HDU 1530 Maximum Clique【最大团问题】

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=1530

Maximum Clique

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

题解：

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <vector>
#include <set>
#include <map>
using namespace std;
const int maxn=55;
int n;
int sum;
int x[maxn];
int e[maxn][maxn];
int cn;
bool Place(int t){//判断是否可以将t号结点加入团中
    for(int i=1;i<t;i++){//结点t 与前t-1 个结点中被选中的结点是否相连
        if(x[i]){
            if(e[t][i]==0)//x[j]表示j 是被选中的结点,e[t][j]==0 表示t 和j 没有边相连
                return false;
        }
    }
    return true;
}
void Backtrack(int t){
    if(t>n){//到达叶结点
        sum=cn;
        return ;
    }
    if(Place(t)){//满足约束条件，进入左子树，即把结点t 加入团中
        cn++;
        x[t]=1;
        Backtrack(t+1);
        cn--;
    }
    if(cn+n-t>sum){//满足限界条件，进入右子树
        x[t]=0;
        Backtrack(t+1);
    }
}
int main()
{
    while(scanf("%d",&n)&&n){
        sum=0;
        cn=0;
        for(int i=1;i<=n;i++){
            for(int j=1;j<=n;j++){
                scanf("%d",&e[i][j]);
            }
        }
        Backtrack(1);
        printf("%d\n",sum);
    }
    return 0;
}