2013
12-12

# Maximum Clique

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 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.

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

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

4

#include <set>
#include <map>
#include <list>
#include <cmath>
#include <queue>
#include <stack>
#include <string>
#include <vector>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>

using namespace std;

typedef long long ll;
typedef unsigned long long ull;

#define debug puts("here")
#define rep(i,n) for(int i=0;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define REP(i,a,b) for(int i=a;i<=b;i++)
#define foreach(i,vec) for(unsigned i=0;i<vec.size();i++)
#define pb push_back
#define RD(n) scanf("%d",&n)
#define RD2(x,y) scanf("%d%d",&x,&y)
#define RD3(x,y,z) scanf("%d%d%d",&x,&y,&z)
#define RD4(x,y,z,w) scanf("%d%d%d%d",&x,&y,&z,&w)
#define All(vec) vec.begin(),vec.end()
#define MP make_pair
#define PII pair<int,int>
#define PQ priority_queue
#define cmax(x,y) x = max(x,y)
#define cmin(x,y) x = min(x,y)
#define Clear(x) memset(x,0,sizeof(x))
/*

int size = 256 << 20; // 256MB
char *p = (char*)malloc(size) + size;
__asm__("movl %0, %%esp\n" :: "r"(p) );

*/

char IN;
bool NEG;
inline void Int(int &x){
NEG = 0;
while(!isdigit(IN=getchar()))
if(IN=='-')NEG = 1;
x = IN-'0';
while(isdigit(IN=getchar()))
x = x*10+IN-'0';
if(NEG)x = -x;
}
inline void LL(ll &x){
NEG = 0;
while(!isdigit(IN=getchar()))
if(IN=='-')NEG = 1;
x = IN-'0';
while(isdigit(IN=getchar()))
x = x*10+IN-'0';
if(NEG)x = -x;
}

/******** program ********************/

const int MAXN = 50;

int g[MAXN][MAXN],n;
bool use[MAXN];
int dp[MAXN],best;
//int pre[MAXN],path[MAXN]; // 记录路径

bool dfs(int *id,int top,int cnt){
if(!top){
if(best<cnt){
//copy( pre+1,pre+cnt+1,path ); // 记录路径
best = cnt;
return true;
}
return false;
}
int a[MAXN];
rep(i,top){
if(cnt+top-i<=best)return false;
if(cnt+dp[id[i]]<=best)return false;
//pre[cnt] = id[i]; // 记录路径
int k = 0;
for(int j=i+1;j<top;j++)
if(g[id[i]][id[j]])
a[k++] = id[j];
if(dfs(a,k,cnt+1))return true;
}
return false;
}

inline int solve(){
int id[MAXN];
best = 0;
for(int i=n-1;i>=0;i--){
int top = 0;
for(int j=i+1;j<n;j++)
if(g[i][j])
id[top++] = j;
dfs(id,top,1);
dp[i] = best;
}
return best;
}

int main(){

#ifndef ONLINE_JUDGE
freopen("sum.in","r",stdin);
//freopen("sum.out","w",stdout);
#endif

while(1){
Int(n);
if(!n)break;
rep(i,n)
rep(j,n)
Int(g[i][j]);
cout<<solve()<<endl;
}

return 0;
}

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