Linear rmq nits (#148)

* nits to linear lca

* [auto-verifier] verify commit 5e627d0

* fix buggy test

* [auto-verifier] verify commit 660858f

---------

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

Author: lrvideckis

.verify-helper/timestamps.remote.json

@@ -72,7 +72,7 @@
 "tests/library_checker_aizu_tests/handmade_tests/edge_cd_small_trees.test.cpp": "2025-04-27 21:47:37 -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": "2025-07-08 19:28:25 -0600",
-"tests/library_checker_aizu_tests/handmade_tests/lca_ladder_forest.test.cpp": "2025-02-10 23:30:47 -0700",
+"tests/library_checker_aizu_tests/handmade_tests/lca_ladder_forest.test.cpp": "2025-08-03 23:02:28 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/manacher.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/merge_st_and_wavelet.test.cpp": "2025-07-10 12:34:21 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/mobius.test.cpp": "2025-02-10 14:50:36 -0700",
@@ -133,9 +133,9 @@
 "tests/library_checker_aizu_tests/trees/edge_cd_count_paths_per_length.test.cpp": "2025-04-27 21:47:37 -0600",
 "tests/library_checker_aizu_tests/trees/edge_cd_reroot_dp.test.cpp": "2025-04-27 21:47:37 -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_linear.test.cpp": "2025-08-03 22:53:52 -0600",
 "tests/library_checker_aizu_tests/trees/kth_path_tree_lift.test.cpp": "2025-02-10 14:50:36 -0700",
-"tests/library_checker_aizu_tests/trees/lca_all_methods_aizu.test.cpp": "2025-02-10 14:50:36 -0700",
-"tests/library_checker_aizu_tests/trees/lca_all_methods_lib_checker.test.cpp": "2025-02-10 14:50:36 -0700",
+"tests/library_checker_aizu_tests/trees/lca_all_methods_aizu.test.cpp": "2025-08-03 22:53:52 -0600",
+"tests/library_checker_aizu_tests/trees/lca_all_methods_lib_checker.test.cpp": "2025-08-03 22:53:52 -0600",
 "tests/library_checker_aizu_tests/trees/subtree_isomorphism.test.cpp": "2024-12-15 14:34:10 -0600"
 }

library/trees/linear_lca.hpp

@@ -10,41 +10,35 @@
 //! @endcode
 //! @time O(n + q)
 //! @space O(n)
+int lsb(int x) { return x & -x; }
 struct linear_lca {
-  struct node {
-    int d, label, asc;
-  };
-  vector<node> t;
-  vi head;
+  int n;
+  vi d, in, asc, head;
   linear_lca(const auto& adj):
-    t(sz(adj)), head(sz(t) + 1) {
+    n(sz(adj)), d(n), in(n), asc(n), head(n + 1) {
     vector<pii> order;
     auto dfs = [&](auto&& self, int v, int p) -> void {
       order.emplace_back(v, p);
-      t[v].label = sz(order);
+      in[v] = sz(order);
       for (int u : adj[v])
         if (u != p) {
-          t[u].d = 1 + t[v].d;
+          d[u] = 1 + d[v];
           self(self, u, v);
-          head[t[u].label] = v;
-          if ((t[u].label & -t[u].label) >
-            (t[v].label & -t[v].label))
-            t[v].label = t[u].label;
+          head[in[u]] = v;
+          if (lsb(in[v]) < lsb(in[u])) in[v] = in[u];
         }
     };
-    rep(i, 0, sz(t)) if (t[i].d == 0) dfs(dfs, i, i);
-    for (auto [v, p] : order)
-      t[v].asc = t[p].asc | (t[v].label & -t[v].label);
+    dfs(dfs, 0, 0);
+    for (auto [v, p] : order) asc[v] = asc[p] | lsb(in[v]);
   }
   int lca(int u, int v) {
-    if (unsigned j = t[u].label ^ t[v].label; j) {
-      j = t[u].asc & t[v].asc & -bit_floor(j);
-      if (unsigned k = t[u].asc ^ j; k)
-        k = bit_floor(k), u = head[(t[u].label & -k) | k];
-      if (unsigned k = t[v].asc ^ j; k)
-        k = bit_floor(k), v = head[(t[v].label & -k) | k];
+    if (unsigned j = in[u] ^ in[v]; j) {
+      j = asc[u] & asc[v] & -bit_floor(j);
+      if (unsigned k = asc[u] ^ j; k)
+        k = bit_floor(k), u = head[(in[u] & -k) | k];
+      if (unsigned k = asc[v] ^ j; k)
+        k = bit_floor(k), v = head[(in[v] & -k) | k];
     }
-    return t[u].d < t[v].d ? u : v;
+    return d[u] < d[v] ? u : v;
   }
-#include "extra_members/dist_edges.hpp"
 };

tests/library_checker_aizu_tests/handmade_tests/lca_ladder_forest.test.cpp

@@ -6,10 +6,8 @@
 #include "../../../library/monotonic_stack/monotonic_stack.hpp"
 #include "../../../library/trees/tree_lift/tree_lift.hpp"
 #include "../../../library/trees/lca_rmq/lca_rmq.hpp"
-#include "../../../library/trees/linear_lca.hpp"
 #include "../../../library/trees/ladder_decomposition/ladder_decomposition.hpp"
 #include "../../../library/trees/ladder_decomposition/linear_kth_par.hpp"
-#include "../../../library/trees/linear_kth_path.hpp"
 int main() {
   cin.tie(0)->sync_with_stdio(0);
   for (int n = 1; n <= 100; n++) {
@@ -26,31 +24,20 @@ int main() {
     }
     tree_lift tl(adj);
     LCA lc(adj);
-    linear_lca lin_lca(adj);
     ladder lad(adj);
-    linear_kth_path lin_kth_path(adj);
     for (int i = 0; i < 100; i++) {
       int u = rnd<int>(0, n - 1);
       int v = rnd<int>(0, n - 1);
       if (u == v || !dsu.same_set(u, v)) continue;
       auto lca_1 = tl.lca(u, v);
       auto lca_2 = lc.lca(u, v);
-      auto lca_3 = lin_lca.lca(u, v);
       assert(lca_1 == lca_2);
-      assert(lca_1 == lca_3);
       assert(tl.dist_edges(u, v) == lc.dist_edges(u, v));
-      assert(
-        tl.dist_edges(u, v) == lin_lca.dist_edges(u, v));
       assert(
         tl.kth_path(u, v, 1) == lc.next_on_path(u, v));
-      assert(lin_kth_path.kth_path(u, v, 1) ==
-        lc.next_on_path(u, v));
       if (tl.t[u].d > tl.t[v].d) swap(u, v);
       auto res = tl.kth_par(v, tl.t[v].d - tl.t[u].d);
       assert(res == lad.kth_par(v, tl.t[v].d - tl.t[u].d));
-      assert(res ==
-        lin_kth_path.lin_kp.kth_par(v,
-          tl.t[v].d - tl.t[u].d));
       assert((u == res) == lc.in_subtree(u, v));
     }
   }