shallowest decomp tree

Author: lrvideckis

library/trees/shallowest_decomp_tree.hpp

@@ -0,0 +1,25 @@
+#pragma once
+void shallowest(auto& adj, auto f) {
+  vector<vi> order(bit_width(size(adj)));
+  auto dfs = [&](auto&& self, int v, int p) -> int {
+    int once = 0, twice = 0;
+    for (int u : adj[v])
+      if (u != p) {
+        int dp = self(self, u, v);
+        twice |= once & dp, once |= dp;
+      }
+    auto dp = (once | (bit_ceil(twice + 1u) - 1)) + 1;
+    order[countr_zero(dp)].push_back(v);
+    return dp;
+  };
+  dfs(dfs, 0, 0);
+  for (auto& vec : order | views::reverse)
+    for (int cent : vec) {
+      f(cent);
+      for (int v : adj[cent]) {
+        iter_swap(ranges::find(adj[v], cent),
+          rbegin(adj[v]));
+        adj[v].pop_back();
+      }
+    }
+}

tests/library_checker_aizu_tests/trees/shallowest_aizu_tree_height.test.cpp

@@ -0,0 +1,45 @@
+#define PROBLEM \
+  "https://onlinejudge.u-aizu.ac.jp/problems/GRL_5_B"
+#include "../template.hpp"
+#include "../../../library/trees/shallowest_decomp_tree.hpp"
+int main() {
+  cin.tie(0)->sync_with_stdio(0);
+  int n;
+  cin >> n;
+  vector<vector<int>> adj(n);
+  map<pair<int, int>, int> weight;
+  for (int i = 0; i < n - 1; i++) {
+    int u, v, w;
+    cin >> u >> v >> w;
+    weight[{u, v}] = w;
+    weight[{v, u}] = w;
+    adj[u].push_back(v);
+    adj[v].push_back(u);
+  }
+  vector<int> res(n);
+  shallowest(adj, [&](int cent) {
+    int lowest = 0;
+    int curr_lowest = 0;
+    auto dfs = [&](auto&& self, int v, int p,
+                 int height) -> void {
+      res[v] = max(res[v], height + lowest);
+      res[cent] = max(res[cent], height);
+      curr_lowest = max(curr_lowest, height);
+      for (int u : adj[v])
+        if (u != p)
+          self(self, u, v, height + weight[{u, v}]);
+    };
+    for (int v : adj[cent]) {
+      curr_lowest = 0;
+      dfs(dfs, v, cent, weight[{v, cent}]);
+      lowest = max(lowest, curr_lowest);
+    }
+    lowest = 0;
+    for (int v : adj[cent] | views::reverse) {
+      curr_lowest = 0;
+      dfs(dfs, v, cent, weight[{v, cent}]);
+      lowest = max(lowest, curr_lowest);
+    }
+  });
+  for (int i = 0; i < n; i++) cout << res[i] << '\n';
+}