#include <cstdio> #include <cstring> #include <algorithm> #include <iostream> using namespace std; const int maxn = 110; const int maxm = maxn * maxn; struct Edge { int to, next; }; Edge edge[maxm]; int head[maxn], tol, v, n, low[maxn], DFN[maxn], Stack[maxn], Belong[maxn], index, top, scc; bool Instack[maxn]; void addedge(int u, int v) { edge[tol].to = v; edge[tol].next = head[u]; head[u] = tol++; } void Tarjan(int u) { int v; low[u] = DFN[u] = ++index; Stack[top++] = u; Instack[u] = true; for (int i = head[u]; i != -1; i = edge[i].next) { v = edge[i].to; if (!DFN[v]) { Tarjan(v); if (low[u] > low[v]) low[u] = low[v]; } else if (Instack[v] && low[u] > DFN[v]) low[u] = DFN[v]; } if (low[u] == DFN[u]) { scc++; do { v = Stack[--top]; Belong[v] = scc; Instack[v] = false; } while (v != u); } } int in[maxn], out[maxn]; void solve(int N) { memset(DFN, 0, sizeof(DFN)); memset(Instack, 0, sizeof(Instack)); index = scc = top = 0; for (int i = 1; i <= N; i++) if (!DFN[i]) Tarjan(i); if (scc == 1) {printf("1\n0\n"); return;} for (int i = 1; i <= scc; i++) in[i] = out[i] = 0; for (int u = 1; u <= N; u++) for (int i = head[u]; i != -1; i = edge[i].next) { int v = edge[i].to; if (Belong[u] != Belong[v]) in[Belong[v]]++, out[Belong[u]]++; } int ans1 = 0, ans2 = 0; for (int i = 1; i <= scc; i++) { if (in[i] == 0) ans1++; if (out[i] == 0) ans2++; } printf("%d\n%d\n", ans1, max(ans1, ans2)); } int main(int argc, char const *argv[]) { while (~scanf("%d", &n)) { tol = 0; memset(head, -1, sizeof(head)); for (int i = 1; i <= n; i++) while (~scanf("%d", &v) && v) addedge(i, v); solve(n); } return 0; }
这题给了一个有向图。需要解决两个问题:
第一是需要给多少个点,才能传遍所有点。
第二问是加多少条边,使得整个图变得强连通。
使用Tarjan进行缩点,得到一个SCC图,统计有n个入度为零,m个出度为零的;
问题一答案为n, 问题二答案为max(n,m);