algo/graph/lca.h

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• Last update: 2024-12-10 21:37:51-05:00

Depends on

• algo/common.h
• algo/ds/common.h
• algo/ds/sparse_table.h
• algo/utils/bits.h

Verified with

• verify/graph/tree_lca.test.cpp

Code

#pragma once
#include "algo/common.h"
#include "algo/ds/sparse_table.h"
#include "algo/utils/bits.h"

namespace algo::graph {

struct lca {
    // Note that adj must be a tree. Don't forget to set root!
    lca(const std::vector<std::vector<int>> &adj, int root = 0)
        : n(sz(adj)), height(n), first(n), st(2 * n, [&](int a, int b) {
              return height[a] < height[b] ? a : b;
          }) {
        euler.reserve(2 * n);
        dfs(root, root, 0, adj);
        st.init(euler);
    }
    // Lowest common ancestor of u, v
    int par(int u, int v) {
        int l = first[u], r = first[v];
        if (l > r) std::swap(l, r);
        return st.query(l, r);
    }

private:
    int n;
    std::vector<int> height, euler, first;
    ds::sparse_table<int> st;

    void dfs(int v, int p, int h, const std::vector<std::vector<int>> &adj) {
        height[v] = h;
        first[v] = sz(euler);
        euler.push_back(v);
        for (int u : adj[v]) {
            if (u != p) {
                dfs(u, v, h + 1, adj);
                euler.push_back(v);
            }
        }
    }
};

}; // namespace algo::graph

#line 2 "algo/common.h"
#ifndef PREPROCESS
#include <bits/stdc++.h>
#endif

namespace algo {}

#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
#line 3 "algo/ds/common.h"

namespace algo::ds {

template <typename T>
T min(const T &a, const T &b) {
    return std::min(a, b);
}

}; // namespace algo::ds
#line 3 "algo/utils/bits.h"

namespace algo::utils {

// Returns number of set bits in x
constexpr int popcnt(int64_t x) {
    return __builtin_popcountll(x);
}
// Returns floor(log_2(x))
constexpr int lg2(uint64_t x) {
    return std::bit_width(x) - 1;
}

} // namespace algo::utils
#line 5 "algo/ds/sparse_table.h"

namespace algo::ds {

template <typename T>
struct sparse_table {
    // Must be constructed with idempotent function. Call init() after if using
    // this constructor.
    sparse_table(int _n, const std::function<T(T, T)> &op = min<T>)
        : n(_n), k(utils::lg2(n)), op(op), st(k + 1, std::vector<T>(n)) {
    }
    // Must be constructed with idempotent function
    sparse_table(const std::vector<T> &a,
                 const std::function<T(T, T)> &op = min<T>)
        : sparse_table(sz(a), op) {
        init(a);
    }
    void init(const std::vector<T> &a) {
        assert(sz(a) <= n);
        std::copy(all(a), st[0].begin());
        for (int i = 1; i <= k; i++) {
            for (int j = 0; j + (1 << i) <= n; j++) {
                st[i][j] = op(st[i - 1][j], st[i - 1][j + (1 << (i - 1))]);
            }
        }
    }
    // Queries on [l, r]
    T query(int l, int r) {
        int i = utils::lg2(r - l + 1);
        return op(st[i][l], st[i][r - (1 << i) + 1]);
    }
    friend std::ostream &operator<<(std::ostream &os, const sparse_table &t) {
        return os << t.st[0];
    }

private:
    int n, k;
    std::function<T(T, T)> op;
    std::vector<std::vector<T>> st;
};

} // namespace algo::ds
#line 5 "algo/graph/lca.h"

namespace algo::graph {

struct lca {
    // Note that adj must be a tree. Don't forget to set root!
    lca(const std::vector<std::vector<int>> &adj, int root = 0)
        : n(sz(adj)), height(n), first(n), st(2 * n, [&](int a, int b) {
              return height[a] < height[b] ? a : b;
          }) {
        euler.reserve(2 * n);
        dfs(root, root, 0, adj);
        st.init(euler);
    }
    // Lowest common ancestor of u, v
    int par(int u, int v) {
        int l = first[u], r = first[v];
        if (l > r) std::swap(l, r);
        return st.query(l, r);
    }

private:
    int n;
    std::vector<int> height, euler, first;
    ds::sparse_table<int> st;

    void dfs(int v, int p, int h, const std::vector<std::vector<int>> &adj) {
        height[v] = h;
        first[v] = sz(euler);
        euler.push_back(v);
        for (int u : adj[v]) {
            if (u != p) {
                dfs(u, v, h + 1, adj);
                euler.push_back(v);
            }
        }
    }
};

}; // namespace algo::graph

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