Schieber-Vishkin LCA
木上の LCA を build: O(N), query: O(1) で処理する実装です。
Interface
| SchieberVishkinLCA lca(n);
lca.add_edge(u, v);
lca.build(root);
int a = lca.lca(u, v);
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Verify
Code
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108 | #pragma once
#include <algorithm>
#include <bit>
#include <vector>
struct SchieberVishkinLCA {
using uint = unsigned int;
static uint lowbit(uint x) { return x & (~x + 1); }
static uint msb_minus_1_mask(uint x) { return std::bit_floor(x | 1u) - 1u; }
int n;
int root = -1;
std::vector<std::vector<int>> g;
std::vector<int> ord, par;
std::vector<uint> idx, inlabel, ascendant;
std::vector<int> head;
explicit SchieberVishkinLCA(int n = 0) : n(n), g(n), par(n, -1), idx(n, 0) { ord.reserve(n); }
void add_edge(int x, int y) {
g[x].push_back(y);
g[y].push_back(x);
}
// build: O(N), query: O(1)
void build(int r = 0) {
if (n == 0) return;
ord.clear();
std::fill(par.begin(), par.end(), -1);
root = r;
std::vector<int> st;
st.reserve(n);
st.push_back(r);
par[r] = -1;
while (!st.empty()) {
int v = st.back();
st.pop_back();
ord.push_back(v);
for (int i = (int)g[v].size() - 1; i >= 0; --i) {
int to = g[v][i];
if (to == par[v]) continue;
par[to] = v;
st.push_back(to);
}
}
for (int i = 0; i < n; ++i) {
idx[ord[i]] = (uint)(i + 1);
}
inlabel = idx;
for (int i = n - 1; i > 0; --i) {
int v = ord[i];
int p = par[v];
if (lowbit(inlabel[p]) < lowbit(inlabel[v])) inlabel[p] = inlabel[v];
}
ascendant.assign(n, 0);
head.assign(n, 0);
ascendant[r] = 0;
head[0] = r;
for (int i = 1; i < n; ++i) {
int v = ord[i];
int p = par[v];
ascendant[v] = ascendant[p] | lowbit(inlabel[v]);
}
for (int i = 1; i < n; ++i) {
int v = ord[i];
int p = par[v];
if (inlabel[v] != inlabel[p]) {
head[idx[v] - 1] = p;
} else {
head[idx[v] - 1] = head[idx[p] - 1];
}
}
}
int lca(int u, int v) const {
uint Iv = inlabel[v];
uint Iu = inlabel[u];
uint hIv = lowbit(Iv);
uint hIu = lowbit(Iu);
uint mask = msb_minus_1_mask((Iv ^ Iu) | hIv | hIu);
uint j = lowbit(ascendant[v] & ascendant[u] & ~mask);
int x, y;
if (j == hIv) {
x = v;
} else {
mask = msb_minus_1_mask(ascendant[v] & (j - 1));
x = head[(idx[v] & ~mask | (mask + 1)) - 1];
}
if (j == hIu) {
y = u;
} else {
mask = msb_minus_1_mask(ascendant[u] & (j - 1));
y = head[(idx[u] & ~mask | (mask + 1)) - 1];
}
return idx[x] < idx[y] ? x : y;
}
};
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