Edge cd upd (#131)

* adding progress

* [auto-verifier] verify commit 5072068

* updates

* Delete library/trees/edge_centroid_decomp_uncommon/README.md

* format

* fix

* update complexity

---------

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

Author: lrvideckis

.verify-helper/timestamps.remote.json

@@ -65,7 +65,7 @@
 "tests/library_checker_aizu_tests/graphs/two_edge_components.test.cpp": "2025-02-10 23:30:47 -0700",
 "tests/library_checker_aizu_tests/handmade_tests/count_paths_forest.test.cpp": "2024-12-15 14:34:10 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/dsu_size.test.cpp": "2024-12-14 19:50:29 -0600",
-"tests/library_checker_aizu_tests/handmade_tests/edge_cd_small_trees.test.cpp": "2024-12-15 17:01:11 -0600",
+"tests/library_checker_aizu_tests/handmade_tests/edge_cd_small_trees.test.cpp": "2025-04-22 19:30:56 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/fib_matrix_expo.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/functional_graph.test.cpp": "2025-02-10 23:30:47 -0700",
 "tests/library_checker_aizu_tests/handmade_tests/lca_ladder_forest.test.cpp": "2025-02-10 23:30:47 -0700",
@@ -124,10 +124,10 @@
 "tests/library_checker_aizu_tests/strings/trie.test.cpp": "2024-12-05 10:41:42 -0600",
 "tests/library_checker_aizu_tests/strings/wildcard_pattern_matching.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/trees/count_paths_per_length.test.cpp": "2024-12-15 14:34:10 -0600",
-"tests/library_checker_aizu_tests/trees/edge_cd_contour_range_query.test.cpp": "2024-12-15 17:01:11 -0600",
-"tests/library_checker_aizu_tests/trees/edge_cd_contour_range_update.test.cpp": "2024-12-15 17:01:11 -0600",
-"tests/library_checker_aizu_tests/trees/edge_cd_count_paths_per_length.test.cpp": "2024-12-15 17:01:11 -0600",
-"tests/library_checker_aizu_tests/trees/edge_cd_reroot_dp.test.cpp": "2024-12-15 17:01:11 -0600",
+"tests/library_checker_aizu_tests/trees/edge_cd_contour_range_query.test.cpp": "2025-04-22 19:30:56 -0600",
+"tests/library_checker_aizu_tests/trees/edge_cd_contour_range_update.test.cpp": "2025-04-22 19:30:56 -0600",
+"tests/library_checker_aizu_tests/trees/edge_cd_count_paths_per_length.test.cpp": "2025-04-22 19:30:56 -0600",
+"tests/library_checker_aizu_tests/trees/edge_cd_reroot_dp.test.cpp": "2025-04-22 19:30:56 -0600",
 "tests/library_checker_aizu_tests/trees/kth_path_ladder.test.cpp": "2025-02-10 23:30:47 -0700",
 "tests/library_checker_aizu_tests/trees/kth_path_linear.test.cpp": "2025-02-10 23:30:47 -0700",
 "tests/library_checker_aizu_tests/trees/kth_path_tree_lift.test.cpp": "2025-02-10 14:50:36 -0700",

library/trees/edge_cd.hpp

@@ -19,44 +19,41 @@
 //!   });
 //! @endcode
 //! handle single-edge-paths separately
-//! @time O(n log1.5 n)
+//! @time O(n logφ n)
 //! @space O(n)
 template<class F, class G> struct edge_cd {
   vector<G> adj;
   F f;
-  vi sub_sz;
+  vi siz;
   edge_cd(const vector<G>& adj, F f):
-    adj(adj), f(f), sub_sz(sz(adj)) {
-    dfs(0, sz(adj));
+    adj(adj), f(f), siz(sz(adj)) {
+    dfs(0, sz(adj) - 1);
   }
-  int find_cent(int v, int p, int siz) {
-    sub_sz[v] = 1;
+  int find_cent(int v, int p, int m) {
+    siz[v] = 1;
     for (int u : adj[v])
       if (u != p) {
-        int cent = find_cent(u, v, siz);
+        int cent = find_cent(u, v, m);
         if (cent != -1) return cent;
-        sub_sz[v] += sub_sz[u];
+        siz[v] += siz[u];
       }
     if (p == -1) return v;
-    return 2 * sub_sz[v] >= siz
-           ? sub_sz[p] = siz - sub_sz[v],
-             v : -1;
+    return 2 * siz[v] > m     ? siz[p] = m + 1 - siz[v],
+                            v : -1;
   }
-  void dfs(int v, int siz) {
-    if (siz <= 2) return;
-    v = find_cent(v, -1, siz);
+  void dfs(int v, int m) {
+    if (m < 2) return;
+    v = find_cent(v, -1, m);
     int sum = 0;
     auto it = partition(all(adj[v]), [&](int u) {
-      bool ret = 2 * sum + sub_sz[u] < siz - 1 &&
-        3 * (sum + sub_sz[u]) <= 2 * (siz - 1);
-      if (ret) sum += sub_sz[u];
-      return ret;
+      ll x = sum + siz[u];
+      return x * x < m * (m - x) ? sum += siz[u], 1 : 0;
     });
     f(adj, v, it - begin(adj[v]));
     G oth(it, end(adj[v]));
     adj[v].erase(it, end(adj[v]));
-    dfs(v, sum + 1);
+    dfs(v, sum);
     swap(adj[v], oth);
-    dfs(v, siz - sum);
+    dfs(v, m - sum);
   }
 };

library/trees/edge_centroid_decomp_uncommon/README.md

@@ -1,7 +1,7 @@
 #pragma once
 #include "../../data_structures/bit.hpp"
-#include "sum_adjacent.hpp"
 #include "../edge_cd.hpp"
+#include "sum_adjacent.hpp"
 //! https://judge.yosupo.jp/problem/vertex_add_range_contour_sum_on_tree
 struct contour_range_query {
   int n;
@@ -10,8 +10,8 @@ struct contour_range_query {
   vector<array<BIT, 2>> bits;
   //! @param adj unrooted, undirected tree
   //! @param a a[v] = initial number for node v
-  //! @time O(n log1.5 n)
-  //! @space O(n log1.5 n) for `info` and `bits`
+  //! @time O(n logφ n)
+  //! @space O(n logφ n) for `info` and `bits`
   contour_range_query(const vector<vi>& adj,
     const vector<ll>& a):
     n(sz(a)), sum_a(adj, a), info(n) {
@@ -34,7 +34,7 @@ struct contour_range_query {
   }
   //! @param v node
   //! @param delta number to add to node v's number
-  //! @time O(log1.5(n) * log2(n))
+  //! @time O(logφ(n) * log2(n))
   //! @space O(1)
   void update(int v, ll delta) {
     sum_a.update(v, delta);
@@ -46,7 +46,7 @@ struct contour_range_query {
   //! @returns sum of node u's number over all u such that
   //! l
   //! <= dist_edges(u, v) < r
-  //! @time O(log1.5(n) * log2(n))
+  //! @time O(logφ(n) * log2(n))
   //! @space O(1)
   ll query(int v, int l, int r) {
     ll sum = 0;

library/trees/edge_centroid_decomp_uncommon/contour_range_query.hpp

@@ -1,7 +1,7 @@
 #pragma once
 #include "../../data_structures/bit_uncommon/rupq.hpp"
-#include "sum_adjacent.hpp"
 #include "../edge_cd.hpp"
+#include "sum_adjacent.hpp"
 //! https://judge.yosupo.jp/problem/vertex_get_range_contour_add_on_tree
 struct contour_range_update {
   int n;
@@ -11,8 +11,8 @@ struct contour_range_update {
   vector<array<bit_rupq, 2>> bits;
   //! @param adj unrooted, undirected tree
   //! @param a a[v] = initial number for node v
-  //! @time O(n log1.5 n)
-  //! @space O(n log1.5 n) for `info` and `bits`
+  //! @time O(n logφ n)
+  //! @space O(n logφ n) for `info` and `bits`
   contour_range_update(const vector<vi>& adj,
     const vector<ll>& a):
     n(sz(a)), a(a), sum_a(adj, vector<ll>(n)), info(n) {
@@ -34,7 +34,7 @@ struct contour_range_update {
   }
   //! @param v,l,r,delta add delta to all nodes u such
   //! that l <= dist_edges(v, u) < r
-  //! @time O(log1.5(n) * log2(n))
+  //! @time O(logφ(n) * log2(n))
   //! @space O(1)
   void update(int v, int l, int r, ll delta) {
     if (l <= 0 && 0 < r) a[v] += delta;
@@ -48,7 +48,7 @@ struct contour_range_update {
   }
   //! @param v node
   //! @returns number of node v
-  //! @time O(log1.5(n) * log2(n))
+  //! @time O(logφ(n) * log2(n))
   //! @space O(1)
   ll query(int v) {
     ll sum = a[v] + sum_a.query(v);

library/trees/edge_centroid_decomp_uncommon/contour_range_update.hpp

@@ -4,7 +4,7 @@
 //! @param adj unrooted, connected tree
 //! @returns array `num_paths` where `num_paths[i]` = # of
 //! paths in tree with `i` edges. `num_paths[1]` = # edges
-//! @time O(n * log1.5(n) * log2(n))
+//! @time O(n * logφ(n) * log2(n))
 //! @space this function allocates/returns various vectors
 //! which are each O(n)
 vector<ll> count_paths_per_length(const vector<vi>& adj) {

library/trees/edge_centroid_decomp_uncommon/count_paths_per_length.hpp

@@ -11,12 +11,36 @@ void edge_cd_asserts(const vector<vi>& adj, int cent,
   int sz_all = dfs(dfs, cent, -1);
   assert(sz_all >= 3);
   array<int, 2> cnts = {0, 0};
+  array<int, 2> max_cnt = {0, 0};
   for (int i = 0; i < sz(adj[cent]); i++) {
     int sz_subtree = dfs(dfs, adj[cent][i], cent);
     assert(2 * sz_subtree <= sz_all);
     cnts[i < split] += sz_subtree;
+    max_cnt[i < split] =
+      max(max_cnt[i < split], sz_subtree);
   }
   assert(cnts[0] + cnts[1] + 1 == sz_all);
-  for (int i = 0; i < 2; i++)
-    assert(0 < cnts[i] && cnts[i] <= 2 * cnts[!i]);
+  if (sz_all == 4) return;
+  // a is the number of edges in the smaller edge set
+  // b is the number of edges in the larger edge set
+  // so we know 1/2 <= b/(a+b)
+  // returns true iff b/(a+b) <= 1/phi
+  auto is_balanced = [&](ll a, ll b) -> bool {
+    assert(a <= b);
+    return b * b <= a * (a + b);
+  };
+  if (cnts[0] > cnts[1]) {
+    swap(cnts[0], cnts[1]);
+    swap(max_cnt[0], max_cnt[1]);
+  }
+  if (!is_balanced(cnts[0], cnts[1])) {
+    int a = max_cnt[1];
+    int b = cnts[1] - max_cnt[1];
+    assert(a > 0);
+    assert(b > 0);
+    if (a > b) swap(a, b);
+    assert(is_balanced(a, b));
+    assert(!is_balanced(a, cnts[0] + b));
+    assert(!is_balanced(b, cnts[0] + a));
+  }
 }

tests/library_checker_aizu_tests/edge_cd_asserts.hpp

@@ -1,4 +1,5 @@
-#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/ITP1_1_A"
+#define PROBLEM \
+  "https://onlinejudge.u-aizu.ac.jp/problems/ITP1_1_A"
 #include "../template.hpp"
 #include "../../../library/contest/random.hpp"
 #include "../../../library/graphs/functional_graph_processor.hpp"
@@ -8,7 +9,7 @@ struct functional_graph_processor {
     init(sz(next));
     build(next);
   }
-  template <class Graph_t>
+  template<class Graph_t>
   functional_graph_processor(const Graph_t &g) {
     init(g.n);
     build(g);
@@ -100,31 +101,30 @@ struct functional_graph_processor {
   }
   int n;
   vector<vector<int>> cycle;
-  vector<int> cycle_id;        // id of the cycle it belongs to,
-                               // -1 if not part of one
-  vector<int> cycle_pos;       // position in its cycle, -1 if
-                               // not part of one
-  vector<int> cycle_prev;      // previous vertex in its cycle,
-                               // -1 if not part of one
-  vector<int> component_size;  // size of its weakly
-                               // connected component
-  vector<int> root_of;         // first reachable node in a cycle
-  vector<int> depth;           // distance to its root
-  vector<vector<int>> abr;     // forest of arborescences of reversed edges not
-                               // on the cycles
-  vector<int> order;           // dfs order of abr
-  vector<int> pos;             // pos in the dfs order
-  vector<int> end;             // [pos[u], end[u]) denotes the subtree
-  vector<int> size;            // size of the subtree in abr
+  vector<int> cycle_id; // id of the cycle it belongs to,
+                        // -1 if not part of one
+  vector<int> cycle_pos; // position in its cycle, -1 if
+                         // not part of one
+  vector<int> cycle_prev; // previous vertex in its cycle,
+                          // -1 if not part of one
+  vector<int> component_size; // size of its weakly
+                              // connected component
+  vector<int> root_of; // first reachable node in a cycle
+  vector<int> depth; // distance to its root
+  vector<vector<int>>
+    abr; // forest of arborescences of reversed edges not
+         // on the cycles
+  vector<int> order; // dfs order of abr
+  vector<int> pos; // pos in the dfs order
+  vector<int> end; // [pos[u], end[u]) denotes the subtree
+  vector<int> size; // size of the subtree in abr
 };
-
 bool equal(const basic_string<int> &a, const vi &b) {
   if (sz(a) != sz(b)) return 0;
   for (int i = 0; i < sz(a); i++)
     if (a[i] != b[i]) return 0;
   return 1;
 }
-
 int main() {
   cin.tie(0)->sync_with_stdio(0);
   for (int num_tests = 100; num_tests--;) {
@@ -135,19 +135,23 @@ int main() {
     functional_graph_processor fgp(a);
     assert(cycle == fgp.cycle);
     for (int i = 0; i < n; i++) {
-      int root = cycle[t[i].root_of.first][t[i].root_of.second];
+      int root =
+        cycle[t[i].root_of.first][t[i].root_of.second];
       assert(root == fgp.root_of[i]);
       assert(equal(t[i].childs, fgp.abr[i]));
       assert((root == i) == (fgp.cycle_id[i] != -1));
       if (root == i) {
         assert(t[i].root_of.first == fgp.cycle_id[i]);
         assert(t[i].root_of.second == fgp.cycle_pos[i]);
         int cyc_len = ssize(cycle[t[i].root_of.first]);
-        assert(cycle[t[i].root_of.first][(t[i].root_of.second + 1) % cyc_len] ==
-               a[i]);
+        assert(
+          cycle[t[i].root_of.first]
+               [(t[i].root_of.second + 1) % cyc_len] ==
+          a[i]);
         assert(fgp.cycle_prev[i] ==
-               cycle[t[i].root_of.first]
-                    [(t[i].root_of.second - 1 + cyc_len) % cyc_len]);
+          cycle[t[i].root_of.first]
+               [(t[i].root_of.second - 1 + cyc_len) %
+                 cyc_len]);
       } else {
         assert(fgp.cycle_prev[i] == -1);
       }

tests/library_checker_aizu_tests/handmade_tests/functional_graph.test.cpp

@@ -26,7 +26,8 @@ int main() {
       int64_t val2 = unordered.shrink(val1);
       assert(val1 == val2);
       for (int64_t v : unordered.b)
-        assert((bit_floor((unsigned long long)v) & val2) == 0);
+        assert(
+          (bit_floor((unsigned long long)v) & val2) == 0);
       bool inserted_unordered = unordered.insert(elem);
       bool inserted_ordered_ll = ordered_ll.insert(elem);
       bool inserted_ordered_bitset =

tests/library_checker_aizu_tests/math/xor_basis.test.cpp

@@ -30,7 +30,6 @@ rm ../library/monotonic_stack/mono_stack_ri.png || exit 1
 rm ../library/strings/manacher/longest_palindrome_query.hpp || exit 1
 rm ../library/trees/centroid_decomp_uncommon/count_paths_per_length.hpp || exit 1
 rm ../library/trees/centroid_decomp_uncommon/count_paths_per_node.hpp || exit 1
-rm ../library/trees/edge_centroid_decomp_uncommon/README.md || exit 1
 rm ../library/trees/edge_centroid_decomp_uncommon/contour_range_query.hpp || exit 1
 rm ../library/trees/edge_centroid_decomp_uncommon/contour_range_update.hpp || exit 1
 rm ../library/trees/edge_centroid_decomp_uncommon/count_paths_per_length.hpp || exit 1