P4172 [WC2006]水管局长

https://www.luogu.com.cn/record/98634479

Luogu/P4172/P4172.cpp

@@ -0,0 +1,264 @@
+#include <iostream>
+#include <algorithm>
+#include <iterator>
+#include <numeric>
+#include <queue>
+#include <stack>
+#include <tuple>
+#include <vector>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 1005,
+          M = 2e5 + 5;
+
+int n, m, q, id[N][N], a[M];
+std::tuple<int, int, int, bool> edges[M];
+std::tuple<int, int, int> qs[M];
+
+class LinkCutTree {
+  private:
+    struct node {
+        size_t lchild, rchild, father;
+        int val, max;
+        bool reversed;
+
+        size_t& child(const bool& x) {
+            return !x ? lchild : rchild;
+        }
+    } tr[M];
+
+    void pushup(const size_t& u) {
+        tr[u].max = std::max({tr[u].val, tr[tr[u].lchild].max, tr[tr[u].rchild].max});
+    }
+
+    void pushdown(const size_t& u) {
+        if (!tr[u].reversed) return;
+
+        std::swap(tr[u].lchild, tr[u].rchild);
+        tr[tr[u].lchild].reversed ^= 1;
+        tr[tr[u].rchild].reversed ^= 1;
+        tr[u].reversed = false;
+    }
+
+    bool relation(const size_t& u) {
+        return u == tr[tr[u].father].lchild ? 0 : 1;
+    }
+
+    bool is_root(const size_t& u) {
+        return tr[tr[u].father].lchild != u && tr[tr[u].father].rchild != u;
+    }
+
+    void rotate(const size_t& u) {
+        size_t p = tr[u].father;
+        bool x = relation(u);
+
+        if (!is_root(p)) tr[tr[p].father].child(relation(p)) = u;
+        tr[u].father = tr[p].father;
+
+        if (tr[u].child(x ^ 1)) tr[tr[u].child(x ^ 1)].father = p;
+        tr[p].child(x) = tr[u].child(x ^ 1);
+
+        tr[u].child(x ^ 1) = p;
+        tr[p].father = u;
+
+        pushup(p);
+        pushup(u);
+    }
+
+    void splay(size_t u) {
+        std::stack<size_t> st;
+
+        size_t cur = u;
+        st.emplace(cur);
+
+        while (!is_root(cur)) {
+            st.emplace(tr[cur].father);
+            cur = tr[cur].father;
+        }
+
+        while (!st.empty()) {
+            pushdown(st.top());
+            st.pop();
+        }
+
+        while (!is_root(u)) {
+            if (is_root(tr[u].father)) {
+                rotate(u);
+            } else if (relation(u) == relation(tr[u].father)) {
+                rotate(tr[u].father);
+                rotate(u);
+            } else {
+                rotate(u);
+                rotate(u);
+            }
+        }
+    }
+
+    void access(size_t u) {
+        for (size_t f = 0; u; u = tr[f = u].father) {
+            splay(u);
+            tr[u].rchild = f;
+            pushup(u);
+        }
+    }
+
+    void make_root(const size_t& u) {
+        access(u);
+        splay(u);
+        tr[u].reversed ^= 1;
+    }
+
+    size_t find_root(size_t u) {
+        access(u);
+        splay(u);
+
+        while (tr[u].lchild) {
+            u = tr[u].lchild;
+        }
+
+        return u;
+    }
+
+    void split(const size_t& x, const size_t& y) {
+        make_root(x);
+        access(y);
+        splay(y);
+    }
+
+  public:
+    void set(int p, int v) {
+        tr[p].max = tr[p].val = v;
+    }
+
+    bool check(const int& x, const int& y) {
+        return find_root(x) == find_root(y);
+    }
+
+    int query(const int& x, const int& y) {
+        split(x, y);
+
+        return tr[y].max;
+    }
+
+    void link(const int& x, const int& y) {
+        make_root(x);
+
+        if (find_root(y) != x) {
+            tr[x].father = y;
+        }
+    }
+
+    void cut(const int& x, const int& y) {
+        split(x, y);
+
+        if (tr[y].lchild == x) {
+            tr[y].lchild = tr[x].father = 0;
+        }
+    }
+
+    int find(const int& u, const int& x) {
+        if (a[u] == x) return u;
+        if (tr[tr[u].lchild].max == x) return find(tr[u].lchild, x);
+        return find(tr[u].rchild, x);
+    }
+} lct;
+
+struct DSU : private std::vector<int> {
+    DSU(const int& _n)
+        : std::vector<int>(_n + 1) {
+        std::iota(begin(), end(), 0);
+    }
+
+    int find(const int& x) {
+        return x == at(x) ? x : at(x) = find(at(x));
+    }
+
+    bool check(const int& x, const int& y) {
+        return find(x) == find(y);
+    }
+
+    void merge(int x, int y) {
+        x = find(x);
+        y = find(y);
+
+        if (x != y) at(x) = y;
+    }
+};
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> n >> m >> q;
+
+    for (int i = 1, u, v, w; i <= m; i++) {
+        cin >> u >> v >> w;
+
+        edges[i] = {u, v, w, true};
+    }
+
+    std::sort(edges + 1, edges + 1 + m, [&](std::tuple<int, int, int, bool> a, std::tuple<int, int, int, bool> b) { return std::get<2>(a) < std::get<2>(b); });
+
+    for (int i = 1, u, v, w; i <= m; i++) {
+        std::tie(u, v, w, std::ignore) = edges[i];
+
+        a[n + i] = w;
+        lct.set(n + i, w);
+        id[u][v] = id[v][u] = i;
+    }
+
+    for (int i = 1, k, u, v; i <= q; i++) {
+        cin >> k >> u >> v;
+
+        qs[i] = {k, u, v};
+
+        if (k == 2) std::get<3>(edges[id[u][v]]) = false;
+    }
+
+    DSU dsu(n);
+    std::vector<int> ans;
+
+    for (int i = 1; i <= m; i++) {
+        int u, v;
+        bool available;
+
+        std::tie(u, v, std::ignore, available) = edges[i];
+
+        if (available && !dsu.check(u, v)) {
+            dsu.merge(u, v);
+            lct.link(u, n + i);
+            lct.link(v, n + i);
+        }
+    }
+
+    for (int i = q; i; i--) {
+        int k, u, v;
+
+        std::tie(k, u, v) = qs[i];
+
+        int s = lct.query(u, v);
+
+        if (k == 1) {
+            ans.emplace_back(s);
+        } else {
+            int t = lct.find(v, s),
+                u2, v2;
+
+            std::tie(u2, v2, std::ignore, std::ignore) = edges[t - n];
+
+            if (a[id[u][v] + n] < s) {
+                lct.cut(u2, t);
+                lct.cut(v2, t);
+                lct.link(u, id[u][v] + n);
+                lct.link(v, id[u][v] + n);
+            }
+        }
+    }
+
+    std::copy(ans.crbegin(), ans.crend(), std::ostream_iterator<decltype(ans)::value_type>(cout, "\n"));
+
+    return 0;
+}