CSU1612Destroy Tunnels（强连通）传递闭包
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
1 #include <map> 2 #include <set> 3 #include <stack> 4 #include <queue> 5 #include <cmath> 6 #include <ctime> 7 #include <vector> 8 #include <cstdio> 9 #include <cctype> 10 #include <cstring> 11 #include <cstdlib> 12 #include <iostream> 13 #include <algorithm> 14 using namespace std; 15 #define INF 0x3f3f3f3f 16 #define inf (-((LL)1<<40)) 17 #define lson k<<1, L, (L + R)>>1 18 #define rson k<<1|1, ((L + R)>>1) + 1, R 19 #define mem0(a) memset(a,0,sizeof(a)) 20 #define mem1(a) memset(a,-1,sizeof(a)) 21 #define mem(a, b) memset(a, b, sizeof(a)) 22 #define FIN freopen("in.txt", "r", stdin) 23 #define FOUT freopen("out.txt", "w", stdout) 24 #define rep(i, a, b) for(int i = a; i <= b; i ++) 25 #define dec(i, a, b) for(int i = a; i >= b; i --) 26 27 template<class T> T CMP_MIN(T a, T b) { return a < b; } 28 template<class T> T CMP_MAX(T a, T b) { return a > b; } 29 template<class T> T MAX(T a, T b) { return a > b ? a : b; } 30 template<class T> T MIN(T a, T b) { return a < b ? a : b; } 31 template<class T> T GCD(T a, T b) { return b ? GCD(b, a%b) : a; } 32 template<class T> T LCM(T a, T b) { return a / GCD(a,b) * b; } 33 34 //typedef __int64 LL; 35 typedef long long LL; 36 const int MAXN = 11000; 37 const int MAXM = 1100; 38 const double eps = 1e-4; 39 LL MOD = 1000000007; 40 41 vector<int> G[MAXN]; 42 int pre[MAXN], lowlink[MAXN], sccno[MAXN], dfs_clock, scc_cnt; 43 stack<int>S; 44 45 void dfs(int u) 46 { 47 pre[u] = lowlink[u] = ++dfs_clock; 48 S.push(u); 49 int si = G[u].size(); 50 for(int i = 0; i < si; i ++) 51 { 52 int v = G[u][i]; 53 if(!pre[v]) { 54 dfs(v); 55 lowlink[u] = min(lowlink[u], lowlink[v]); 56 } 57 else if(!sccno[v]) { 58 lowlink[u] = min(lowlink[u], pre[v]); 59 } 60 } 61 if(lowlink[u] == pre[u]) { 62 scc_cnt++; 63 for(;;) { 64 int x = S.top(); S.pop(); 65 sccno[x] = scc_cnt; 66 if(x == u) break; 67 } 68 } 69 } 70 71 72 void find_scc(int n) 73 { 74 dfs_clock = scc_cnt = 0; 75 mem0(sccno); mem0(pre); 76 for(int i = 0; i < n; i ++ ) 77 if(!pre[i]) dfs(i); 78 } 79 80 int t, n, x; 81 82 int main() 83 { 84 while(~scanf("%d", &t)) while(t--) { 85 scanf("%d", &n); 86 rep (i, 0, n) G[i].clear(); 87 rep (i, 0, n - 1) rep (j, 0, n - 1) { 88 scanf("%d", &x); 89 if(x) G[i].push_back(j); 90 } 91 find_scc(n); 92 puts(scc_cnt == 1 ? "not exists" : "exists"); 93 } 94 return 0; 95 } 96
