test/library_checker/tree/vertex_add_path_sum.test.cpp

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• Last update: 2024-11-15 16:06:01+09:00
• Problem: https://judge.yosupo.jp/problem/vertex_add_path_sum

Depends on

• Binary Indexed Tree (lib/data_structure/binary_indexed_tree.hpp)
• Heavy Light Decomposition (重軽分解) (lib/graph/heavy_light_decomposition.hpp)

Code

#define PROBLEM "https://judge.yosupo.jp/problem/vertex_add_path_sum"
#include <bits/stdc++.h>
using namespace std;

#include "../../../lib/data_structure/binary_indexed_tree.hpp"
#include "../../../lib/graph/heavy_light_decomposition.hpp"

int main(){
    int n, q; cin >> n >> q;
    vector<int> a(n);
    for(int i = 0; i < n; i++){
        cin >> a[i];
    }
    HeavyLightDecomposition hl(n);
    for(int i = 0; i < n - 1; i++){
        int u, v; cin >> u >> v;
        hl.add_edge(u, v);
    }
    hl.build();
    BinaryIndexedTree<long long> BIT(n);
    for(int i = 0; i < n; i++){
        BIT.add(hl.get(i), a[i]);
    }
    long long ans = 0;
    auto query = [&](int l, int r){
        ans += BIT.sum(l, r);
    };
    while(q--){
        int t; cin >> t;
        if(t == 0){
            int p, x; cin >> p >> x;
            BIT.add(hl.get(p), x);
        }else{
            int u, v; cin >> u >> v;
            ans = 0;
            hl.path_query(u, v, query);
            cout << ans << "\n";
        }
    }
}

#line 1 "test/library_checker/tree/vertex_add_path_sum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_add_path_sum"
#include <bits/stdc++.h>
using namespace std;

#line 2 "lib/data_structure/binary_indexed_tree.hpp"

/**
 * @brief Binary Indexed Tree
 * @docs docs/data_structure/binary_indexed_tree.md
 */

#line 9 "lib/data_structure/binary_indexed_tree.hpp"

template <typename T>
struct BinaryIndexedTree{
    int N;
    std::vector<T> BIT;
    BinaryIndexedTree(const int N) : N(N), BIT(N + 1, 0){
    }

    T get(int i){
        return sum(i + 1) - sum(i);
    }

    void add(int i, T x){
        i++;
        while(i <= N){
            BIT[i] += x;
            i += i & -i;
        }
    }

    T sum(int i) const {
        T ans = 0;
        while(i > 0){
            ans += BIT[i];
            i -= i & -i;
        }
        return ans;
    }

    T sum(int L, int R) const {
        return sum(R) - sum(L);
    }

    int lower_bound(T x) const {
        if(x <= 0){
            return 0;
        } else{
            int v = 0, r = 1;
            while(r < N) r = r << 1;
            for(int len = r; len > 0; len = len >> 1){
                if(v + len < N && BIT[v + len] < x){
                    x -= BIT[v + len];
                    v += len;
                }
            }
            return v;
        }
    }

    int upper_bound(T x) const {
        if(x < 0){
            return 0;
        } else{
            int v = 0, r = 1;
            while(r <= N) r = r << 1;
            for(int len = r; len > 0; len = len >> 1){
                if(v + len <= N && BIT[v + len] <= x){
                    x -= BIT[v + len];
                    v += len;
                }
            }
            return v;
        }
    }

    T operator [](int i) const {
        return sum(i, i + 1);
    }
};
#line 2 "lib/graph/heavy_light_decomposition.hpp"

/**
 * @brief Heavy Light Decomposition (重軽分解)
 * @docs docs/graph/heavy_light_decomposition.md
 */

class HeavyLightDecomposition{
protected:
    int V;
    vector<vector<int>> G;
    vector<int> stsize, parent, pathtop, depth, in, reverse_in, out;
    int root;

private:
    // Subtree Size
    void buildStsize(int curr, int prev){
        stsize[curr] = 1, parent[curr] = prev;
        for(int &v : G[curr]){
            if(v == prev){
                if(v == G[curr].back()) break;
                else swap(v, G[curr].back());
            }
            buildStsize(v, curr);
            stsize[curr] += stsize[v];
            if(stsize[v] > stsize[G[curr][0]]){
                swap(v, G[curr][0]);
            }
        }
    }

    void buildPath(int curr, int prev, int &t){
        in[curr] = t++;
        reverse_in[in[curr]] = curr;
        for(int v : G[curr]){
            if(v == prev) continue;

            if(v == G[curr][0]){
                pathtop[v] = pathtop[curr];
            } else{
                pathtop[v] = v;
            }
            depth[v] = depth[curr] + 1;
            buildPath(v, curr, t);
        }
        out[curr] = t;
    }

public:
    HeavyLightDecomposition(int node_size) : V(node_size), G(V), stsize(V, 0), parent(V, -1),
        pathtop(V, -1), depth(V, 0), in(V, -1), reverse_in(V, -1), out(V, -1){}

    void add_edge(int u, int v){
        G[u].push_back(v);
        G[v].push_back(u);
    }

    void build(int _root = 0){
        root = _root;
        int t = 0;
        buildStsize(root, -1);
        pathtop[root] = root;
        buildPath(root, -1, t);
    }

    inline int get(int a){
        return in[a];
    }

    int la(int a, int k) {
        while(true){
            int u = pathtop[a];
            if(in[a] - k >= in[u]) return reverse_in[in[a] - k];
            k -= in[a] - in[u] + 1;
            a = parent[u];
        }
    }

    int lca(int a, int b){
        int pa = pathtop[a], pb = pathtop[b];
        while(pathtop[a] != pathtop[b]){
            if(in[pa] > in[pb]){
                a = parent[pa], pa = pathtop[a];
            } else{
                b = parent[pb], pb = pathtop[b];
            }
        }
        if(in[a] > in[b]) swap(a, b);
        return a;
    }

    int dist(int a, int b){ return depth[a] + depth[b] - 2 * depth[lca(a, b)]; }

    int jump(int from, int to, int k) {
        if(!k) return from;
        int l = lca(from, to);
        int d = dist(from, to);
        if(d < k) return -1;
        if(depth[from] - depth[l] >= k) return la(from, k);
        k -= depth[from] - depth[l];
        return la(to, depth[to] - depth[l] - k);
    }

    void subtree_query(int a, const function<void(int, int)> &func){
        func(in[a], out[a]);
    }

    void path_query(int a, int b, const function<void(int, int)> &func, bool include_root = true, bool reverse_path = false){
        vector<pair<int, int>> path;
        int pa = pathtop[a], pb = pathtop[b];
        while(pathtop[a] != pathtop[b]){
            if(in[pa] > in[pb]){
                path.emplace_back(in[pa], in[a] + 1);
                a = parent[pa], pa = pathtop[a];
            } else{
                path.emplace_back(in[pb], in[b] + 1);
                b = parent[pb], pb = pathtop[b];
            }
        }
        if(in[a] > in[b]) swap(a, b);

        if(include_root) path.emplace_back(in[a], in[b] + 1);
        else path.emplace_back(in[a] + 1, in[b] + 1);

        if(!reverse_path) reverse(path.begin(), path.end());
        else for(auto &p : path) p = make_pair(V - p.second, V - p.first);

        for(auto [u, v] : path){
            func(u, v);
        }
    }

    void path_noncommutative_query(int a, int b, const function<void(int, int)> &func, const function<void(int, int)> &func2){
        int l = lca(a, b);
        path_query(a, l, func2, false, true);
        path_query(l, b, func, true, false);
    }
};
#line 7 "test/library_checker/tree/vertex_add_path_sum.test.cpp"

int main(){
    int n, q; cin >> n >> q;
    vector<int> a(n);
    for(int i = 0; i < n; i++){
        cin >> a[i];
    }
    HeavyLightDecomposition hl(n);
    for(int i = 0; i < n - 1; i++){
        int u, v; cin >> u >> v;
        hl.add_edge(u, v);
    }
    hl.build();
    BinaryIndexedTree<long long> BIT(n);
    for(int i = 0; i < n; i++){
        BIT.add(hl.get(i), a[i]);
    }
    long long ans = 0;
    auto query = [&](int l, int r){
        ans += BIT.sum(l, r);
    };
    while(q--){
        int t; cin >> t;
        if(t == 0){
            int p, x; cin >> p >> x;
            BIT.add(hl.get(p), x);
        }else{
            int u, v; cin >> u >> v;
            ans = 0;
            hl.path_query(u, v, query);
            cout << ans << "\n";
        }
    }
}

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