Maximum Clique

Posted 2020-08-31 勿忘初心0924

Maximum Clique

Time Limit: 20000/10000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)

Total Submission(s): 92 Accepted Submission(s): 60

Problem Description Given a graph G(V, E), a clique is a sub-graph g(v, e), so that for all vertex pairs v1, v2 in v, there exists an edge (v1, v2) in e. Maximum clique is the clique that has maximum number of vertex.

Input Input contains multiple tests. For each test: The first line has one integer n, the number of vertex. (1 < n <= 50) The following n lines has n 0 or 1 each, indicating whether an edge exists between i (line number) and j (column number). A test with n = 0 signals the end of input. This test should not be processed.

Output             One number for each test, the number of vertex in maximum clique.

Sample Input 5 0 1 1 0 1 1 0 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 0 0

Sample Output 4

Author CHENG, Long

Source ZOJ Monthly, February 2003

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/*
题意：就是给你一个图，然后输出最大团嘛
*/
#include<bits/stdc++.h>
using namespace std;

/***********************************最大团模板************************************/
struct MAX_CLIQUE {
    static const int N=60;

    bool G[N][N];
    int n, Max[N], Alt[N][N], ans;

    bool DFS(int cur, int tot) {
        if(cur==0) {
            if(tot>ans) {
                ans=tot;
                return 1;
            }
            return 0;
        }
        for(int i=0; i<cur; i++) {
            if(cur-i+tot<=ans) return 0;
            int u=Alt[tot][i];
            if(Max[u]+tot<=ans) return 0;
            int nxt=0;
            for(int j=i+1; j<cur; j++)
                if(G[u][Alt[tot][j]]) Alt[tot+1][nxt++]=Alt[tot][j];
            if(DFS(nxt, tot+1)) return 1;
        }
        return 0;
    }

    int MaxClique() {
        ans=0, memset(Max, 0, sizeof Max);
        for(int i=n-1; i>=0; i--) {
            int cur=0;
            for(int j=i+1; j<n; j++) if(G[i][j]) Alt[1][cur++]=j;
            DFS(cur, 1);
            Max[i]=ans;
        }
        return ans;
    }
};

MAX_CLIQUE fuck;
/***********************************最大团模板************************************/
int n;
int main(){
    // freopen("in.txt","r",stdin);
    while(scanf("%d",&fuck.n)!=EOF&&fuck.n){
        for(int i=0;i<fuck.n;i++){
            for(int j=0;j<fuck.n;j++){
                scanf("%d",&fuck.G[i][j]);
            }
        }
        printf("%d\n",fuck.MaxClique());
    }
    return 0;
}