Verify/hld_path.test.cpp

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Last update: 2020-11-05 12:15:41+09:00
Problem: https://judge.yosupo.jp/problem/vertex_add_path_sum

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Code

#define PROBLEM "https://judge.yosupo.jp/problem/vertex_add_path_sum"

#include "../DataStructure/segment_tree.hpp"
#include "../Graph/heavy_light_decomposition.hpp"

#include <iostream>

using lint = long long;

int main() {
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);

    int n, q;
    std::cin >> n >> q;

    std::vector<lint> xs(n);
    for (auto& x : xs) std::cin >> x;

    Graph<> graph(n);
    for (int i = n - 1; i--;) {
        int u, v;
        std::cin >> u >> v;
        graph.span(false, u, v);
    }

    HeavyLightDecomposition hld(graph);
    {
        auto pxs = xs;
        for (int i = 0; i < n; ++i) xs[i] = pxs[hld.vs[i]];
    }

    SegmentTree<lint> seg(xs, 0, [](auto a, auto b) { return a + b; });

    while (q--) {
        int t;
        std::cin >> t;

        switch (t) {
            case 0: {
                int v, x;
                std::cin >> v >> x;

                int i = hld.id[v];
                seg.update(i, seg.get(i) + x);
                break;
            }
            case 1: {
                int u, v;
                std::cin >> u >> v;

                lint sum = 0;
                for (auto [l, r] : hld.path(u, v, false)) {
                    sum += seg.fold(l, r);
                }
                std::cout << sum << "\n";
                break;
            }
        }
    }

    return 0;
}

#line 1 "Verify/hld_path.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_add_path_sum"

#line 2 "DataStructure/segment_tree.hpp"

#include <vector>
#include <functional>

template <class T>
struct SegmentTree {
    using Merger = std::function<T(T, T)>;

    int length;
    std::vector<T> dat;
    T unit;
    Merger merge;

    SegmentTree() = default;

    SegmentTree(int n, const T& unit, const Merger& merge)
        : length(1), unit(unit), merge(merge) {
        while (length < n) length <<= 1;
        dat.assign(length * 2, unit);
    }

    template <class Container>
    SegmentTree(const Container& elems, const T& unit, const Merger& merge)
        : length(1), unit(unit), merge(merge) {
        int n = elems.size();
        while (length < n) length <<= 1;

        dat.assign(length * 2, unit);

        std::copy(elems.begin(), elems.end(), dat.begin() + length);

        for (int nidx = length - 1; nidx >= 1; --nidx) {
            T vl = dat[nidx * 2 + 0];
            T vr = dat[nidx * 2 + 1];
            dat[nidx] = merge(vl, vr);
        }
    }

    void update(int nidx, const T& elem) {
        nidx += length;
        dat[nidx] = elem;

        while (nidx > 0) {
            nidx >>= 1;
            T vl = dat[nidx * 2 + 0];
            T vr = dat[nidx * 2 + 1];
            dat[nidx] = merge(vl, vr);
        }
    }

    T fold(int ql, int qr) const {
        ql = std::max(ql, 0);
        qr = std::min(qr, length);
        ql += length, qr += length;

        T lacc = unit, racc = unit;
        while (ql < qr) {
            if (ql & 1) {
                lacc = merge(lacc, dat[ql]);
                ++ql;
            }
            if (qr & 1) {
                --qr;
                racc = merge(dat[qr], racc);
            }
            ql >>= 1, qr >>= 1;
        }

        return merge(lacc, racc);
    }

    T get(int idx) const { return dat[idx + length]; }
    T fold_all() const { return dat[1]; }
};
#line 2 "Graph/heavy_light_decomposition.hpp"

#line 2 "Graph/graph.hpp"

#line 4 "Graph/graph.hpp"

template <class Cost = int>
struct Edge {
    int src, dst;
    Cost cost;

    Edge() = default;
    Edge(int src, int dst, Cost cost = 1)
        : src(src), dst(dst), cost(cost){};

    bool operator<(const Edge<Cost>& e) const { return cost < e.cost; }
    bool operator>(const Edge<Cost>& e) const { return cost > e.cost; }
};

template <class Cost = int>
struct Graph : public std::vector<std::vector<Edge<Cost>>> {
    using std::vector<std::vector<Edge<Cost>>>::vector;

    void span(bool direct, int src, int dst, Cost cost = 1) {
        (*this)[src].emplace_back(src, dst, cost);
        if (!direct) (*this)[dst].emplace_back(dst, src, cost);
    }
};
#line 4 "Graph/heavy_light_decomposition.hpp"

#line 6 "Graph/heavy_light_decomposition.hpp"

template <class Cost>
struct HeavyLightDecomposition {
    // indexing
    // v: a vertex in original graph
    // i: assigned label of a vertex

    Graph<Cost> graph;
    std::vector<int> id, vs;  // id: v -> i, vs: i -> v
    std::vector<int> par, sz, head, dep, out;
    // these are all v-indexed
    // in equals to id
    int time;

    explicit HeavyLightDecomposition(const Graph<Cost>& graph)
        : graph(graph),
          id(graph.size()),
          vs(graph.size()),
          par(graph.size()),
          sz(graph.size()),
          head(graph.size()),
          dep(graph.size()),
          out(graph.size()),
          time(0) {
        dfs_sz(0, -1, 0);
        head[0] = 0;
        dfs_hld(0, -1);
    }

    void dfs_sz(int v, int p, int d) {
        par[v] = p;
        sz[v] = 1;
        dep[v] = d;

        if (!graph[v].empty() && graph[v].front().dst == p) {
            std::swap(graph[v].front(), graph[v].back());
        }

        for (auto& e : graph[v]) {
            if (e.dst == p) continue;

            dfs_sz(e.dst, v, d + 1);
            sz[v] += sz[e.dst];

            // heavy edge first
            if (sz[graph[v].front().dst] < sz[e.dst]) {
                std::swap(graph[v].front(), e);
            }
        }
    }

    void dfs_hld(int v, int p) {
        id[v] = time++;
        vs[id[v]] = v;

        bool first = true;
        for (auto e : graph[v]) {
            if (e.dst == p) continue;

            head[e.dst] = (first ? head[v] : e.dst);
            first = false;
            dfs_hld(e.dst, v);
        }

        out[v] = time;
    }

    int lca(int u, int v) {
        while (true) {
            if (id[u] > id[v]) std::swap(u, v);
            if (head[u] == head[v]) return u;
            v = par[head[v]];
        }
    }

    int dist(int u, int v) {
        return dep[u] + dep[v] - dep[lca(u, v)] * 2;
    }

    std::vector<std::pair<int, int>> path(int u, int v, bool is_edge) {
        std::vector<std::pair<int, int>> segs;

        while (true) {
            if (id[u] > id[v]) std::swap(u, v);

            if (head[u] == head[v]) {
                // when edge path, the lca has to be excluded
                segs.emplace_back(id[u] + is_edge, id[v] + 1);
                return segs;
            }

            segs.emplace_back(id[head[v]], id[v] + 1);
            v = par[head[v]];
        }
    }

    std::pair<int, int> subtree(int v, bool is_edge) {
        // when edge path, the root has to be excluded
        return {id[v] + is_edge, out[v]};
    }
};
#line 5 "Verify/hld_path.test.cpp"

#include <iostream>

using lint = long long;

int main() {
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);

    int n, q;
    std::cin >> n >> q;

    std::vector<lint> xs(n);
    for (auto& x : xs) std::cin >> x;

    Graph<> graph(n);
    for (int i = n - 1; i--;) {
        int u, v;
        std::cin >> u >> v;
        graph.span(false, u, v);
    }

    HeavyLightDecomposition hld(graph);
    {
        auto pxs = xs;
        for (int i = 0; i < n; ++i) xs[i] = pxs[hld.vs[i]];
    }

    SegmentTree<lint> seg(xs, 0, [](auto a, auto b) { return a + b; });

    while (q--) {
        int t;
        std::cin >> t;

        switch (t) {
            case 0: {
                int v, x;
                std::cin >> v >> x;

                int i = hld.id[v];
                seg.update(i, seg.get(i) + x);
                break;
            }
            case 1: {
                int u, v;
                std::cin >> u >> v;

                lint sum = 0;
                for (auto [l, r] : hld.path(u, v, false)) {
                    sum += seg.fold(l, r);
                }
                std::cout << sum << "\n";
                break;
            }
        }
    }

    return 0;
}