test/graph/Tree-size.test.cpp

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Last update: 2023-06-10 18:20:45+09:00
Problem: https://yukicoder.me/problems/no/872

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#define PROBLEM "https://yukicoder.me/problems/no/872"

#include <vector>
#include <iostream>
#include <cassert>
#include <algorithm>
#include <stack>
#include <numeric>
#include <array>
using namespace std;
#include "../../lib/40-graph/Graph.cpp"
#include "../../lib/40-graph/StaticTree.cpp"

int main(void){
    int N;
	cin >> N;
	Graph<long long> g(N);
	for(int i = 0; i < N-1; ++i){
		int u,v,w;
		cin >> u >> v >> w;
		u--,v--;
		g.make_bidirectional_edge(u,v,w);
	}
	auto tree = StaticTree<StaticTreeOperator<long long>>::builder(g).root(0).child().subtree_size().build();
	long long ans = 0;
	for(int pa:tree.order) for(auto e:tree.child[pa]) ans += e.second*tree.subtree_size[e.first]*(N-tree.subtree_size[e.first])*2LL;
	cout << ans << endl;
	return 0;
}

#line 1 "test/graph/Tree-size.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/872"

#include <vector>
#include <iostream>
#include <cassert>
#include <algorithm>
#include <stack>
#include <numeric>
#include <array>
using namespace std;
#line 1 "lib/40-graph/Graph.cpp"
/*
 * @title Graph
 * @docs md/graph/Graph.md
 */
template<class T> class Graph{
private:
    const size_t N,H,W;
public:
    vector<vector<pair<size_t,T>>> edges;
    Graph(const size_t N):H(-1),W(-1),N(N), edges(N) {}
    Graph(const size_t H, const size_t W):H(H),W(W),N(H*W), edges(H*W) {}
    inline void make_edge(size_t from, size_t to, T w) {
        edges[from].emplace_back(to,w);
    }
    //{from_y,from_x} -> {to_y,to_x} 
    inline void make_edge(pair<size_t,size_t> from, pair<size_t,size_t> to, T w) {
        make_edge(from.first*W+from.second,to.first*W+to.second,w);
    }
    inline void make_bidirectional_edge(size_t from, size_t to, T w) {
        make_edge(from,to,w);
        make_edge(to,from,w);
    }
    inline void make_bidirectional_edge(pair<size_t,size_t> from, pair<size_t,size_t> to, T w) {
        make_edge(from.first*W+from.second,to.first*W+to.second,w);
        make_edge(to.first*W+to.second,from.first*W+from.second,w);
    }
    inline size_t size(){return N;}
    inline size_t idx(pair<size_t,size_t> yx){return yx.first*W+yx.second;}
};
#line 1 "lib/40-graph/StaticTree.cpp"
/*
 * @title StaticTree - 木
 * @docs md/graph/StaticTree.md
 */
template<class Operator> class StaticTreeBuilder;
template<class Operator> class StaticTree {
private:
    using TypeEdge = typename Operator::TypeEdge;
    size_t num;
    size_t ord;
    Graph<TypeEdge>& g;
    friend StaticTreeBuilder<Operator>;
    StaticTree(Graph<TypeEdge>& graph):
            g(graph),
            num(graph.size()),
            depth(graph.size(),-1),
            order(graph.size()),
            edge_dist(graph.size()){
    }
    //for make_depth
    void dfs(int curr, int prev){
        for(const auto& e:g.edges[curr]){
            const int& next = e.first;
            if(next==prev) continue;
            depth[next] = depth[curr] + 1;
            edge_dist[next]  = Operator::func_edge_merge(edge_dist[curr],e.second);
            dfs(next,curr);
            order[ord++] = next;
        }
    }
    //for make_eulertour
    void dfs(int from){
        eulertour.push_back(from);
        for(auto& e:child[from]){
            int to = e.first;
            dfs(to);
            eulertour.push_back(from);
        }
    }
    void make_root(const int root) {
        depth[root] = 0;
        edge_dist[root] = Operator::unit_edge;
        ord = 0;
        dfs(root,-1);
        order[ord++] = root;
        reverse_copy(order.begin(),order.end(),back_inserter(reorder));
    }
    void make_root() {
        ord = 0;
        for(int i=0;i<num;++i) {
            if(depth[i]!=-1) continue;
            depth[i] = 0;
            edge_dist[i] = Operator::unit_edge;
            dfs(i,-1);
            order[ord++] = i;
        }
        reverse_copy(order.begin(),order.end(),back_inserter(reorder));
    }
    void make_child(const int root = 0) {
        child.resize(num);
        for (size_t i = 0; i < num; ++i) for (auto& e : g.edges[i]) if (depth[i] < depth[e.first]) child[i].push_back(e);
    }
    void make_subtree_size() {
        subtree_size.resize(num,1);
        for (size_t i:order) for (auto e : child[i]) subtree_size[i] += subtree_size[e.first];
    }
    void make_parent() {
        parent.resize(num,make_pair(num,Operator::unit_edge));
        for (size_t i = 0; i < num; ++i) for (auto& e : g.edges[i]) if (depth[i] > depth[e.first]) parent[i] = e;
    }
    void make_ancestor() {
        ancestor.resize(num);
        for (size_t i = 0; i < num; ++i) ancestor[i][0] = (parent[i].first!=num?parent[i]:make_pair(i,Operator::unit_lca_edge));
        for (size_t j = 1; j < Operator::bit; ++j) {
            for (size_t i = 0; i < num; ++i) {
                size_t k = ancestor[i][j - 1].first;
                ancestor[i][j] = Operator::func_lca_edge_merge(ancestor[k][j - 1],ancestor[i][j - 1]);
            }
        }
    }
    pair<size_t,TypeEdge> lca_impl(size_t l, size_t r) {
        if (depth[l] < depth[r]) swap(l, r);
        int diff = depth[l] - depth[r];
        auto ancl = make_pair(l,Operator::unit_lca_edge);
        auto ancr = make_pair(r,Operator::unit_lca_edge);
        for (int j = 0; j < Operator::bit; ++j) {
            if (diff & (1 << j)) ancl = Operator::func_lca_edge_merge(ancestor[ancl.first][j],ancl);
        }
        if(ancl.first==ancr.first) return ancl;
        for (int j = Operator::bit - 1; 0 <= j; --j) {
            if(ancestor[ancl.first][j].first!=ancestor[ancr.first][j].first) {
                ancl = Operator::func_lca_edge_merge(ancestor[ancl.first][j],ancl);
                ancr = Operator::func_lca_edge_merge(ancestor[ancr.first][j],ancr);
            }
        }
        ancl = Operator::func_lca_edge_merge(ancestor[ancl.first][0],ancl);
        ancr = Operator::func_lca_edge_merge(ancestor[ancr.first][0],ancr);
        return Operator::func_lca_edge_merge(ancl,ancr);
    }
    pair<TypeEdge,vector<size_t>> diameter_impl() {
        StaticTree tree = StaticTree::builder(g).build();
        size_t root = 0;
        {
            tree.make_root(0);
        }
        root = max_element(tree.edge_dist.begin(),tree.edge_dist.end()) - tree.edge_dist.begin();
        {
            tree.make_root(root);
        }
        size_t leaf = max_element(tree.edge_dist.begin(),tree.edge_dist.end()) - tree.edge_dist.begin();
        TypeEdge sz = tree.edge_dist[leaf];
        vector<size_t> st;
        {
            tree.make_parent();
            while(leaf != root) {
                st.push_back(leaf);
                leaf = tree.parent[leaf].first;
            }
            st.push_back(root);
        }
        return make_pair(sz,st);
    }
    template<class TypeReroot> vector<TypeReroot> rerooting_impl(vector<TypeReroot> rerootdp,vector<TypeReroot> rerootparent) {
        for(size_t pa:order) for(auto& e:child[pa]) rerootdp[pa] = Operator::func_reroot_dp(rerootdp[pa],rerootdp[e.first]);
        for(size_t pa:reorder) {
            if(depth[pa]) rerootdp[pa] = Operator::func_reroot_dp(rerootdp[pa],rerootparent[pa]);
            size_t m = child[pa].size();
            for(int j = 0; j < m && depth[pa]; ++j){
                size_t ch = child[pa][j].first;
                rerootparent[ch] = Operator::func_reroot_dp(rerootparent[ch],rerootparent[pa]);
            }
            if(m <= 1) continue;
            vector<TypeReroot> l(m),r(m);
            for(int j = 0; j < m; ++j) {
                size_t ch = child[pa][j].first;
                l[j] = rerootdp[ch];
                r[j] = rerootdp[ch];
            }
            for(int j = 1; j+1 < m; ++j) l[j] = Operator::func_reroot_merge(l[j],l[j-1]);
            for(int j = m-2; 0 <=j; --j) r[j] = Operator::func_reroot_merge(r[j],r[j+1]);
            size_t chl = child[pa].front().first;
            size_t chr = child[pa].back().first;
            rerootparent[chl] = Operator::func_reroot_dp(rerootparent[chl],r[1]);
            rerootparent[chr] = Operator::func_reroot_dp(rerootparent[chr],l[m-2]);
            for(int j = 1; j+1 < m; ++j) {
                size_t ch = child[pa][j].first;
                rerootparent[ch] = Operator::func_reroot_dp(rerootparent[ch],l[j-1]);
                rerootparent[ch] = Operator::func_reroot_dp(rerootparent[ch],r[j+1]);
            }
        }
        return rerootdp;
    }
    void make_eulertour() {
        dfs(reorder.front());
        eulertour_range.resize(num);
        for(int i = 0; i < eulertour.size(); ++i) eulertour_range[eulertour[i]].second = i+1;
        for(int i = eulertour.size()-1; 0 <= i; --i) eulertour_range[eulertour[i]].first = i;
    }
    void make_heavy_light_decomposition(){
        head.resize(num);
        hld.resize(num);
        iota(head.begin(),head.end(),0);
        for(size_t& pa:reorder) {
            pair<size_t,size_t> maxi = {0,num};
            for(auto& p:child[pa]) maxi = max(maxi,{subtree_size[p.first],p.first});
            if(maxi.first) head[maxi.second] = head[pa];
        }
        stack<size_t> st_head,st_sub;
        size_t cnt = 0;
        //根に近い方から探索
        for(size_t& root:reorder){
            if(depth[root]) continue;
            //根をpush
            st_head.push(root);
            while(st_head.size()){
                size_t h = st_head.top();
                st_head.pop();
                //部分木の根をpush
                st_sub.push(h);
                while (st_sub.size()){
                    size_t pa = st_sub.top();
                    st_sub.pop();
                    //部分木をカウントしていく
                    hld[pa] = cnt++;
                    //子を探索
                    for(auto& p:child[pa]) {
                        //子のheadが親と同じなら、そのまま進む
                        if(head[p.first]==head[pa]) st_sub.push(p.first);
                            //そうじゃない場合は、そこから新しく部分木としてみなす
                        else st_head.push(p.first);
                    }
                }
            }
        }
    }
    //type 0: vertex, 1: edge
    vector<pair<size_t,size_t>> path_impl(size_t u,size_t v,int type = 0) {
        vector<pair<size_t,size_t>> path;
        while(1){
            if(hld[u]>hld[v]) swap(u,v);
            if(head[u]!=head[v]) {
                path.push_back({hld[head[v]],hld[v]});
                v=parent[head[v]].first;
            }
            else {
                path.push_back({hld[u],hld[v]});
                break;
            }
        }
        reverse(path.begin(),path.end());
        if(type) path.front().first++;
        return path;
    }
    pair<vector<pair<size_t,size_t>>,vector<pair<size_t,size_t>>> ordered_path_impl(size_t u,size_t v,int type = 0) {
        vector<pair<size_t,size_t>> path_lca_to_u;
        vector<pair<size_t,size_t>> path_lca_to_v;
        while(1){
            if(head[u] == head[v]) {
                if(depth[u] < depth[v]) path_lca_to_v.emplace_back(hld[u]+type,hld[v]);
                else path_lca_to_u.emplace_back(hld[v]+type,hld[u]);
                break;
            }
            else if(hld[u] < hld[v]) {
                path_lca_to_v.emplace_back(hld[head[v]],hld[v]);
                v = parent[head[v]].first;
            }
            else if(hld[u] > hld[v]) {
                path_lca_to_u.emplace_back(hld[head[u]],hld[u]);
                u = parent[head[u]].first;
            }
        }
        reverse(path_lca_to_v.begin(),path_lca_to_v.end());
        return {path_lca_to_u,path_lca_to_v};
    }
    size_t lca_idx_impl(size_t u,size_t v){
        while(1){
            if(hld[u]>hld[v]) swap(u,v);
            if(head[u]==head[v]) return u;
            v=parent[head[v]].first;
        }
    }
    vector<size_t> head;
public:
    vector<size_t> depth;
    vector<size_t> order;
    vector<size_t> reorder;
    vector<size_t> subtree_size;
    vector<pair<size_t,TypeEdge>> parent;
    vector<vector<pair<size_t,TypeEdge>>> child;
    vector<TypeEdge> edge_dist;
    vector<array<pair<size_t,TypeEdge>,Operator::bit>> ancestor;
    vector<size_t> eulertour;
    vector<pair<size_t,size_t>> eulertour_range;
    vector<size_t> hld;

    /**
     * O(N) builder
     */
    static StaticTreeBuilder<Operator> builder(Graph<TypeEdge>& graph) { return StaticTreeBuilder<Operator>(graph);}
    /**
     * O(logN) after make_ancestor
     * return {lca,lca_dist} l and r must be connected
     */
    pair<size_t,TypeEdge> lca(size_t l, size_t r) {return lca_impl(l,r);}
    /**
     * O(N) anytime
     * return {diameter size,diameter set}
     */
    pair<TypeEdge,vector<size_t>> diameter(void){return diameter_impl();}
    /**
     * O(N) after make_child
     */
    template<class TypeReroot> vector<TypeReroot> rerooting(const vector<TypeReroot>& rerootdp,const vector<TypeReroot>& rerootparent) {return rerooting_impl(rerootdp,rerootparent);}
    /**
     * O(logN)
     */
    vector<pair<size_t,size_t>> vertex_set_on_path(size_t u, size_t v) {return path_impl(u,v,0);}
    /**
    /**
     * O(logN)
     */
    vector<pair<size_t,size_t>> edge_set_on_path(size_t u, size_t v) {return path_impl(u,v,1);}
    /**
     * O(logN)
     * {lca to u path,lca to v path}
     */
    pair<vector<pair<size_t,size_t>>,vector<pair<size_t,size_t>>> vertex_ordered_set_on_path(size_t u, size_t v) {return ordered_path_impl(u,v,0);}
    /**
     * O(logN)
     * {lca to u path,lca to v path}
     */
    pair<vector<pair<size_t,size_t>>,vector<pair<size_t,size_t>>> edge_ordered_set_on_path(size_t u, size_t v) {return ordered_path_impl(u,v,1);}
    /**
     * O(logN) ancestorのlcaより定数倍軽め。idxだけ
     */
    size_t lca_idx(size_t u, size_t v) {return lca_idx_impl(u,v);}
};

template<class Operator> class StaticTreeBuilder {
    bool is_root_made =false;
    bool is_child_made =false;
    bool is_parent_made=false;
    bool is_subtree_size_made=false;
public:
    using TypeEdge = typename Operator::TypeEdge;
    StaticTreeBuilder(Graph<TypeEdge>& g):tree(g){}
    StaticTreeBuilder& root(const int rt) { is_root_made=true; tree.make_root(rt); return *this;}
    StaticTreeBuilder& root() { is_root_made=true; tree.make_root(); return *this;}
    StaticTreeBuilder& child() { assert(is_root_made); is_child_made=true;  tree.make_child();  return *this;}
    StaticTreeBuilder& parent() { assert(is_root_made); is_parent_made=true; tree.make_parent(); return *this;}
    StaticTreeBuilder& subtree_size() { assert(is_child_made); is_subtree_size_made=true; tree.make_subtree_size(); return *this;}
    StaticTreeBuilder& ancestor() { assert(is_parent_made); tree.make_ancestor(); return *this;}
    StaticTreeBuilder& eulertour() { assert(is_child_made); tree.make_eulertour(); return *this;}
    StaticTreeBuilder& heavy_light_decomposition() { assert(is_subtree_size_made); assert(is_parent_made); tree.make_heavy_light_decomposition(); return *this;}
    StaticTree<Operator>&& build() {return move(tree);}
private:
    StaticTree<Operator> tree;
};
template<class T> struct StaticTreeOperator{
    using TypeEdge = T;
    inline static constexpr size_t bit = 20;
    inline static constexpr TypeEdge unit_edge = 0;
    inline static constexpr TypeEdge unit_lca_edge = 0;
    inline static constexpr TypeEdge func_edge_merge(const TypeEdge& parent,const TypeEdge& w){return parent+w;}
    inline static constexpr pair<size_t,TypeEdge> func_lca_edge_merge(const pair<size_t,TypeEdge>& l,const pair<size_t,TypeEdge>& r){return make_pair(l.first,l.second+r.second);}
    template<class TypeReroot> inline static constexpr TypeReroot func_reroot_dp(const TypeReroot& l,const TypeReroot& r) {return {l.first+r.first+r.second,l.second+r.second};}
    template<class TypeReroot> inline static constexpr TypeReroot func_reroot_merge(const TypeReroot& l,const TypeReroot& r) {return {l.first+r.first,l.second+r.second};}
};
//auto tree = StaticTree<StaticTreeOperator<int>>::builder(g).build();
#line 13 "test/graph/Tree-size.test.cpp"

int main(void){
    int N;
	cin >> N;
	Graph<long long> g(N);
	for(int i = 0; i < N-1; ++i){
		int u,v,w;
		cin >> u >> v >> w;
		u--,v--;
		g.make_bidirectional_edge(u,v,w);
	}
	auto tree = StaticTree<StaticTreeOperator<long long>>::builder(g).root(0).child().subtree_size().build();
	long long ans = 0;
	for(int pa:tree.order) for(auto e:tree.child[pa]) ans += e.second*tree.subtree_size[e.first]*(N-tree.subtree_size[e.first])*2LL;
	cout << ans << endl;
	return 0;
}