P10940

Author: fei0319

code/luogu/P10940.cpp

@@ -0,0 +1,163 @@
+#include <iostream>
+#include <iterator>
+#include <queue>
+#include <unordered_set>
+#include <vector>
+
+template <typename T>
+struct Flow {
+    int n;
+    struct Edge {
+        int to;
+        T cap;
+        Edge(int to, T cap) : to(to), cap(cap) {}
+    };
+    std::vector<Edge> edge;
+    std::vector<std::vector<int>> adj;
+    std::vector<int> cur, dep;
+    explicit Flow(int n) : n(n), adj(n) {}
+    bool bfs(int s, int t) {
+        dep.assign(n, -1);
+        std::queue<int> q;
+        dep[s] = 0;
+        q.push(s);
+        while (!q.empty()) {
+            int node = q.front();
+            q.pop();
+            for (int i : adj[node]) {
+                int to = edge[i].to;
+                T c = edge[i].cap;
+                if (c > 0 && dep[to] == -1) {
+                    dep[to] = dep[node] + 1;
+                    if (to == t) return true;
+                    q.push(to);
+                }
+            }
+        }
+        return false;
+    }
+    T dfs(int node, int t, T flow) {
+        if (node == t || flow == 0) return flow;
+        T f, res = 0;
+        for (int &i = cur[node]; i < int(adj[node].size()); ++i) {
+            int j = adj[node][i], to = edge[j].to;
+            T c = edge[j].cap;
+            if (dep[to] == dep[node] + 1 &&
+                (f = dfs(to, t, std::min(flow, c)))) {
+                res += f, flow -= f;
+                edge[j].cap -= f, edge[j ^ 1].cap += f;
+            }
+            if (flow == 0) break;
+        }
+        if (!res) dep[node] = -1;
+        return res;
+    }
+    int add_edge(int u, int v, T c) {
+        int j = edge.size();
+        adj[u].push_back(edge.size());
+        edge.emplace_back(v, c);
+        adj[v].push_back(edge.size());
+        edge.emplace_back(u, 0);
+        return j;
+    }
+    T operator()(int s, int t, const T INF = 1e9) {
+        T ans = 0;
+        while (bfs(s, t)) cur.assign(n, 0), ans += dfs(s, t, INF);
+        return ans;
+    }
+};
+
+struct SCC {
+    int n;
+    std::vector<std::vector<int>> adj;
+    std::vector<int> stk;
+    std::vector<int> dfn, low, bel;
+    int cur, cnt;
+    void dfs(int x) {
+        dfn[x] = low[x] = cur++;
+        stk.push_back(x);
+        for (int to : adj[x]) {
+            if (dfn[to] == -1) {
+                dfs(to);
+                low[x] = std::min(low[x], low[to]);
+            } else if (bel[to] == -1) {
+                low[x] = std::min(low[x], dfn[to]);
+            }
+        }
+        if (dfn[x] == low[x]) {
+            int y;
+            do {
+                y = stk.back();
+                bel[y] = cnt;
+                stk.pop_back();
+            } while (y != x);
+            ++cnt;
+        }
+    }
+
+public:
+    explicit SCC(int n)
+        : n(n), adj(n), dfn(n, -1), low(n), bel(n, -1), cur(0), cnt(0) {}
+
+    void add_edge(int u, int v) { adj[u].push_back(v); }
+    std::vector<int> operator()() {
+        for (int i = 0; i < n; i++)
+            if (dfn[i] == -1) dfs(i);
+        return bel;
+    }
+};
+
+void solve() {
+    int n, m, t;
+    std::cin >> n >> m >> t;
+
+    std::vector<std::pair<int, int>> edge_list(t);
+    for (auto &[u, v] : edge_list) {
+        std::cin >> u >> v;
+        --u, --v;
+    }
+
+    auto f = Flow<int>(n + m + 2);
+    for (const auto [u, v] : edge_list) {
+        f.add_edge(u, n + v, 1);
+    }
+    for (int i = 0; i < n; ++i) f.add_edge(n + m, i, 1);
+    for (int i = 0; i < m; ++i) f.add_edge(n + i, n + m + 1, 1);
+    f(n + m, n + m + 1);
+
+    auto b = SCC(f.n);
+    std::unordered_set<int> matching;
+    for (int u = 0; u < f.n; ++u) {
+        for (int id : f.adj[u]) {
+            auto [v, cap] = f.edge[id];
+            if (cap) {
+                // std::cout << u << ' ' << v << '\n';
+                b.add_edge(u, v);
+            }
+            if (u < n && v < n + m && !cap) {
+                matching.insert(u * m + v - n);
+            }
+        }
+    }
+    auto bel = b();
+
+    std::vector<int> ans;
+    for (int i = 0; i < t; ++i) {
+        auto [u, v] = edge_list[i];
+        if (bel[u] != bel[n + v] && !matching.contains(u * m + v)) {
+            ans.push_back(i + 1);
+        }
+    }
+
+    std::cout << ans.size() << '\n';
+    std::copy(ans.begin(), ans.end(),
+              std::ostream_iterator<int>(std::cout, " "));
+    std::cout << '\n';
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    std::cin.tie(nullptr);
+
+    solve();
+}