CSU1612Destroy Tunnels（强连通）传递闭包

Destroy Tunnels

原来早忘记了离散里含有这么一个叫传递闭包的东西

矩阵A的闭包B = A U A^2 U A^3 U ... 

所以这里直接如果A[i][j]！= 0，建边i->j跑一遍强连通，看是不是只有一个强连通分量，>=2说明不能所有点都!=0输出exists

否则说明所有i->j(i!=j)都有B[i][j]！= 0输出not exists

#include <map>
#include <set>
#include <stack>
#include <queue>
#include <cmath>
#include <ctime>
#include <vector>
#include <cstdio>
#include <cctype>
#include <cstring>
#include <cstdlib>
#include <iostream>
#include <algorithm>
using namespace std;
#define INF 0x3f3f3f3f
#define inf (-((LL)1<<40))
#define lson k<<1, L, (L + R)>>1
#define rson k<<1|1,  ((L + R)>>1) + 1, R
#define mem0(a) memset(a,0,sizeof(a))
#define mem1(a) memset(a,-1,sizeof(a))
#define mem(a, b) memset(a, b, sizeof(a))
#define FIN freopen("in.txt", "r", stdin)
#define FOUT freopen("out.txt", "w", stdout)
#define rep(i, a, b) for(int i = a; i <= b; i ++)
#define dec(i, a, b) for(int i = a; i >= b; i --)
 
template<class T> T CMP_MIN(T a, T b) { return a < b; }
template<class T> T CMP_MAX(T a, T b) { return a > b; }
template<class T> T MAX(T a, T b) { return a > b ? a : b; }
template<class T> T MIN(T a, T b) { return a < b ? a : b; }
template<class T> T GCD(T a, T b) { return b ? GCD(b, a%b) : a; }
template<class T> T LCM(T a, T b) { return a / GCD(a,b) * b;    }
 
//typedef __int64 LL;
typedef long long LL;
const int MAXN = 11000;
const int MAXM = 1100;
const double eps = 1e-4;
LL MOD = 1000000007;
 
vector<int> G[MAXN];
int pre[MAXN], lowlink[MAXN], sccno[MAXN], dfs_clock, scc_cnt;
stack<int>S;
 
void dfs(int u)
{
    pre[u] = lowlink[u] = ++dfs_clock;
    S.push(u);
    int si = G[u].size();
    for(int i = 0; i < si; i ++)
    {
        int v = G[u][i];
        if(!pre[v]) {
            dfs(v);
            lowlink[u] = min(lowlink[u], lowlink[v]);
        }
        else if(!sccno[v]) {
            lowlink[u] = min(lowlink[u], pre[v]);
        }
    }
    if(lowlink[u] == pre[u]) {
        scc_cnt++;
        for(;;) {
            int x = S.top(); S.pop();
            sccno[x] = scc_cnt;
            if(x == u) break;
        }
    }
}
 
 
void find_scc(int n)
{
    dfs_clock = scc_cnt = 0;
    mem0(sccno); mem0(pre);
    for(int i = 0; i < n; i ++ )
        if(!pre[i]) dfs(i);
}
 
int t, n, x;
 
int main()
{
    while(~scanf("%d", &t)) while(t--) {
        scanf("%d", &n);
        rep (i, 0, n) G[i].clear();
        rep (i, 0, n - 1) rep (j, 0, n - 1) {
            scanf("%d", &x);
            if(x) G[i].push_back(j);
        }
        find_scc(n);
        puts(scc_cnt == 1 ? "not exists" : "exists");
    }
    return 0;
}