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Kth par improvement #81

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Merged
lrvideckis merged 2 commits into from
Oct 16, 2024
Merged

Kth par improvement #81

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c8b7231
better constant
lrvideckis Oct 16, 2024
8efc4e7
[auto-verifier] verify commit c8b7231f87515850168b10a690a1c5881e4d585e
web-flow Oct 16, 2024
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6 changes: 3 additions & 3 deletions .verify-helper/timestamps.remote.json
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Original file line number Diff line number Diff line change
Expand Up @@ -70,7 +70,7 @@
"tests/library_checker_aizu_tests/handmade_tests/dsu_size.test.cpp": "2024-09-22 18:42:16 -0500",
"tests/library_checker_aizu_tests/handmade_tests/edge_cd_small_trees.test.cpp": "2024-09-21 13:04:45 -0500",
"tests/library_checker_aizu_tests/handmade_tests/fib_matrix_expo.test.cpp": "2024-09-23 11:20:46 -0500",
"tests/library_checker_aizu_tests/handmade_tests/lca_ladder_forest.test.cpp": "2024-10-07 00:04:04 -0700",
"tests/library_checker_aizu_tests/handmade_tests/lca_ladder_forest.test.cpp": "2024-10-16 11:17:12 -0700",
"tests/library_checker_aizu_tests/handmade_tests/manacher.test.cpp": "2024-10-06 21:59:37 -0700",
"tests/library_checker_aizu_tests/handmade_tests/merge_sort_trees.test.cpp": "2024-09-22 18:42:16 -0500",
"tests/library_checker_aizu_tests/handmade_tests/mobius.test.cpp": "2024-09-19 12:57:45 -0700",
Expand Down Expand Up @@ -138,8 +138,8 @@
"tests/library_checker_aizu_tests/trees/edge_cd_contour_range_update.test.cpp": "2024-09-22 18:42:16 -0500",
"tests/library_checker_aizu_tests/trees/edge_cd_count_paths_per_length.test.cpp": "2024-09-21 13:04:45 -0500",
"tests/library_checker_aizu_tests/trees/edge_cd_reroot_dp.test.cpp": "2024-09-21 13:04:45 -0500",
"tests/library_checker_aizu_tests/trees/kth_node_on_path.test.cpp": "2024-10-07 00:04:04 -0700",
"tests/library_checker_aizu_tests/trees/ladder_decomposition.test.cpp": "2024-09-27 10:44:49 -0500",
"tests/library_checker_aizu_tests/trees/kth_node_on_path.test.cpp": "2024-10-16 11:17:12 -0700",
"tests/library_checker_aizu_tests/trees/ladder_decomposition.test.cpp": "2024-10-16 11:17:12 -0700",
"tests/library_checker_aizu_tests/trees/lca_all_methods_aizu.test.cpp": "2024-10-07 00:04:04 -0700",
"tests/library_checker_aizu_tests/trees/lca_all_methods_lib_checker.test.cpp": "2024-10-07 00:04:04 -0700",
"tests/library_checker_aizu_tests/trees/subtree_isomorphism.test.cpp": "2024-09-19 12:57:45 -0700"
Expand Down
22 changes: 12 additions & 10 deletions library/trees/ladder_decomposition/linear_kth_par.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -5,21 +5,22 @@
//! int kth_par = kp.kth_par(v, k);
//! @endcode
//! kth_par = a node k edges up from v
//! @time O(3.5*n + q)
//! @space O(3.5*n)
//! @time O(n + q)
//! @space O(n)
struct linear_kth_par {
struct node {
int d, p = -1, idx, dl;
vi lad;
};
vector<node> t;
vi j;
vector<pii> j;
linear_kth_par(const vector<vi>& adj):
t(sz(adj)), j(2 * sz(t)) {
vi st;
int pos = 1;
auto add_j = [&]() -> void {
j[pos] = st[max(0, sz(st) - 1 - 2 * (pos & -pos))];
j[pos] = {st[max(0, sz(st) - 1 - 2 * (pos & -pos))],
st[max(0, sz(st) - 1 - 4 * (pos & -pos))]};
pos++;
};
auto dfs = [&](auto&& self, int v) -> void {
Expand All @@ -37,26 +38,27 @@ struct linear_kth_par {
}
st.pop_back();
};
rep(i, 0, sz(t)) if (t[i].p == -1) t[i].p = i,
dfs(dfs, i);
rep(i, 0, sz(t)) if (t[i].p == -1) dfs(dfs, i);
rep(i, 0, sz(t)) if (
t[i].p == i || t[t[i].p].dl != t[i].dl) {
t[i].p == -1 || t[t[i].p].dl != t[i].dl) {
int leaf = t[i].dl;
vi& lad = t[leaf].lad;
lad.resize(
min((t[leaf].d - t[i].d) * 7 / 2, t[leaf].d + 1),
min((t[leaf].d - t[i].d) * 2, t[leaf].d + 1),
leaf);
rep(k, 1, sz(lad)) lad[k] = t[lad[k - 1]].p;
}
}
int kth_par(int v, int k) {
assert(0 <= k && k <= t[v].d);
switch (k) {
case 0: return v;
case 1: return t[v].p;
case 2: return t[t[v].p].p;
default:
int i = 1 << __lg(k / 3),
leaf = t[j[(t[v].idx & -i) | i]].dl;
int i = 1 << __lg(k / 3);
auto [j1, j2] = j[(t[v].idx & -i) | i];
int leaf = t[t[v].d - t[j2].d <= k ? j2 : j1].dl;
return t[leaf].lad[k + t[leaf].d - t[v].d];
}
}
Expand Down