#650930 (C++17) No.1488 Max Score of the Tree

提出ソース
結果

問題	No.1488 Max Score of the Tree
ユーザー	ningenMe
提出日時	2021-04-23 22:41:22
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	25 ms / 2,000 ms
コード長	17,084 bytes
コンパイル時間	2,929 ms
コンパイル使用メモリ	232,528 KB
実行使用メモリ	6,944 KB
最終ジャッジ日時	2024-07-04 08:25:28
合計ジャッジ時間	4,088 ms
ジャッジサーバーID （参考情報）	judge4 / judge5
このコードへのチャレンジ
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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	23 ms 6,812 KB
testcase_01	AC	23 ms 6,940 KB
testcase_02	AC	24 ms 6,944 KB
testcase_03	AC	25 ms 6,940 KB
testcase_04	AC	25 ms 6,944 KB
testcase_05	AC	2 ms 6,940 KB
testcase_06	AC	8 ms 6,940 KB
testcase_07	AC	15 ms 6,940 KB
testcase_08	AC	11 ms 6,944 KB
testcase_09	AC	9 ms 6,940 KB
testcase_10	AC	16 ms 6,940 KB
testcase_11	AC	25 ms 6,940 KB
testcase_12	AC	2 ms 6,940 KB
testcase_13	AC	6 ms 6,940 KB
testcase_14	AC	13 ms 6,944 KB
testcase_15	AC	9 ms 6,944 KB
testcase_16	AC	3 ms 6,940 KB
testcase_17	AC	6 ms 6,940 KB
testcase_18	AC	17 ms 6,940 KB
testcase_19	AC	11 ms 6,940 KB
testcase_20	AC	5 ms 6,944 KB
testcase_21	AC	4 ms 6,940 KB
testcase_22	AC	8 ms 6,940 KB
testcase_23	AC	2 ms 6,940 KB
testcase_24	AC	2 ms 6,944 KB
testcase_25	AC	2 ms 6,940 KB
testcase_26	AC	7 ms 6,944 KB
testcase_27	AC	3 ms 6,940 KB
testcase_28	AC	4 ms 6,944 KB
testcase_29	AC	5 ms 6,944 KB
testcase_30	AC	20 ms 6,944 KB
testcase_31	AC	25 ms 6,944 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> 
using namespace std; 
using int128  = __int128_t; 
using int64   = long long; 
using int32   = int; 
using uint128 = __uint128_t; 
using uint64  = unsigned long long; 
using uint32  = unsigned int; 

#define ALL(obj) (obj).begin(),(obj).end() 
template<class T> using priority_queue_reverse = priority_queue<T,vector<T>,greater<T>>; 

constexpr int64 MOD = 1'000'000'000LL + 7; //' 
constexpr int64 MOD2 = 998244353; 
constexpr int64 HIGHINF = 1'000'000'000'000'000'000LL; 
constexpr int64 LOWINF = 1'000'000'000'000'000LL; //' 
constexpr long double PI = 3.1415926535897932384626433L; 

template <class T> vector<T> multivector(size_t N,T init){return vector<T>(N,init);} 
template <class... T> auto multivector(size_t N,T... t){return vector<decltype(multivector(t...))>(N,multivector(t...));} 
template <class T> void corner(bool flg, T hoge) {if (flg) {cout << hoge << endl; exit(0);}} 
template <class T, class U>ostream &operator<<(ostream &o, const map<T, U>&obj) {o << "{"; for (auto &x : obj) o << " {" << x.first << " : " << x.second << "}" << ","; o << " }"; return o;} 
template <class T>ostream &operator<<(ostream &o, const set<T>&obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;} 
template <class T>ostream &operator<<(ostream &o, const multiset<T>&obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;} 
template <class T>ostream &operator<<(ostream &o, const vector<T>&obj) {o << "{"; for (int i = 0; i < (int)obj.size(); ++i)o << (i > 0 ? ", " : "") << obj[i]; o << "}"; return o;} 
template <class T>ostream &operator<<(ostream &o, const deque<T>&obj) {o << "{"; for (int i = 0; i < (int)obj.size(); ++i)o << (i > 0 ? ", " : "") << obj[i]; o << "}"; return o;} 
template <class T, class U>ostream &operator<<(ostream &o, const pair<T, U>&obj) {o << "{" << obj.first << ", " << obj.second << "}"; return o;} 
void print(void) {cout << endl;} 
template <class Head> void print(Head&& head) {cout << head;print();} 
template <class Head, class... Tail> void print(Head&& head, Tail&&... tail) {cout << head << " ";print(forward<Tail>(tail)...);} 
template <class T> void chmax(T& a, const T b){a=max(a,b);} 
template <class T> void chmin(T& a, const T b){a=min(a,b);} 
vector<string> split(const string &str, const char delemiter) {vector<string> res;stringstream ss(str);string buffer; while( getline(ss, buffer, delemiter) ) res.push_back(buffer); return res;} 
inline constexpr int msb(int x) {return x?31-__builtin_clz(x):-1;} 
inline constexpr int64 ceil_div(const int64 a,const int64 b) {return (a+(b-1))/b;}// return ceil(a/b) 
void YN(bool flg) {cout << (flg ? "YES" : "NO") << endl;} 
void Yn(bool flg) {cout << (flg ? "Yes" : "No") << endl;} 
void yn(bool flg) {cout << (flg ? "yes" : "no") << endl;} 

/*
 * @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;}
};

/*
 * @title Tree - 木
 * @docs md/graph/Tree.md
 */
template<class Operator> class TreeBuilder;
template<class Operator> class Tree {
private:
	using TypeEdge = typename Operator::TypeEdge;
	size_t num;
	size_t ord;
	Graph<TypeEdge>& g;
	friend TreeBuilder<Operator>;
	Tree(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() {
		Tree tree = Tree::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 TreeBuilder<Operator> builder(Graph<TypeEdge>& graph) { return TreeBuilder<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 TreeBuilder {
	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;
	TreeBuilder(Graph<TypeEdge>& g):tree(g){}
	TreeBuilder& root(const int rt) { is_root_made=true; tree.make_root(rt); return *this;}
	TreeBuilder& root() { is_root_made=true; tree.make_root(); return *this;}
	TreeBuilder& child() { assert(is_root_made); is_child_made=true;  tree.make_child();  return *this;}
	TreeBuilder& parent() { assert(is_root_made); is_parent_made=true; tree.make_parent(); return *this;}
	TreeBuilder& subtree_size() { assert(is_child_made); is_subtree_size_made=true; tree.make_subtree_size(); return *this;}
	TreeBuilder& ancestor() { assert(is_parent_made); tree.make_ancestor(); return *this;}
	TreeBuilder& eulertour() { assert(is_child_made); tree.make_eulertour(); return *this;}
	TreeBuilder& heavy_light_decomposition() { assert(is_subtree_size_made); assert(is_parent_made); tree.make_heavy_light_decomposition(); return *this;}
	Tree<Operator>&& build() {return move(tree);}
private:
	Tree<Operator> tree;
}; 
template<class T> struct TreeOperator{
	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 = Tree<TreeOperator<int>>::builder(g).build();

/** 
 * @url  
 * @est 
 */  
int main() { 
    cin.tie(0);ios::sync_with_stdio(false);
    int N,K; cin >> N >> K;
    Graph<int> g(N);
    for(int i=0;i<N-1;++i) {
        int a,b,c; cin >> a >> b >> c;
        a--,b--;
        g.make_bidirectional_edge(a,b,c);
    }
    auto tree = Tree<TreeOperator<int>>::builder(g).root(0).parent().child().build();
    vector<int64> cnt(N,0);
    int sum = 0;
    vector<int> cost,value;
    for(int pa:tree.order) {
        if(tree.child[pa].empty()) {
            cnt[pa]++;
            sum += tree.edge_dist[pa];
        }
        for(auto p:tree.child[pa]) {
            int ch = p.first;
            cnt[pa] += cnt[ch];
        }        
        auto w = tree.parent[pa].second;
        if(tree.depth[pa]) {
            value.push_back(cnt[pa]*w);
            cost.push_back(w);
        }
    }
    vector<int> dp(K+1,0),tp(K+1,0);
    for(int i=0;i<N-1;++i) {
        for(int j=0;j<=K;++j) tp[j]=0;
        for(int j=0;j<=K;++j) {
            if(j+cost[i]<=K)chmax(tp[j+cost[i]],dp[j]+value[i]);
            chmax(tp[j],dp[j]);          
        }
        swap(tp,dp);
    }
    int ans = sum + (*max_element(ALL(dp)));
    cout << ans << endl;
    return 0; 
}
yukicoder

結果

テストケース

ソースコード
