D - Best Edge Weight

https://codeforces.com/contest/827/submission/188272065

Codeforces/827/D/D.cpp

@@ -0,0 +1,304 @@
+#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 = 5e5 + 5;
+const int INF = 0x3f3f3f3f;
+
+int n, m, fa[N], ans[N];
+std::tuple<int, int, int, int> edges[N];
+std::vector<int> g[N];
+std::vector<std::tuple<int, int, int>> qs;
+int dep[N], siz[N], son[N], top[N];
+std::priority_queue<
+    std::pair<int, int>,
+    std::vector<std::pair<int, int>>,
+    std::greater<std::pair<int, int>>>
+    q[N];
+
+class LinkCutTree {
+  private:
+    struct node {
+        size_t lchild, rchild, father;
+        int val, max;
+        bool reversed;
+
+        node()
+            : lchild(0),
+              rchild(0),
+              father(0),
+              val(0),
+              max(0),
+              reversed(false) {}
+
+        size_t& child(const unsigned& x) {
+            return !x ? lchild : rchild;
+        }
+    } tr[N << 1];
+
+    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 = !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);
+    }
+
+    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;
+        }
+    }
+
+    void set(const int& x, const int& y) {
+        tr[x].max = tr[x].val = y;
+    }
+} lct;
+
+int find(const int& x) {
+    return fa[x] == x ? x : fa[x] = find(fa[x]);
+}
+
+void dfs1(int u, int f) {
+    dep[u] = dep[f] + 1;
+    siz[u] = 1;
+    fa[u] = f;
+
+    for (int v : g[u]) {
+        if (v == f) continue;
+
+        dfs1(v, u);
+
+        siz[u] += siz[v];
+
+        if (siz[son[u]] < siz[v]) son[u] = v;
+    }
+}
+
+void dfs2(int u, int t) {
+    top[u] = t;
+
+    if (!son[u]) return;
+
+    dfs2(son[u], t);
+
+    for (int v : g[u]) {
+        if (v == fa[u]) continue;
+        if (v == son[u]) continue;
+
+        dfs2(v, v);
+    }
+}
+
+int lca(int u, int v) {
+    while (top[u] != top[v]) {
+        if (dep[top[u]] < dep[top[v]]) std::swap(u, v);
+        u = fa[top[u]];
+    }
+
+    return dep[u] < dep[v] ? u : v;
+}
+
+void dfs3(int u) {
+    for (int v : g[u]) {
+        if (v == fa[u]) continue;
+
+        dfs3(v);
+
+        if (q[v].size() > q[u].size()) std::swap(q[u], q[v]);
+
+        while (!q[v].empty()) {
+            if (dep[q[v].top().second] <= dep[u]) q[u].emplace(q[v].top());
+            q[v].pop();
+        }
+    }
+
+    while (!q[u].empty() && dep[q[u].top().second] > dep[u]) q[u].pop();
+    if (u > n && !q[u].empty()) ans[u - n] = q[u].top().first;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    std::iota(fa, fa + N, 0);
+    std::fill(std::begin(ans), std::end(ans), -1);
+
+    cin >> n >> m;
+
+    for (int i = 1, u, v, w; i <= m; i++) {
+        cin >> u >> v >> w;
+
+        edges[i] = {u, v, w, i};
+    }
+
+    std::sort(edges + 1, edges + 1 + m, [&](const std::tuple<int, int, int, int>& a, const std::tuple<int, int, int, int>& b) {
+        return std::get<2>(a) < std::get<2>(b);
+    });
+
+    for (int i = 1; i <= m; i++) {
+        int u, v, w, id;
+
+        std::tie(u, v, w, id) = edges[i];
+
+        int x = find(u),
+            y = find(v);
+
+        lct.set(id + n, w);
+
+        if (x != y) {
+            fa[x] = y;
+            lct.link(u, id + n);
+            lct.link(id + n, v);
+            g[u].emplace_back(id + n);
+            g[v].emplace_back(id + n);
+            g[id + n].emplace_back(u);
+            g[id + n].emplace_back(v);
+        } else {
+            ans[id] = lct.query(v, u) - 1;
+            qs.emplace_back(u, v, w - 1);
+        }
+    }
+
+    std::fill(std::begin(fa), std::end(fa), 0);
+    dfs1(1, 0);
+    dfs2(1, 1);
+
+    for (auto o : qs) {
+        int u, v, w;
+
+        std::tie(u, v, w) = o;
+
+        int x = lca(u, v);
+
+        if (u != x) q[u].emplace(w, x);
+        if (v != x) q[v].emplace(w, x);
+    }
+
+    dfs3(1);
+
+    std::copy_n(ans + 1, m, std::ostream_iterator<int>(cout, " "));
+
+    cout << endl;
+
+    return 0;
+}