Lowest Common Ancestor (最小共通祖先)
(graph/lowest_common_ancestor.hpp)

• View this file on GitHub
• Last update: 2024-01-25 10:46:02+09:00
• Include: #include "graph/lowest_common_ancestor.hpp"

• LowestCommonAncestor tq(G, root); で作成
• tq.lca(u, v) で u と v の最小共通祖先を出力
• tq.level_ancestor(u, d) で u から d 本の辺を昇った頂点を出力(辺の重みは考慮しない)

Depends on

• graph/graph_template.hpp

Verified with

• verify/lc_tree/lc_lowest_common_ancestor.test.cpp

Code

#pragma once

#include "graph/graph_template.hpp"

template <class T> struct LowestCommonAncestor {
    std::vector<int> depth;
    std::vector<std::vector<int>> parent;
    int n, LOG;

    LowestCommonAncestor(const Graph<T> &G, int root = 0) : n(int(G.size())), LOG(32 - __builtin_clz(n)) {
        depth.assign(n, 0);
        parent.assign(LOG, std::vector<int>(n));
        auto dfs = [&](auto f, int cur, int par) -> void {
            parent[0][cur] = par;
            for (auto &e : G[cur]) {
                if (e.to == par) continue;
                depth[e.to] = depth[cur] + 1;
                f(f, e.to, cur);
            }
        };
        dfs(dfs, root, -1);
        for (int k = 0; k + 1 < LOG; k++) {
            for (int v = 0; v < n; v++) {
                parent[k + 1][v] = (parent[k][v] < 0 ? -1 : parent[k][parent[k][v]]);
            }
        }
    }

    int lca(int u, int v) {
        assert((int)depth.size() == n);
        if (depth[u] > depth[v]) std::swap(u, v);
        // depth[u] <= depth[v]
        for (int k = 0; k < LOG; k++)
            if ((depth[v] - depth[u]) >> k & 1) v = parent[k][v];

        if (u == v) return u;
        for (int k = LOG - 1; k >= 0; k--) {
            if (parent[k][u] != parent[k][v]) {
                u = parent[k][u];
                v = parent[k][v];
            }
        }
        return parent[0][u];
    }

    int level_ancestor(int u, int d) {
        assert((int)depth.size() == n);
        if (depth[u] < d) return -1;
        for (int k = 0; k < LOG; k++)
            if (d >> k & 1) u = parent[k][u];
        return u;
    }

    int distance(int u, int v) {
        int par = lca(u, v);
        return depth[u] + depth[v] - 2 * depth[par];
    }
};

#line 2 "graph/lowest_common_ancestor.hpp"

#line 2 "graph/graph_template.hpp"

#include <vector>
template <class T> struct Edge {
    int from, to;
    T cost;
    int id;

    Edge() = default;
    Edge(int from, int to, T cost = 1, int id = -1) : from(from), to(to), cost(cost), id(id) {}

    friend std::ostream &operator<<(std::ostream &os, const Edge<T> &e) {
        // output format: "{ id : from -> to, cost }"
        return os << "{ " << e.id << " : " << e.from << " -> " << e.to << ", " << e.cost << " }";
    }
};

template <class T> using Edges = std::vector<Edge<T>>;
template <class T> using Graph = std::vector<std::vector<Edge<T>>>;
#line 4 "graph/lowest_common_ancestor.hpp"

template <class T> struct LowestCommonAncestor {
    std::vector<int> depth;
    std::vector<std::vector<int>> parent;
    int n, LOG;

    LowestCommonAncestor(const Graph<T> &G, int root = 0) : n(int(G.size())), LOG(32 - __builtin_clz(n)) {
        depth.assign(n, 0);
        parent.assign(LOG, std::vector<int>(n));
        auto dfs = [&](auto f, int cur, int par) -> void {
            parent[0][cur] = par;
            for (auto &e : G[cur]) {
                if (e.to == par) continue;
                depth[e.to] = depth[cur] + 1;
                f(f, e.to, cur);
            }
        };
        dfs(dfs, root, -1);
        for (int k = 0; k + 1 < LOG; k++) {
            for (int v = 0; v < n; v++) {
                parent[k + 1][v] = (parent[k][v] < 0 ? -1 : parent[k][parent[k][v]]);
            }
        }
    }

    int lca(int u, int v) {
        assert((int)depth.size() == n);
        if (depth[u] > depth[v]) std::swap(u, v);
        // depth[u] <= depth[v]
        for (int k = 0; k < LOG; k++)
            if ((depth[v] - depth[u]) >> k & 1) v = parent[k][v];

        if (u == v) return u;
        for (int k = LOG - 1; k >= 0; k--) {
            if (parent[k][u] != parent[k][v]) {
                u = parent[k][u];
                v = parent[k][v];
            }
        }
        return parent[0][u];
    }

    int level_ancestor(int u, int d) {
        assert((int)depth.size() == n);
        if (depth[u] < d) return -1;
        for (int k = 0; k < LOG; k++)
            if (d >> k & 1) u = parent[k][u];
        return u;
    }

    int distance(int u, int v) {
        int par = lca(u, v);
        return depth[u] + depth[v] - 2 * depth[par];
    }
};

Back to top page