Shallowest decomp tree (#160)

* shallowest decomp tree

* [auto-verifier] verify commit 41b4a59

* nits

* [auto-verifier] verify commit b04851b

* revert constexpr -> const as it was causing build issues

* fix

---------

Co-authored-by: GitHub <noreply@github.com>

Author: lrvideckis

.verify-helper/timestamps.remote.json

@@ -144,5 +144,6 @@
 "tests/library_checker_aizu_tests/trees/kth_path_tree_lift.test.cpp": "2025-08-14 10:27:46 -0600",
 "tests/library_checker_aizu_tests/trees/lca_all_methods_aizu.test.cpp": "2025-08-21 12:17:27 -0600",
 "tests/library_checker_aizu_tests/trees/lca_all_methods_lib_checker.test.cpp": "2025-08-21 12:17:27 -0600",
+"tests/library_checker_aizu_tests/trees/shallowest_aizu_tree_height.test.cpp": "2025-08-28 13:09:33 -0600",
 "tests/library_checker_aizu_tests/trees/subtree_isomorphism.test.cpp": "2025-08-14 10:27:46 -0600"
 }

library/convolution/gcd_convolution.hpp

@@ -7,7 +7,7 @@
 //!   for all pairs (i,j) where gcd(i,j)==k
 //! @time O(n log n)
 //! @space O(n)
-constexpr int mod = 998'244'353;
+const int mod = 998'244'353;
 vi gcd_convolution(const vi& a, const vi& b) {
   int n = sz(a);
   vi c(n);

library/convolution/lcm_convolution.hpp

@@ -7,7 +7,7 @@
 //!   for all pairs (i,j) where lcm(i,j)==k
 //! @time O(n log n)
 //! @space O(n)
-constexpr int mod = 998'244'353;
+const int mod = 998'244'353;
 vi lcm_convolution(const vi& a, const vi& b) {
   int n = sz(a);
   vector<ll> sum_a(n), sum_b(n);

library/data_structures/seg_tree_uncommon/implicit.hpp

@@ -8,7 +8,7 @@ template<int N> struct implicit_seg_tree {
     if (l[0] == r[0]) return {l[0], l[1] + r[1]};
     return min(l, r);
   }
-  static constexpr dt unit{LLONG_MAX, 0LL};
+  const dt unit{LLONG_MAX, 0LL};
   struct node {
     dt num;
     ll lazy = 0;

library/math/fibonacci.hpp

@@ -11,7 +11,7 @@
 //! @endcode
 //! @time O(log n)
 //! @space O(log n)
-constexpr int mod = 998'244'353;
+const int mod = 998'244'353;
 array<ll, 2> fib(ll n) {
   if (n == 0) return {0LL, 1LL};
   auto [x, y] = fib(n >> 1);

library/math/mod_int.hpp

@@ -1,5 +1,5 @@
 #pragma once
-constexpr int mod = 998244353;
+const int mod = 998244353;
 //! https://github.com/kth-competitive-programming/kactl/blob/main/content/number-theory/ModularArithmetic.h
 //! https://codeforces.com/blog/entry/122714
 struct mint {

library/math/n_choose_k/grow.hpp

@@ -1,5 +1,5 @@
 #pragma once
-constexpr int mod = 17; //!< must be prime
+const int mod = 17; //!< must be prime
 struct comb {
   ll inv = 1, fact = 1, inv_fact = 1;
 };

library/math/n_choose_k/pascals_identity.hpp

@@ -1,5 +1,5 @@
 #pragma once
-constexpr int mod = 17; //!< composite ok
+const int mod = 17; //!< composite ok
 vector<vector<ll>> ch(1010); //!< ch[n][k] = n choose k
 rep(i, 0, sz(ch)) {
   ch[i].resize(i + 1, 1);

library/math/partitions.hpp

@@ -1,5 +1,5 @@
 #pragma once
-constexpr int mod = 998'244'353;
+const int mod = 998'244'353;
 //! https://oeis.org/A000041
 //! @code
 //!   auto p = partitions(n);

library/trees/shallowest_decomp_tree.hpp

@@ -0,0 +1,31 @@
+#pragma once
+//! https://codeforces.com/blog/entry/125018
+//! @code
+//!   vector<basic_string<int>> adj(n);
+//!   shallowest(adj, [&](int cent) {
+//!   });
+//! @endcode
+//! @time O(n log n)
+//! @space O(n)
+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 (const auto& vec : order | views::reverse)
+    for (int v : vec) {
+      f(v);
+      for (int u : adj[v])
+        iter_swap(ranges::find(adj[u], v), rbegin(adj[u])),
+          adj[u].pop_back();
+    }
+}