CSU1612Destroy Tunnels（强连通）

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 = ;
 const int MAXM = ;
 const double eps = 1e-;
 LL MOD = ;

 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 = ; 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 = ;
     mem0(sccno); mem0(pre);
     for(int i = ; 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, , n) G[i].clear();
         rep (i, , n - ) rep (j, , n - ) {
             scanf("%d", &x);
             if(x) G[i].push_back(j);
         }
         find_scc(n);
         puts(scc_cnt ==  ? "not exists" : "exists");
     }
     return ;
 }