#571820 (C++17) No.399 動的な領主

提出ソース
結果

問題	No.399 動的な領主
ユーザー	theory_and_me
提出日時	2020-10-27 00:45:43
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	556 ms / 2,000 ms
コード長	15,143 bytes
コンパイル時間	3,136 ms
コンパイル使用メモリ	238,340 KB
実行使用メモリ	34,360 KB
最終ジャッジ日時	2024-07-21 21:48:19
合計ジャッジ時間	9,492 ms
ジャッジサーバーID （参考情報）	judge3 / judge1
このコードへのチャレンジ
（要ログイン）
テストケース

テストケース表示
入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 5,248 KB
testcase_01	AC	2 ms 5,376 KB
testcase_02	AC	2 ms 5,376 KB
testcase_03	AC	2 ms 5,376 KB
testcase_04	AC	4 ms 5,376 KB
testcase_05	AC	35 ms 5,888 KB
testcase_06	AC	551 ms 29,384 KB
testcase_07	AC	551 ms 29,380 KB
testcase_08	AC	541 ms 29,368 KB
testcase_09	AC	539 ms 29,364 KB
testcase_10	AC	5 ms 5,376 KB
testcase_11	AC	25 ms 5,888 KB
testcase_12	AC	400 ms 29,224 KB
testcase_13	AC	371 ms 29,108 KB
testcase_14	AC	101 ms 34,360 KB
testcase_15	AC	140 ms 34,344 KB
testcase_16	AC	222 ms 32,288 KB
testcase_17	AC	556 ms 29,348 KB
testcase_18	AC	548 ms 29,428 KB
権限があれば一括ダウンロードができます
ソースコード

raw source code
#include <bits/stdc++.h>
#include <atcoder/lazysegtree>
using namespace std;
using namespace atcoder;

#define REP(i,n) for(ll i=0;i<(ll)n;i++)
#define dump(x)  cerr << "Line " << __LINE__ << ": " <<  #x << " = " << (x) << "\n";
#define spa << " " <<
#define fi first
#define se second
#define ALL(a)  (a).begin(),(a).end()
#define ALLR(a)  (a).rbegin(),(a).rend()

using ld = long double;
using ll = long long;
using ull = unsigned long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdd = pair<ld, ld>;

template<typename T> using V = vector<T>;
template<typename T> using P = pair<T, T>;
template<typename T> vector<T> make_vec(size_t n, T a) { return vector<T>(n, a); }
template<typename... Ts> auto make_vec(size_t n, Ts... ts) { return vector<decltype(make_vec(ts...))>(n, make_vec(ts...)); }
template<class S, class T> ostream& operator << (ostream& os, const pair<S, T> v){os << "(" << v.first << ", " << v.second << ")"; return os;}
template<typename T> ostream& operator<<(ostream &os, const vector<T> &v) { for (auto &e : v) os << e << ' '; return os; }
template<class T> ostream& operator<<(ostream& os, const vector<vector<T>> &v){ for(auto &e : v){os << e << "\n";} return os;}
struct fast_ios { fast_ios(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;

template <class T> void UNIQUE(vector<T> &x) {sort(ALL(x));x.erase(unique(ALL(x)), x.end());}
template<class T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T> bool chmin(T &a, const T &b) { if (a>b) { a=b; return 1; } return 0; }
void fail() { cout << -1 << '\n'; exit(0); }
inline int popcount(const int x) { return __builtin_popcount(x); }
inline int popcount(const ll x) { return __builtin_popcountll(x); }
template<typename T> void debug(vector<vector<T>>&v,ll h,ll w){for(ll i=0;i<h;i++)
{cerr<<v[i][0];for(ll j=1;j<w;j++)cerr spa v[i][j];cerr<<"\n";}};
template<typename T> void debug(vector<T>&v,ll n){if(n!=0)cerr<<v[0];
for(ll i=1;i<n;i++)cerr spa v[i];
cerr<<"\n";};

const ll INF = (1ll<<62);
// const ld EPS   = 1e-10;
// const ld PI    = acos(-1.0);
const ll mod = (int)1e9 + 7;
//const ll mod = 998244353;

template<class Operator> class Tree {
	using TypeDist = typename Operator::TypeDist;
	size_t num;
	size_t ord;
	enum METHODS{
		MAKE_DEPTH,
		MAKE_CHILD,
		MAKE_PARENT,
		MAKE_SIZE,
		MAKE_SUBTREE,
		MAKE_ANCESTOR,
		MAKE_EOULERTOUR,
		MAKE_HEAVY_LIGHT_DECOMPOSITION,
		METHODS_SIZE,
	};
	array<int,METHODS_SIZE> executed_flag;
public:
	vector<vector<pair<size_t,TypeDist>>> edge;
	vector<size_t> depth;
	vector<size_t> order; // ord[i]: i番目に「その頂点からのdfsが終了した」頂点の番号．葉の方がdfsが早く完了するため，ord[0], ord[1]などには葉が，ord[num-1] には根が入る．葉から根の方に有向辺を引いたときのトポロジカル順序と思ってもOK．
	vector<size_t> reorder; // ord を逆にしたもの．根から葉の方に有向辺を引いたときのトポロジカル順序と思ってもOK．
	vector<TypeDist> dist;
	vector<pair<size_t,TypeDist>> parent;
	vector<vector<pair<size_t,TypeDist>>> child;
	vector<array<pair<size_t,TypeDist>,Operator::bit>> ancestor;
	vector<size_t> size;
	vector<vector<size_t>> subtree;
	vector<size_t> head;
	vector<size_t> hldorder;
	vector<size_t> eulertour;
	vector<pair<size_t,size_t>> eulertour_range;
	Tree(const int num):num(num),edge(num),depth(num,-1),order(num),dist(num),executed_flag(){}
	//O(1) anytime
	void make_edge(const int& from, const int& to, const TypeDist w = 1) {
		edge[from].push_back({to,w});
	}
	//O(N) anytime
	void make_depth(const int root) {
		executed_flag[MAKE_DEPTH]++;
		depth[root] = 0;
		dist[root] = Operator::unit_dist;
		ord = 0;
		dfs(root,-1);
		order[ord++] = root;
		reverse_copy(order.begin(),order.end(),back_inserter(reorder));
	}
	//O(N) anytime for forest
	void make_depth(void) {
		executed_flag[MAKE_DEPTH]++;
		ord = 0;
		for(size_t root = 0; root < num; ++root) {
			if(depth[root] != -1) continue;
			depth[root] = 0;
			dist[root] = Operator::unit_dist;
			dfs(root,-1);
			order[ord++] = root;
		}
		reverse_copy(order.begin(),order.end(),back_inserter(reorder));
	}
	//for make_depth
	void dfs(int curr, int prev){
		for(auto& e:edge[curr]){
			int next = e.first;
			if(next==prev) continue;
			depth[next] = depth[curr] + 1;
			dist[next]  = Operator::func_dist(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);
		}
	}
	//O(N) after make_depth
	void make_parent(const int root = 0) {
		if(executed_flag[MAKE_PARENT]++) return;
		if(!executed_flag[MAKE_DEPTH]) make_depth(root);
		parent.resize(num,make_pair(num,Operator::unit_dist));
		for (size_t i = 0; i < num; ++i) for (auto& e : edge[i]) if (depth[i] > depth[e.first]) parent[i] = e;
	}
	//O(N) after make_depth
	void make_child(const int root = 0) {
		if(executed_flag[MAKE_CHILD]++) return;
		if(!executed_flag[MAKE_DEPTH]) make_depth(root);
		child.resize(num);
		for (size_t i = 0; i < num; ++i) for (auto& e : edge[i]) if (depth[i] < depth[e.first]) child[i].push_back(e);
	}
	//O(NlogN) after make_parent
	void make_ancestor(const int root = 0) {
		if(executed_flag[MAKE_ANCESTOR]++) return;
		if(!executed_flag[MAKE_PARENT]) make_parent(root);
		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));
		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(ancestor[k][j - 1],ancestor[i][j - 1]);
			}
		}
	}
	//O(logN) after make_ancestor
	//return {lca,lca_dist} l and r must be connected
	pair<size_t,TypeDist> lca(size_t l, size_t r) {
		assert(executed_flag[MAKE_ANCESTOR]);
		if (depth[l] < depth[r]) swap(l, r);
		int diff = depth[l] - depth[r];
		auto ancl = make_pair(l,Operator::unit_lca);
		auto ancr = make_pair(r,Operator::unit_lca);
		for (int j = 0; j < Operator::bit; ++j) {
			if (diff & (1 << j)) {
				ancl = Operator::func_lca(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(ancestor[ancl.first][j],ancl);
				ancr = Operator::func_lca(ancestor[ancr.first][j],ancr);
			}
		}
		ancl = Operator::func_lca(ancestor[ancl.first][0],ancl);
		ancr = Operator::func_lca(ancestor[ancr.first][0],ancr);
		return Operator::func_lca(ancl,ancr);
	}
	//O(N) anytime
	//pair<diameter,vertex_set>
	pair<TypeDist,vector<int>> diameter(void){
		make_depth(0);
		int root = max_element(dist.begin(), dist.end()) - dist.begin();
		make_depth(root);
		int leaf = max_element(dist.begin(), dist.end()) - dist.begin();
		make_parent();
		TypeDist d = dist[leaf];
		vector<int> v;
		while (leaf != root) {
			v.push_back(leaf);
			leaf = parent[leaf].first;
		}
		v.push_back(root);
		return make_pair(d,v);
	}
	//O(N^2) after make_depth
	void make_subtree(const int root = 0) {
		if(executed_flag[MAKE_SUBTREE]++) return;
		if(!executed_flag[MAKE_DEPTH]) make_depth(root);
		subtree.resize(num);
		for (size_t i = 0; i < num; ++i) subtree[i].push_back(i);
		for (size_t i = 0; i < num; ++i) for (auto& e : edge[order[i]]) if (depth[order[i]] < depth[e.first]) for(auto k: subtree[e.first]) subtree[order[i]].push_back(k);
	}
	//O(N) after make_child
	void make_size(const int root = 0) {
		if(executed_flag[MAKE_SIZE]++) return;
		if(!executed_flag[MAKE_CHILD]) make_child(root);
		size.resize(num,1);
		for (size_t i:order) for (auto e : child[i]) size[i] += size[e.first];
	}
	//(N) after make_depth and make_child
	template<class TypeReroot> vector<TypeReroot> rerooting(vector<TypeReroot> rerootdp,vector<TypeReroot> rerootparent) {
		assert(executed_flag[MAKE_CHILD]);
		for(size_t pa:order) for(auto& e:child[pa]) rerootdp[pa] = Operator::func_reroot(rerootdp[pa],rerootdp[e.first]);
		for(size_t pa:reorder) {
			if(depth[pa]) rerootdp[pa] = Operator::func_reroot(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(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(rerootparent[chl],r[1]);
			rerootparent[chr] = Operator::func_reroot(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(rerootparent[ch],l[j-1]);
				rerootparent[ch] = Operator::func_reroot(rerootparent[ch],r[j+1]);
			}
		}
		return rerootdp;
	}
	//O(N) after make_depth,make_parent,make_child
	void make_heavy_light_decomposition(const int root = 0){
		if(executed_flag[MAKE_HEAVY_LIGHT_DECOMPOSITION]++) return;
		if(!executed_flag[MAKE_SIZE]) make_size(root);
		if(!executed_flag[MAKE_PARENT]) make_parent(root);
		head.resize(num); // head[i]: 頂点 i から heavy edge を遡っていった時に最も根に近い頂点
		hldorder.resize(num); // hldorder[i]: hld 順序に並べた場合の 頂点 i が何番目にあるか．hld 順序では，heavy-path が必ず区間になっている & 部分木が必ず区間になっている
		iota(head.begin(),head.end(),0);

        // head を埋める
		for(size_t& pa:reorder) {
			pair<size_t,size_t> maxi = {0,num}; // maxi: (部分木サイズ，頂点)のタプルで，部分木サイズが最大のもの
			for(auto& e:child[pa]) maxi = max(maxi,{size[e.first],e.first});
			if(maxi.first) head[maxi.second] = head[pa]; //　pa から heavy edge が子の方向に生えているなら，heavy edge の先の頂点の head を pa の head と同じにする
		}

        // hldorder を埋める
		stack<size_t> st_head,st_sub;
		size_t cnt = 0;
		for(size_t& root:reorder){ // forest の場合への対応（根が複数ある）
			if(depth[root]) continue; 
			st_head.push(root); // ここから dfs 開始． heavy path を優先して進むような dfs
			while(st_head.size()){
				size_t h = st_head.top();
				st_head.pop();
				st_sub.push(h);
				while (st_sub.size()){
					size_t pa = st_sub.top();
					st_sub.pop();
					hldorder[pa] = cnt++;
					for(auto& e:child[pa]) {
						if(head[e.first]==head[pa]) st_sub.push(e.first);
						else st_head.push(e.first);
					}
				}				
			}
		}
	}
	//after hld type 0: vertex, 1: edge
	vector<pair<size_t,size_t>> path(size_t u,size_t v,int type = 0) {
        // 辺クエリの場合は親方向への辺を処理することにしておく
		assert(executed_flag[MAKE_HEAVY_LIGHT_DECOMPOSITION]);
		vector<pair<size_t,size_t>> path;
		while(1){
			if(hldorder[u]>hldorder[v]) swap(u,v);
			if(head[u]!=head[v]) {
				path.push_back({hldorder[head[v]],hldorder[v]});
				v=parent[head[v]].first;
			}
			else {
				path.push_back({hldorder[u],hldorder[v]});
				break;
			}
		}
		reverse(path.begin(),path.end());
		if(type) path.front().first++; // 辺クエリの場合，LCAだけ省略
		return path;
	}
	size_t hld_lca(size_t u,size_t v){
		assert(executed_flag[MAKE_HEAVY_LIGHT_DECOMPOSITION]);
		while(1){
			if(hldorder[u]>hldorder[v]) swap(u,v);
			if(head[u]==head[v]) return u;
			v=parent[head[v]].first;
		}
	}
	//O(N) after make_child and make_parent
	void make_eulertour(const int root = 0){
		if(executed_flag[MAKE_EOULERTOUR]++) return;
		if(!executed_flag[MAKE_CHILD]) make_child(root);
		if(!executed_flag[MAKE_PARENT]) make_parent(root);
		dfs(reorder.front());
		eulertour_range.resize(num);
		for(int i = 0; i < eulertour.size(); ++i) eulertour_range[eulertour[i]].second = i;
		for(int i = eulertour.size()-1; 0 <= i; --i) eulertour_range[eulertour[i]].first = i;
	}
};
//depth,dist
//https://atcoder.jp/contests/abc126/tasks/abc126_d
//child
//https://atcoder.jp/contests/abc133/tasks/abc133_e
//lca
//https://atcoder.jp/contests/abc014/tasks/abc014_4
//weighted lca
//https://atcoder.jp/contests/code-thanks-festival-2017-open/tasks/code_thanks_festival_2017_h
//https://atcoder.jp/contests/cf16-tournament-round1-open/tasks/asaporo_c
//diameter
//https://atcoder.jp/contests/agc033/tasks/agc033_c
//subtree
//https://atcoder.jp/contests/code-thanks-festival-2018/tasks/code_thanks_festival_2018_f
//rerooting
//https://yukicoder.me/problems/no/922
//size
//https://yukicoder.me/problems/no/872
//eulerTour
//https://yukicoder.me/problems/no/900
//hld
//https://yukicoder.me/problems/no/399
//https://yukicoder.me/problems/no/650
template<class T> struct TreeOperator{
	using TypeDist = T;
	inline static constexpr size_t bit = 20;
	inline static constexpr TypeDist unit_dist = 0;
	inline static constexpr TypeDist unit_lca = 0;
	inline static constexpr TypeDist func_dist(const TypeDist& parent,const TypeDist& w){return parent+w;}
	inline static constexpr pair<size_t,TypeDist> func_lca(const pair<size_t,TypeDist>& l,const pair<size_t,TypeDist>& r){return make_pair(l.first,l.second+r.second);}
	template<class TypeReroot> inline static constexpr TypeReroot func_reroot(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};
	}
};

using S = pll;
using F = ll;

S op(S x, S y){
    return {x.first+y.first, x.second+y.second};
}

S e(){
    return {0, 0};
}

S mapping(F a, S x){
    return {x.first + a * x.second, x.second};
}

F composition(F a, F b){
    return a+b;
}

F id(){
    return 0;
}


int main(){

    ll N;
    cin >> N;
    Tree<TreeOperator<ll>> tree(N);
    REP(i, N-1){
        ll u, v;
        cin >> u >> v;
        u--, v--;
        tree.make_edge(u, v);
        tree.make_edge(v, u);
    }
    tree.make_heavy_light_decomposition();

    V<pll> v(N, {1, 1});
    lazy_segtree<S, op, e, F, mapping, composition, id> seg(v);

    ll Q;
    cin >> Q;
    ll res = 0;
    REP(q, Q){
        ll A, B;
        cin >> A >> B;
        A--, B--;
        auto paths = tree.path(A, B);
        for(auto p: paths){
            ll tmp = seg.prod(p.first, p.second+1).first; // 頂点クエリの場合はアップデートするだけならhldorderにアクセスする必要はない．頂点vの値が欲しい時はseg.get(hldorder[v])で取得
            res += tmp;
            seg.apply(p.first, p.second+1, 1);   
        }
    }

    cout << res << endl;

    return 0;
}