P4180 [BJWC2010] 严格次小生成树

https://www.luogu.com.cn/record/98709657

Luogu/P4180/P4180.cpp

@@ -0,0 +1,265 @@
+#include <iostream>
+#include <algorithm>
+#include <limits>
+#include <numeric>
+#include <queue>
+#include <stack>
+#include <tuple>
+#include <utility>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 1e5 + 5,
+          M = 3e5 + 5;
+
+int n, m, a[N + M];
+long long res, ans = std::numeric_limits<long long>::max();
+std::tuple<int, int, int> edges[M];
+bool vis[M];
+
+class LinkCutTree {
+  private:
+    struct node {
+        size_t lchild, rchild, father;
+        int max1, max2;
+        bool reversed;
+
+        node()
+            : lchild(0),
+              rchild(0),
+              father(0),
+              max1(0),
+              max2(0),
+              reversed(false) {}
+
+        size_t& child(const unsigned& x) {
+            return !x ? lchild : rchild;
+        }
+    } tr[N + M];
+
+    void pushup(const size_t& u) {
+        tr[u].max1 = a[u];
+
+        if (tr[u].max1 < tr[tr[u].lchild].max1) {
+            tr[u].max2 = tr[u].max1;
+            tr[u].max1 = tr[tr[u].lchild].max1;
+        } else if (tr[u].max1 > tr[tr[u].lchild].max1) {
+            tr[u].max2 = std::max(tr[u].max2, tr[tr[u].lchild].max1);
+        }
+
+        if (tr[u].max1 < tr[tr[u].rchild].max1) {
+            tr[u].max2 = tr[u].max1;
+            tr[u].max1 = tr[tr[u].rchild].max1;
+        } else if (tr[u].max1 > tr[tr[u].rchild].max1) {
+            tr[u].max2 = std::max(tr[u].max2, tr[tr[u].rchild].max1);
+        }
+
+        tr[u].max2 = std::max({tr[u].max2, tr[tr[u].lchild].max2, tr[tr[u].rchild].max2});
+    }
+
+    void pushdown(const size_t& u) {
+        if (!tr[u].reversed) return;
+
+        std::swap(tr[u].lchild, tr[u].rchild);
+        tr[tr[u].lchild].reversed = !tr[tr[u].lchild].reversed;
+        tr[tr[u].rchild].reversed = !tr[tr[u].rchild].reversed;
+        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 = !tr[u].reversed;
+    }
+
+    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:
+    bool check(const int& x, const int& y) {
+        return find_root(x) == find_root(y);
+    }
+
+    std::pair<int, int> query(const int& x, const int& y) {
+        split(x, y);
+
+        return {tr[y].max1, tr[y].max2};
+    }
+
+    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;
+        }
+    }
+} 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;
+
+    for (int i = 1; i <= m; ++i) {
+        int u, v, w;
+
+        cin >> u >> v >> w;
+
+        edges[i] = {u, v, w};
+    }
+
+    std::sort(edges + 1, edges + m + 1, [](const std::tuple<int, int, int>& a, const std::tuple<int, int, int>& b) {
+        return std::get<2>(a) < std::get<2>(b);
+    });
+
+    DSU dsu(n);
+
+    for (int i = 1; i <= m; i++) {
+        int u = std::get<0>(edges[i]),
+            v = std::get<1>(edges[i]),
+            x = dsu.find(u),
+            y = dsu.find(v),
+            w = std::get<2>(edges[i]);
+
+        a[n + i] = w;
+
+        if (x != y) {
+            dsu.merge(x, y);
+            lct.link(u, i + n);
+            lct.link(i + n, v);
+            res += w;
+            vis[i] = true;
+        }
+    }
+
+    for (int i = 1; i <= m; i++) {
+        if (vis[i]) continue;
+
+        int u, v, w;
+
+        std::tie(u, v, w) = edges[i];
+
+        if (u == v) continue;
+
+        auto max = lct.query(u, v);
+
+        if (w > max.first) {
+            ans = std::min(ans, static_cast<long long>(w) - max.first);
+        } else {
+            ans = std::min(ans, static_cast<long long>(w) - max.second);
+        }
+    }
+
+    cout << res + ans << endl;
+
+    return 0;
+}