure? If you never have such experiences, you would never know what fun treasure exploring brings to you.

Recently, a company named EUC (Exploring the Unknown Company) plan to explore an unknown place on Mars, which is considered full of treasure. For fast development of technology and bad environment for human beings, EUC sends some robots to explore the treasure.

To make it easy, we use a graph, which is formed by N points (these N points are numbered from 1 to N), to represent the places to be explored. And some points are connected by one-way road, which means that, through the road, a robot can only move from one end to the other end, but cannot move back. For some unknown reasons, there is no circle in this graph. The robots can be sent to any point from Earth by rockets. After landing, the robot can visit some points through the roads, and it can choose some points, which are on its roads, to explore. You should notice that the roads of two different robots may contain some same point.

For financial reason, EUC wants to use minimal number of robots to explore all the points on Mars.

As an ICPCer, who has excellent programming skill, can your help EUC?

Input

The input will consist of several test cases. For each test case, two integers N (1 <= N <= 500) and M (0 <= M <= 5000) are given in the first line, indicating the number of points and the number of one-way roads in the graph respectively. Each of the following M lines contains two different integers A and B, indicating there is a one-way from A to B (0 < A, B <= N). The input is terminated by a single line with two zeros.

Output

For each test of the input, print a line containing the least robots needed.

Sample Input

1 0

2 1

1 2

2 0

0 0

Sample Output

给一张图表示藏宝图，用机器人去探测这张图，求最少需要多少个机器人能把这张图上的所有点探测完

由于是有向图，一个机器人只能照着一条路径一直走下去，但是两个机器人走的路可以相交，所以先求传递闭包，然后再用二分图匹配求最小路径覆盖

#include 
   
    #include 
    
     #include 
     
      #include 
      
       #include 
       
        #include 
        
         #include 
         
          #include 
          
           //#include 
           #include 
            
             #define INF 0x3f3f3f3f#define MAXN 505#define Mod 10001using namespace std;bool vis[MAXN];int map[MAXN][MAXN],pre[MAXN],n; //匹配路径;int find(int cur){ for(int i=1; i<=n; ++i) { if(!vis[i]&&map[cur][i]) { vis[i] = true; if(pre[i] == 0 || find(pre[i])) { pre[i] = cur; return 1; } } } return 0;}void floyd(){ for(int i=1; i<=n; ++i) for(int j=1; j<=n; ++j) if(map[i][j]==0) { for(int k=1; k<=n; ++k) if(map[i][k]&&map[k][j]) map[i][j]=1; }}int main(){ int m; while(~scanf("%d%d",&n,&m)) { if(n==0&&m==0) break; memset(map,0,sizeof(map)); while(m--) { int a,b; scanf("%d%d",&a,&b); map[a][b]=1; } floyd(); memset(pre,0,sizeof(pre)); int ans=0; for(int i=1;i<=n;++i) { memset(vis,0,sizeof(vis)); if(find(i)) ans++; } printf("%d\n",n-ans); } return 0;}

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