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Merged
lrvideckis merged 4 commits into from
Oct 18, 2024
Merged

Ladder optimization #83

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1452e4f
linearize ladder array
lrvideckis Oct 18, 2024
0de555b
[auto-verifier] verify commit 1452e4f5059c3cb46c93f74a7a3635a466f95c9c
web-flow Oct 18, 2024
4747472
nit
lrvideckis Oct 18, 2024
86803fb
consistency
lrvideckis Oct 18, 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": "2024-10-17 00:12:45 -0700",
"tests/library_checker_aizu_tests/handmade_tests/lca_ladder_forest.test.cpp": "2024-10-17 18:15:46 -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": "2024-10-17 00:12:45 -0700",
"tests/library_checker_aizu_tests/trees/ladder_decomposition.test.cpp": "2024-10-17 00:12:45 -0700",
"tests/library_checker_aizu_tests/trees/kth_node_on_path.test.cpp": "2024-10-17 18:15:46 -0700",
"tests/library_checker_aizu_tests/trees/ladder_decomposition.test.cpp": "2024-10-17 18:15:46 -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
17 changes: 8 additions & 9 deletions library/trees/ladder_decomposition/ladder_decomposition.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -10,13 +10,13 @@
//! @endcode
struct ladder {
int n;
vector<vi> b_tbl, l_tbl;
vi d, p, dl; //!< deepest leaf
vector<vi> b_tbl;
vi d, p, dl, idx_l, l_tbl;
//! @param adj forest (rooted or unrooted)
//! @time O(n log n)
//! @space O(n log n) for b_tbl. Everything else is O(n)
ladder(const vector<vi>& adj):
n(sz(adj)), l_tbl(n), d(n), p(n, -1), dl(n) {
n(sz(adj)), d(n), p(n, -1), dl(n), idx_l(n) {
auto dfs = [&](auto&& self, int v) -> void {
dl[v] = v;
for (int u : adj[v])
Expand All @@ -29,11 +29,10 @@ struct ladder {
rep(i, 0, n) {
if (p[i] == -1) p[i] = i, dfs(dfs, i);
if (p[i] == i || dl[p[i]] != dl[i]) {
int leaf = dl[i];
vi& lad = l_tbl[leaf];
lad.resize(min(2 * (d[leaf] - d[i]), d[leaf] + 1),
leaf);
rep(j, 1, sz(lad)) lad[j] = p[lad[j - 1]];
int v = dl[i], len = (d[v] - d[i]) * 2;
idx_l[v] = sz(l_tbl) + d[v];
for (; v != -1 && len--; v = p[v])
l_tbl.push_back(v);
}
}
b_tbl = treeJump(p);
Expand All @@ -50,6 +49,6 @@ struct ladder {
int bit = __lg(k);
v = b_tbl[bit][v], k -= (1 << bit);
int leaf = dl[v];
return l_tbl[leaf][k + d[leaf] - d[v]];
return l_tbl[idx_l[leaf] + k - d[v]];
}
};
22 changes: 10 additions & 12 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 @@ -9,11 +9,11 @@
//! @space O(n)
struct linear_kth_par {
struct node {
int d, p = -1, idx, dl;
vi lad;
int d, p = -1, dl, idx_j, idx_l;
};
vector<node> t;
vector<pii> j;
vi l_tbl;
linear_kth_par(const vector<vi>& adj):
t(sz(adj)), j(2 * sz(t)) {
vi st;
Expand All @@ -25,7 +25,7 @@ struct linear_kth_par {
};
auto dfs = [&](auto&& self, int v) -> void {
st.push_back(v);
t[v].idx = pos, t[v].dl = v;
t[v].idx_j = pos, t[v].dl = v;
add_j();
for (int u : adj[v])
if (u != t[v].p) {
Expand All @@ -40,12 +40,10 @@ struct linear_kth_par {
rep(i, 0, sz(t)) {
if (t[i].p == -1) dfs(dfs, i);
if (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) * 2, t[leaf].d + 1),
leaf);
rep(k, 1, sz(lad)) lad[k] = t[lad[k - 1]].p;
int v = t[i].dl, len = (t[v].d - t[i].d) * 2;
t[v].idx_l = sz(l_tbl) + t[v].d;
for (; v != -1 && len--; v = t[v].p)
l_tbl.push_back(v);
}
}
}
Expand All @@ -57,9 +55,9 @@ struct linear_kth_par {
case 2: return t[t[v].p].p;
default:
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];
auto [j1, j2] = j[(t[v].idx_j & -i) | i];
int up = t[v].d - t[j2].d <= k ? j2 : j1;
return l_tbl[t[t[up].dl].idx_l + k - t[v].d];
}
}
};