Contour Query on Tree
(tree/contour_query_on_tree.hpp)

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Last update: 2024-03-13 15:52:21+09:00
Include: #include "tree/contour_query_on_tree.hpp"

説明

頂点 $v$ と距離が $[l, r)$ である頂点に対するクエリを処理するための構造体。構築 $O(N\log{N})$

できること

できないこと

区間更新区間所得

頂点 $v$ への作用が頂点 $v$ に関わるインデックスすべてに対して行わないといけないため。 $1$ 点更新ならば、更新すべきノードが $O(\log{N})$ であるため可能。 $1$ 点取得ならば、所得の際に頂点 $v$ に関わるインデックスをなめることで可能。

get_contour_from_vertex(int v, int l, int r)

頂点 $v$ と距離が $[l, r)$ であるような頂点の属する区間を返す。 $O(\log{N})$

距離が $0$ であるよう場合は含まれないので別途処理が必要。

get_vertex(int v)

頂点 $v$ に関わるインデックスを返す。 $O(\log{N})$

Depends on

Verified with

Code

#pragma once

#include <cassert>
#include <ranges>
#include <vector>

#include "../graph/base.hpp"
#include "../tree/centroid_decomposition.hpp"

namespace ebi {

template <class T> struct contour_query_on_tree {
    contour_query_on_tree(const Graph<T> &tree) : n(tree.size()) {
        int t = 0;
        range = {0};
        auto f = [&](const std::vector<int> &par, const std::vector<int> &vs,
                     const std::vector<int> &color) -> void {
            int sz = (int)par.size();
            std::vector<int> depth(sz, 0);
            for (const int v : std::views::iota(1, sz)) {
                depth[v] += depth[par[v]] + 1;
            }
            std::vector<int> red, blue;
            for (const int v : std::views::iota(0, sz)) {
                if (color[v] == 0) {
                    red.emplace_back(v);
                } else if (color[v] == 1) {
                    blue.emplace_back(v);
                } else
                    assert(color[v] == -1);
            }
            if (red.empty() || blue.empty()) return;
            int max_red = -1;
            for (const int v : red) {
                vertexs.emplace_back(vs[v]);
                number.emplace_back(t);
                dep.emplace_back(depth[v]);
                max_red = max_red < depth[v] ? depth[v] : max_red;
            }
            range.emplace_back(range.back() + max_red + 1);
            t++;
            int max_blue = -1;
            for (const int v : blue) {
                vertexs.emplace_back(vs[v]);
                number.emplace_back(t);
                dep.emplace_back(depth[v]);
                max_blue = max_blue < depth[v] ? depth[v] : max_blue;
            }
            range.emplace_back(range.back() + max_blue + 1);
            t++;
        };
        centroid_decomposition<2>(tree, f);
        index_ptr.assign(n + 1, 0);
        for (const int v : vertexs) {
            index_ptr[v + 1]++;
        }
        for (const int v : std::views::iota(0, n)) {
            index_ptr[v + 1] += index_ptr[v];
        }
        index.resize(index_ptr.back());
        auto counter = index_ptr;
        for (int i = 0; const int v : vertexs) {
            index[counter[v]++] = i;
            i++;
        }
    }

    std::vector<std::pair<int, int>> get_contour_from_vertex(int v, int l,
                                                             int r) const {
        assert(0 <= v && v < n);
        std::vector<std::pair<int, int>> res;
        for (const int idx :
             std::ranges::subrange(index.begin() + index_ptr[v],
                                   index.begin() + index_ptr[v + 1])) {
            int label = number[idx] ^ 1;
            int left = l - dep[idx], right = r - dep[idx];
            int max = range[label + 1] - range[label];
            if (left < 0) left = 0;
            if (right > max) right = max;
            if (left < right) {
                res.emplace_back(range[label] + left, range[label] + right);
            }
        }
        return res;
    }

    std::vector<int> get_vertex(int v) const {
        assert(0 <= v && v < n);
        std::vector<int> res;
        for (const int idx :
             std::ranges::subrange(index.begin() + index_ptr[v],
                                   index.begin() + index_ptr[v + 1])) {
            int label = number[idx];
            assert(range[label] + dep[idx] < range[label + 1]);
            res.emplace_back(range[label] + dep[idx]);
        }
        return res;
    }

    int size() const {
        return range.back();
    }

  private:
    int n;
    std::vector<int> vertexs, number, dep;
    std::vector<int> index, index_ptr;
    std::vector<int> range;
};

}  // namespace ebi

#line 2 "tree/contour_query_on_tree.hpp"

#include <cassert>
#include <ranges>
#include <vector>

#line 2 "graph/base.hpp"

#line 4 "graph/base.hpp"
#include <iostream>
#line 7 "graph/base.hpp"

#line 2 "data_structure/simple_csr.hpp"

#line 4 "data_structure/simple_csr.hpp"
#include <utility>
#line 6 "data_structure/simple_csr.hpp"

namespace ebi {

template <class E> struct simple_csr {
    simple_csr() = default;

    simple_csr(int n, const std::vector<std::pair<int, E>>& elements)
        : start(n + 1, 0), elist(elements.size()) {
        for (auto e : elements) {
            start[e.first + 1]++;
        }
        for (auto i : std::views::iota(0, n)) {
            start[i + 1] += start[i];
        }
        auto counter = start;
        for (auto [i, e] : elements) {
            elist[counter[i]++] = e;
        }
    }

    simple_csr(const std::vector<std::vector<E>>& es)
        : start(es.size() + 1, 0) {
        int n = es.size();
        for (auto i : std::views::iota(0, n)) {
            start[i + 1] = (int)es[i].size() + start[i];
        }
        elist.resize(start.back());
        for (auto i : std::views::iota(0, n)) {
            std::copy(es[i].begin(), es[i].end(), elist.begin() + start[i]);
        }
    }

    int size() const {
        return (int)start.size() - 1;
    }

    const auto operator[](int i) const {
        return std::ranges::subrange(elist.begin() + start[i],
                                     elist.begin() + start[i + 1]);
    }
    auto operator[](int i) {
        return std::ranges::subrange(elist.begin() + start[i],
                                     elist.begin() + start[i + 1]);
    }

    const auto operator()(int i, int l, int r) const {
        return std::ranges::subrange(elist.begin() + start[i] + l,
                                     elist.begin() + start[i + 1] + r);
    }
    auto operator()(int i, int l, int r) {
        return std::ranges::subrange(elist.begin() + start[i] + l,
                                     elist.begin() + start[i + 1] + r);
    }

  private:
    std::vector<int> start;
    std::vector<E> elist;
};

}  // namespace ebi
#line 9 "graph/base.hpp"

namespace ebi {

template <class T> struct Edge {
    int from, to;
    T cost;
    int id;
};

template <class E> struct Graph {
    using cost_type = E;
    using edge_type = Edge<cost_type>;

    Graph(int n_) : n(n_) {}

    Graph() = default;

    void add_edge(int u, int v, cost_type c) {
        buff.emplace_back(u, edge_type{u, v, c, m});
        edges.emplace_back(edge_type{u, v, c, m++});
    }

    void add_undirected_edge(int u, int v, cost_type c) {
        buff.emplace_back(u, edge_type{u, v, c, m});
        buff.emplace_back(v, edge_type{v, u, c, m});
        edges.emplace_back(edge_type{u, v, c, m});
        m++;
    }

    void read_tree(int offset = 1, bool is_weighted = false) {
        read_graph(n - 1, offset, false, is_weighted);
    }

    void read_parents(int offset = 1) {
        for (auto i : std::views::iota(1, n)) {
            int p;
            std::cin >> p;
            p -= offset;
            add_undirected_edge(p, i, 1);
        }
        build();
    }

    void read_graph(int e, int offset = 1, bool is_directed = false,
                    bool is_weighted = false) {
        for (int i = 0; i < e; i++) {
            int u, v;
            std::cin >> u >> v;
            u -= offset;
            v -= offset;
            if (is_weighted) {
                cost_type c;
                std::cin >> c;
                if (is_directed) {
                    add_edge(u, v, c);
                } else {
                    add_undirected_edge(u, v, c);
                }
            } else {
                if (is_directed) {
                    add_edge(u, v, 1);
                } else {
                    add_undirected_edge(u, v, 1);
                }
            }
        }
        build();
    }

    void build() {
        assert(!prepared);
        csr = simple_csr<edge_type>(n, buff);
        buff.clear();
        prepared = true;
    }

    int size() const {
        return n;
    }

    int node_number() const {
        return n;
    }

    int edge_number() const {
        return m;
    }

    edge_type get_edge(int i) const {
        return edges[i];
    }

    std::vector<edge_type> get_edges() const {
        return edges;
    }

    const auto operator[](int i) const {
        return csr[i];
    }
    auto operator[](int i) {
        return csr[i];
    }

  private:
    int n, m = 0;

    std::vector<std::pair<int,edge_type>> buff;

    std::vector<edge_type> edges;
    simple_csr<edge_type> csr;
    bool prepared = false;
};

}  // namespace ebi
#line 2 "tree/centroid_decomposition.hpp"

#include <algorithm>
#line 7 "tree/centroid_decomposition.hpp"

namespace ebi {

namespace internal {

template <class F>
void centroid_decomposition_dfs_naive(const std::vector<int> &par,
                                      const std::vector<int> &original_vs,
                                      F f) {
    const int n = (int)par.size();
    assert(par.size() == original_vs.size());
    int center = -1;
    std::vector<int> sz(n, 1);
    for (const int v : std::views::iota(0, n) | std::views::reverse) {
        if (sz[v] >= (n + 1) / 2) {
            center = v;
            break;
        }
        sz[par[v]] += sz[v];
    }
    std::vector<int> color(n, -1);
    std::vector<int> vs = {center};
    color[center] = 0;
    int c = 1;
    for (const int v : std::views::iota(1, n)) {
        if (par[v] == center) {
            vs.emplace_back(v);
            color[v] = c++;
        }
    }
    if (center > 0) {
        for (int v = par[center]; v != -1; v = par[v]) {
            vs.emplace_back(v);
            color[v] = c;
        }
        c++;
    }
    for (const int v : std::views::iota(0, n)) {
        if (color[v] == -1) {
            vs.emplace_back(v);
            color[v] = color[par[v]];
        }
    }
    std::vector<int> index_ptr(c + 1, 0);
    for (const int v : std::views::iota(0, n)) {
        index_ptr[color[v] + 1]++;
    }
    for (const int i : std::views::iota(0, c)) {
        index_ptr[i + 1] += index_ptr[i];
    }
    auto counter = index_ptr;
    std::vector<int> ord(n);
    for (auto v : vs) {
        ord[counter[color[v]]++] = v;
    }
    std::vector<int> relabel(n);
    for (const int v : std::views::iota(0, n)) {
        relabel[ord[v]] = v;
    }
    std::vector<int> original_vs2(n);
    for (const int v : std::views::iota(0, n)) {
        original_vs2[relabel[v]] = original_vs[v];
    }
    std::vector<int> relabel_par(n, -1);
    for (int v : std::views::iota(1, n)) {
        int a = relabel[v];
        int b = relabel[par[v]];
        if (a > b) std::swap(a, b);
        relabel_par[b] = a;
    }
    f(relabel_par, original_vs2, index_ptr);
    for (const int i : std::views::iota(1, c)) {
        int l = index_ptr[i], r = index_ptr[i + 1];
        std::vector<int> par1(r - l, -1);
        std::vector<int> original_vs1(r - l, -1);
        for (int v : std::views::iota(l, r)) {
            par1[v - l] = (relabel_par[v] == 0 ? -1 : relabel_par[v] - l);
            original_vs1[v - l] = original_vs2[v];
        }
        centroid_decomposition_dfs_naive(par1, original_vs1, f);
    }
    return;
}

template <class F>
void one_third_centroid_decomposition(const std::vector<int> &par,
                                      const std::vector<int> &original_vs,
                                      F f) {
    const int n = (int)par.size();
    assert(n > 1);
    if (n == 2) return;
    int center = -1;
    std::vector<int> sz(n, 1);

    for (const int v : std::views::iota(0, n) | std::views::reverse) {
        if (sz[v] >= (n + 1) / 2) {
            center = v;
            break;
        }
        sz[par[v]] += sz[v];
    }

    std::vector<int> color(n, -1);
    std::vector<int> ord(n, -1);
    ord[center] = 0;
    int t = 1;
    int red = n - sz[center];
    for (int v = par[center]; v != -1; v = par[v]) {
        ord[v] = t++;
        color[v] = 0;
    }
    for (const int v : std::views::iota(1, n)) {
        if (par[v] == center && 3 * (red + sz[v]) <= 2 * (n - 1)) {
            red += sz[v];
            ord[v] = t++;
            color[v] = 0;
        }
    }
    for (const int v : std::views::iota(1, n)) {
        if (v != center && color[v] == -1 && color[par[v]] == 0) {
            ord[v] = t++;
            color[v] = 0;
        }
    }
    const int n0 = t - 1;
    for (const int v : std::views::iota(1, n)) {
        if (v != center && color[v] == -1) {
            ord[v] = t++;
            color[v] = 1;
        }
    }
    assert(t == n);
    const int n1 = n - 1 - n0;
    std::vector<int> par0(n0 + 1, -1), par1(n1 + 1, -1), par2(n, -1);
    std::vector<int> original_vs0(n0 + 1), original_vs1(n1 + 1),
        original_vs2(n);
    for (const int i : std::views::iota(0, n)) {
        int v = ord[i];
        original_vs2[v] = original_vs[i];
        if (color[i] != 1) {
            original_vs0[v] = original_vs[i];
        }
        if (color[i] != 0) {
            int idx = std::max(v - n0, 0);
            original_vs1[idx] = original_vs[i];
        }
    }
    for (const int v : std::views::iota(1, n)) {
        int a = ord[v], b = ord[par[v]];
        if (a > b) std::swap(a, b);
        par2[b] = a;
        if (color[v] != 1 && color[par[v]] != 1) {
            par0[b] = a;
        }
        if (color[v] != 0 && color[par[v]] != 0) {
            par1[b - n0] = std::max(a - n0, 0);
        }
    }
    f(par2, original_vs2, n0, n1);
    one_third_centroid_decomposition(par0, original_vs0, f);
    one_third_centroid_decomposition(par1, original_vs1, f);
    return;
}

template <class F>
void one_third_centroid_decomposition_virtual_real(
    const std::vector<int> &par, const std::vector<int> &original_vs,
    const std::vector<int> &is_real, F f) {
    const int n = (int)par.size();
    assert(n > 1);
    if (n == 2) {
        if (is_real[0] && is_real[1]) {
            f(par, original_vs, {0, 1});
        }
        return;
    }
    int center = -1;
    std::vector<int> sz(n, 1);

    for (const int v : std::views::iota(0, n) | std::views::reverse) {
        if (sz[v] >= (n + 1) / 2) {
            center = v;
            break;
        }
        sz[par[v]] += sz[v];
    }

    std::vector<int> color(n, -1);
    std::vector<int> ord(n, -1);
    ord[center] = 0;
    int t = 1;
    int red = n - sz[center];
    for (int v = par[center]; v != -1; v = par[v]) {
        ord[v] = t++;
        color[v] = 0;
    }
    for (const int v : std::views::iota(1, n)) {
        if (par[v] == center && 3 * (red + sz[v]) <= 2 * (n - 1)) {
            red += sz[v];
            ord[v] = t++;
            color[v] = 0;
        }
    }
    for (const int v : std::views::iota(1, n)) {
        if (v != center && color[v] == -1 && color[par[v]] == 0) {
            ord[v] = t++;
            color[v] = 0;
        }
    }
    const int n0 = t - 1;
    for (const int v : std::views::iota(1, n)) {
        if (v != center && color[v] == -1) {
            ord[v] = t++;
            color[v] = 1;
        }
    }
    assert(t == n);
    const int n1 = n - 1 - n0;
    std::vector<int> par0(n0 + 1, -1), par1(n1 + 1, -1), par2(n, -1);
    std::vector<int> original_vs0(n0 + 1), original_vs1(n1 + 1),
        original_vs2(n);
    std::vector<int> is_real0(n0 + 1), is_real1(n1 + 1), is_real2(n);
    for (const int i : std::views::iota(0, n)) {
        int v = ord[i];
        original_vs2[v] = original_vs[i];
        is_real2[v] = is_real[i];
        if (color[i] != 1) {
            original_vs0[v] = original_vs[i];
            is_real0[v] = is_real[i];
        }
        if (color[i] != 0) {
            int idx = std::max(v - n0, 0);
            original_vs1[idx] = original_vs[i];
            is_real1[idx] = is_real[i];
        }
    }
    for (const int v : std::views::iota(1, n)) {
        int a = ord[v], b = ord[par[v]];
        if (a > b) std::swap(a, b);
        par2[b] = a;
        if (color[v] != 1 && color[par[v]] != 1) {
            par0[b] = a;
        }
        if (color[v] != 0 && color[par[v]] != 0) {
            par1[b - n0] = std::max(a - n0, 0);
        }
    }
    if (is_real[center]) {
        color.assign(n, -1);
        color[0] = 0;
        for (const int v : std::views::iota(1, n)) {
            if (is_real2[v]) color[v] = 1;
        }
        f(par2, original_vs2, color);
        is_real0[0] = is_real1[0] = is_real2[0] = 0;
    }
    color.assign(n, -1);
    for (const int v : std::views::iota(1, n)) {
        if (is_real2[v]) {
            color[v] = int(v > n0);
        }
    }
    f(par2, original_vs2, color);
    one_third_centroid_decomposition_virtual_real(par0, original_vs0, is_real0,
                                                  f);
    one_third_centroid_decomposition_virtual_real(par1, original_vs1, is_real1,
                                                  f);
    return;
}

}  // namespace internal

template <int MODE, class T, class F>
void centroid_decomposition(const Graph<T> &tree, F f) {
    int n = (int)tree.size();
    if (n == 1) return;
    std::vector<int> bfs_order(n), par(n, -1);
    bfs_order[0] = 0;
    int l = 0, r = 1;
    while (l < r) {
        int v = bfs_order[l++];
        for (auto e : tree[v]) {
            int nv = e.to;
            if (nv == par[v]) continue;
            bfs_order[r++] = nv;
            par[nv] = v;
        }
    }
    assert(l == n && r == n);
    {
        std::vector<int> relabel(n);
        for (int i : std::views::iota(0, n)) {
            relabel[bfs_order[i]] = i;
        }
        std::vector<int> relabel_par(n, -1);
        for (int i : std::views::iota(1, n)) {
            relabel_par[relabel[i]] = relabel[par[i]];
        }
        std::swap(par, relabel_par);
    }
    static_assert(MODE == 0 || MODE == 1 || MODE == 2);
    if constexpr (MODE == 0) {
        internal::centroid_decomposition_dfs_naive(par, bfs_order, f);
    } else if constexpr (MODE == 1) {
        internal::one_third_centroid_decomposition(par, bfs_order, f);
    } else {
        internal::one_third_centroid_decomposition_virtual_real(
            par, bfs_order, std::vector<int>(n, 1), f);
    }
}

}  // namespace ebi
#line 9 "tree/contour_query_on_tree.hpp"

namespace ebi {

template <class T> struct contour_query_on_tree {
    contour_query_on_tree(const Graph<T> &tree) : n(tree.size()) {
        int t = 0;
        range = {0};
        auto f = [&](const std::vector<int> &par, const std::vector<int> &vs,
                     const std::vector<int> &color) -> void {
            int sz = (int)par.size();
            std::vector<int> depth(sz, 0);
            for (const int v : std::views::iota(1, sz)) {
                depth[v] += depth[par[v]] + 1;
            }
            std::vector<int> red, blue;
            for (const int v : std::views::iota(0, sz)) {
                if (color[v] == 0) {
                    red.emplace_back(v);
                } else if (color[v] == 1) {
                    blue.emplace_back(v);
                } else
                    assert(color[v] == -1);
            }
            if (red.empty() || blue.empty()) return;
            int max_red = -1;
            for (const int v : red) {
                vertexs.emplace_back(vs[v]);
                number.emplace_back(t);
                dep.emplace_back(depth[v]);
                max_red = max_red < depth[v] ? depth[v] : max_red;
            }
            range.emplace_back(range.back() + max_red + 1);
            t++;
            int max_blue = -1;
            for (const int v : blue) {
                vertexs.emplace_back(vs[v]);
                number.emplace_back(t);
                dep.emplace_back(depth[v]);
                max_blue = max_blue < depth[v] ? depth[v] : max_blue;
            }
            range.emplace_back(range.back() + max_blue + 1);
            t++;
        };
        centroid_decomposition<2>(tree, f);
        index_ptr.assign(n + 1, 0);
        for (const int v : vertexs) {
            index_ptr[v + 1]++;
        }
        for (const int v : std::views::iota(0, n)) {
            index_ptr[v + 1] += index_ptr[v];
        }
        index.resize(index_ptr.back());
        auto counter = index_ptr;
        for (int i = 0; const int v : vertexs) {
            index[counter[v]++] = i;
            i++;
        }
    }

    std::vector<std::pair<int, int>> get_contour_from_vertex(int v, int l,
                                                             int r) const {
        assert(0 <= v && v < n);
        std::vector<std::pair<int, int>> res;
        for (const int idx :
             std::ranges::subrange(index.begin() + index_ptr[v],
                                   index.begin() + index_ptr[v + 1])) {
            int label = number[idx] ^ 1;
            int left = l - dep[idx], right = r - dep[idx];
            int max = range[label + 1] - range[label];
            if (left < 0) left = 0;
            if (right > max) right = max;
            if (left < right) {
                res.emplace_back(range[label] + left, range[label] + right);
            }
        }
        return res;
    }

    std::vector<int> get_vertex(int v) const {
        assert(0 <= v && v < n);
        std::vector<int> res;
        for (const int idx :
             std::ranges::subrange(index.begin() + index_ptr[v],
                                   index.begin() + index_ptr[v + 1])) {
            int label = number[idx];
            assert(range[label] + dep[idx] < range[label + 1]);
            res.emplace_back(range[label] + dep[idx]);
        }
        return res;
    }

    int size() const {
        return range.back();
    }

  private:
    int n;
    std::vector<int> vertexs, number, dep;
    std::vector<int> index, index_ptr;
    std::vector<int> range;
};

}  // namespace ebi

Contour Query on Tree (tree/contour_query_on_tree.hpp)

説明