#459408 (C++14) No.650 行列木クエリ

提出ソース
結果

問題	No.650 行列木クエリ
ユーザー	ningenMe
提出日時	2020-04-06 00:02:49
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	120 ms / 2,000 ms
コード長	17,298 bytes
コンパイル時間	2,440 ms
コンパイル使用メモリ	208,148 KB
実行使用メモリ	40,684 KB
最終ジャッジ日時	2024-07-04 16:39:03
合計ジャッジ時間	4,292 ms
ジャッジサーバーID （参考情報）	judge5 / judge2
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	2 ms 5,248 KB
testcase_01	AC	50 ms 10,368 KB
testcase_02	AC	120 ms 35,320 KB
testcase_03	AC	2 ms 5,376 KB
testcase_04	AC	51 ms 10,368 KB
testcase_05	AC	119 ms 35,392 KB
testcase_06	AC	2 ms 5,376 KB
testcase_07	AC	2 ms 5,376 KB
testcase_08	AC	47 ms 11,392 KB
testcase_09	AC	99 ms 40,684 KB
testcase_10	AC	2 ms 5,376 KB
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ソースコード

raw source code
#include <bits/stdc++.h>
using namespace std;
using ll = long long;

#define ALL(obj) (obj).begin(),(obj).end()
#define SPEED cin.tie(0);ios::sync_with_stdio(false);

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 array<T,4>&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;}
template <template <class tmp>  class T, class U> ostream &operator<<(ostream &o, const T<U> &obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr)o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; 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)...);}
constexpr long long MOD = 1000000007;

template<long long mod> class ModInt {
public:
	long long x;
	ModInt():x(0) {
		// do nothing
	}
	ModInt(long long y) : x(y>=0?(y%mod): (mod - (-y)%mod)%mod) {
		// do nothing
	}
	ModInt &operator+=(const ModInt &p) {
		if((x += p.x) >= mod) x -= mod;
		return *this;
	}
	ModInt &operator+=(const long long y) {
        ModInt p(y);
		if((x += p.x) >= mod) x -= mod;
		return *this;
	}
	ModInt &operator+=(const int y) {
        ModInt p(y);
		if((x += p.x) >= mod) x -= mod;
		return *this;
	}
	ModInt &operator-=(const ModInt &p) {
		if((x += mod - p.x) >= mod) x -= mod;
		return *this;
	}
	ModInt &operator-=(const long long y) {
        ModInt p(y);
		if((x += mod - p.x) >= mod) x -= mod;
		return *this;
	}
	ModInt &operator-=(const int y) {
        ModInt p(y);
		if((x += mod - p.x) >= mod) x -= mod;
		return *this;
	}
	ModInt &operator*=(const ModInt &p) {
		x = (x * p.x % mod);
		return *this;
	}
	ModInt &operator*=(const long long y) {
        ModInt p(y);
		x = (x * p.x % mod);
		return *this;
	}
	ModInt &operator*=(const int y) {
        ModInt p(y);
		x = (x * p.x % mod);
		return *this;
	}
	ModInt &operator/=(const ModInt &p) {
		*this *= p.inv();
		return *this;
	}
	ModInt &operator/=(const long long y) {
        ModInt p(y);
		*this *= p.inv();
		return *this;
	}
	ModInt &operator/=(const int y) {
        ModInt p(y);
		*this *= p.inv();
		return *this;
	}
	ModInt operator=(const int y) {
        ModInt p(y);
        *this = p;
        return *this;
    }
    ModInt operator=(const long long y) {
        ModInt p(y);
		*this = p;
        return *this;
    }
	ModInt operator-() const { return ModInt(-x); }
	ModInt operator++() { 
        x++;
        if(x>=mod) x-=mod;
        return *this; 
    }
	ModInt operator--() { 
        x--;
        if(x<0) x+=mod;
        return *this; 
    }
	ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
	ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
	ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
	ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
	bool operator==(const ModInt &p) const { return x == p.x; }
	bool operator!=(const ModInt &p) const { return x != p.x; }
	ModInt inv() const {
		int a = x, b = mod, u = 1, v = 0, t;
		while(b > 0) {
			t = a / b;
			swap(a -= t * b, b);
			swap(u -= t * v, v);
		}
		return ModInt(u);
	}
	ModInt pow(long long n) const {
		ModInt ret(1), mul(x);
		while(n > 0) {
			if(n & 1) ret *= mul;
			mul *= mul;
			n >>= 1;
		}
		return ret;
	}
	friend ostream &operator<<(ostream &os, const ModInt &p) {
		return os << p.x;
	}
	friend istream &operator>>(istream &is, ModInt &a) {
		long long t;
		is >> t;
		a = ModInt<mod>(t);
		return (is);
	}
};
using modint = ModInt<MOD>;

template<class Operator> class Tree {
	Operator Op;
	using typeDist = decltype(Op.unitDist);
	size_t num;
	size_t ord;
public:
	vector<vector<pair<size_t,typeDist>>> edge;
	vector<size_t> depth;
	vector<size_t> order;
	vector<size_t> reorder;
	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>> descendant;
	vector<size_t> head;
	vector<size_t> hldorder;
	Tree(const int num):num(num),edge(num),depth(num,-1),order(num),dist(num){}
	//O(1) anytime
	void makeEdge(const int& from, const int& to, const typeDist w = 1) {
		edge[from].push_back({to,w});
	}
	//O(N) anytime
	void makeDepth(const int root) {
		depth[root] = 0;
		dist[root] = Op.unitDist;
		ord = 0;
		dfs1(root);
		order[ord++] = root;
		reverse_copy(order.begin(),order.end(),back_inserter(reorder));
	}
	//O(N) anytime
	void makeDepth(void) {
		ord = 0;
		for(size_t root = 0; root < num; ++root) {
			if(depth[root] != -1) continue;
			depth[root] = 0;
			dist[root] = Op.unitDist;
			dfs1(root);
			order[ord++] = root;
		}
		reverse_copy(order.begin(),order.end(),back_inserter(reorder));
	}
	//for makeDepth
	void dfs1(int curr, int prev = -1){
		for(auto& e:edge[curr]){
			int next = e.first;
			if(next==prev) continue;
			depth[next] = depth[curr] + 1;
			dist[next]  = Op.funcDist(dist[curr],e.second);
			dfs1(next,curr);
			order[ord++] = next;
		}
	}
	//O(N) after makeDepth
	void makeParent(void) {
		parent.resize(num,make_pair(num,Op.unitDist));
		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 makeDepth
	void makeChild(void) {
		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 makeDepth and makeParent
	void makeAncestor(void) {
		ancestor.resize(num);
		for (size_t i = 0; i < num; ++i) ancestor[i][0] = (parent[i].first!=num?parent[i]:make_pair(i,Op.unitLca));
		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] = Op.funcLca(ancestor[k][j - 1],ancestor[i][j - 1]);
			}
		}
	}
	//O(logN) after makeAncestor
	//return {lca,lca_dist} l and r must be connected
	pair<size_t,typeDist> lca(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,Op.unitLca);
		auto ancr = make_pair(r,Op.unitLca);
		for (int j = 0; j < Operator::bit; ++j) {
			if (diff & (1 << j)) {
				ancl = Op.funcLca(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 = Op.funcLca(ancestor[ancl.first][j],ancl);
				ancr = Op.funcLca(ancestor[ancr.first][j],ancr);
			}
		}
		ancl = Op.funcLca(ancestor[ancl.first][0],ancl);
		ancr = Op.funcLca(ancestor[ancr.first][0],ancr);
		return Op.funcLca(ancl,ancr);
	}
	//O(N) anytime
	int diameter(void){
		makeDepth(0);
		int tmp = max_element(depth.begin(), depth.end()) - depth.begin();
		makeDepth(tmp);
		return *max_element(depth.begin(), depth.end());
	}
	//O(N^2) after makeDepth (include self)
	void makeDescendant(void) {
		descendant.resize(num);
		for (size_t i = 0; i < num; ++i) descendant[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: descendant[e.first]) descendant[order[i]].push_back(k);
	}
	//O(N) after makeChild
	void makeSize(void) {
		size.resize(num,1);
		for (size_t i:order) for (auto e : child[i]) size[i] += size[e.first];
	}
	//(N) after makeDepth and makeChild
	template<class typeReroot> vector<typeReroot> rerooting(vector<typeReroot> rerootdp,vector<typeReroot> rerootparent) {
		for(size_t pa:order) for(auto& e:child[pa]) rerootdp[pa] = Op.funcReroot(rerootdp[pa],rerootdp[e.first]);
		for(size_t pa:reorder) {
			if(depth[pa]) rerootdp[pa] = Op.funcReroot(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] = Op.funcReroot(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] = Op.funcRerootMerge(l[j],l[j-1]);
			for(int j = m-2; 0 <=j; --j) r[j] = Op.funcRerootMerge(r[j],r[j+1]);
			size_t chl = child[pa].front().first;
			size_t chr = child[pa].back().first;
			rerootparent[chl] = Op.funcReroot(rerootparent[chl],r[1]);
			rerootparent[chr] = Op.funcReroot(rerootparent[chr],l[m-2]);
			for(int j = 1; j+1 < m; ++j) {
				size_t ch = child[pa][j].first;
				rerootparent[ch] = Op.funcReroot(rerootparent[ch],l[j-1]);
				rerootparent[ch] = Op.funcReroot(rerootparent[ch],r[j+1]);
			}
		}
		return rerootdp;
    }
	//O(N) after makeDepth,makeParent,makeChild
	void heavyLightDecomposition(){
		head.resize(num);
		hldorder.resize(num);
		iota(head.begin(),head.end(),0);
		for(size_t& pa:reorder) {
			pair<size_t,size_t> maxi = {0,num};
			for(auto& e:child[pa]) maxi = max(maxi,{size[e.first],e.first});
			if(maxi.first) head[maxi.second] = head[pa];
		}
		stack<size_t> st;
		size_t cnt = 0;
		for(size_t& top:reorder){
			if(head[top]!=top) continue;
			st.push(top);
			while(st.size()){
				size_t pa = st.top();
				st.pop();
				hldorder[pa] = cnt++;
				for(auto& e:child[pa]) if(head[e.first]==head[pa]) st.push(e.first);
			}
		}
	}
	//after hld 
	vector<pair<size_t,size_t>> path(size_t u,size_t v) {
		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());
		return path;
	}
	size_t hldLca(size_t u,size_t v){
		while(1){
			if(hldorder[u]>hldorder[v]) swap(u,v);
			if(head[u]==head[v]) return u;
			v=parent[head[v]].first;
		}
	}
};
//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
//descendant
//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
template<class typeDist> struct treeOperator{
	static const size_t bit = 20;
	typeDist unitDist = 0;
	typeDist unitLca = 0;
	typeDist funcDist(const typeDist& parent,const typeDist& w){return parent+w;}
	pair<size_t,typeDist> funcLca(const pair<size_t,typeDist>& l,const pair<size_t,typeDist>& r){return make_pair(l.first,l.second+r.second);}
	template<class typeReroot> typeReroot funcReroot(const typeReroot& l,const typeReroot& r) {
		return {l.first+r.first+r.second,l.second+r.second};
	}
	template<class typeReroot> typeReroot funcRerootMerge(const typeReroot& l,const typeReroot& r) {
		return {l.first+r.first,l.second+r.second};
	}
};
// Tree<treeOperator<int>> tree(N);


using matrix = array<modint, 4>;
 
template<class Operator> class SegmentTree {
	Operator Op;                            
	using typeNode = decltype(Op.unitNode); 
	size_t length;
	size_t num;
	vector<typeNode> node;
	vector<pair<size_t,size_t>> range;
public:
 
	//unitで初期化
	SegmentTree(const size_t num): num(num) {
		for (length = 1; length < num; length *= 2);
		node.resize(2 * length, Op.unitNode);
		range.resize(2 * length);
		for (int i = 0; i < length; ++i) range[i+length] = make_pair(i,i+1);
		for (int i = length - 1; i >= 0; --i) range[i] = make_pair(range[(i<<1)+0].first,range[(i<<1)+1].second);
	}
 
	//vectorで初期化
	SegmentTree(const vector<typeNode> & vec) : num(vec.size()) {
		for (length = 1; length < vec.size(); length *= 2);
		node.resize(2 * length, Op.unitNode);
		for (int i = 0; i < vec.size(); ++i) node[i + length] = vec[i];
		for (int i = length - 1; i >= 0; --i) node[i] = Op.funcNode(node[(i<<1)+0],node[(i<<1)+1]);
		range.resize(2 * length);
		for (int i = 0; i < length; ++i) range[i+length] = make_pair(i,i+1);
		for (int i = length - 1; i >= 0; --i) range[i] = make_pair(range[(i<<1)+0].first,range[(i<<1)+1].second);
	}
 
	//同じinitで初期化
	SegmentTree(const size_t num, const typeNode init) : num(num) {
		for (length = 1; length < num; length *= 2);
		node.resize(2 * length, init);
		range.resize(2 * length);
		for (int i = 0; i < length; ++i) range[i+length] = make_pair(i,i+1);
		for (int i = length - 1; i >= 0; --i) range[i] = make_pair(range[(i<<1)+0].first,range[(i<<1)+1].second);
	}
	
	//[idx,idx+1)
	void update(size_t idx, const typeNode var) {
		if(idx < 0 || length <= idx) return;
		idx += length;
		node[idx] = Op.funcMerge(node[idx],var);
		while(idx >>= 1) node[idx] = Op.funcNode(node[(idx<<1)+0],node[(idx<<1)+1]);
	}
 
	//[l,r)
	typeNode get(int l, int r) {
		if (l < 0 || length <= l || r < 0 || length < r) return Op.unitNode;
		typeNode vl = Op.unitNode, vr = Op.unitNode;
		for(l += length, r += length; l < r; l >>=1, r >>=1) {
			if(l&1) vl = Op.funcNode(vl,node[l++]);
			if(r&1) vr = Op.funcNode(node[--r],vr);
		}
		return Op.funcNode(vl,vr);
	}
 
	//return [0,length]
	int PrefixBinarySearch(typeNode var) {
		if(!Op.funcCheck(node[1],var)) return num;
		typeNode ret = Op.unitNode;
		size_t idx = 2;
		for(; idx < 2*length; idx<<=1){
			if(!Op.funcCheck(Op.funcNode(ret,node[idx]),var)) {
				ret = Op.funcNode(ret,node[idx]);
				idx++;
			}
		}
		return min((idx>>1) - length,num);
	}
 
	//range[l,r) return [l,r]
	int BinarySearch(size_t l, size_t r, typeNode var) {
		if (l < 0 || length <= l || r < 0 || length < r) return -1;
		typeNode ret = Op.unitNode;
		size_t off = l;
		for(size_t idx = l+length; idx < 2*length && off < r; ){
			if(range[idx].second<=r && !Op.funcCheck(Op.funcNode(ret,node[idx]),var)) {
				ret = Op.funcNode(ret,node[idx]);
				off = range[idx++].second;
				if(!(idx&1)) idx >>= 1;			
			}
			else{
				idx <<=1;
			}
		}
		return off;
	}
 
	void print(){
		cout << "{ " << get(0,1);
		for(int i = 1; i < length; ++i) cout << ", " << get(i,i+1);
		cout << " }" << endl;
 
		// for(int i = 1,j = 1; i < 2*length; ++i) {
		// 	cout << node[i] << " ";
		// 	if(i==((1<<j)-1) && ++j) cout << endl;
		// }
	}
 
};
 
matrix E = {1,0,0,1};
 
//node:matrix
template<class typeNode> struct nodeMatrixPointUpdate {
    typeNode unitNode = E;
	typeNode funcNode(typeNode l,typeNode r){
        matrix res = {};
        for(int i = 0; i < 2; ++i) {
            for(int j = 0; j < 2; ++j) {
                for(int k = 0; k < 2; ++k) {
                    res[i*2+j] += l[i*2+k]*r[k*2+j];
                }
            }
        }
        return res;
    }
	typeNode funcMerge(typeNode l,typeNode r){
		return r;
    }
};

int main() {
	SPEED
	int N; cin >> N;
	Tree<treeOperator<int>> tree(N);
	vector<pair<int,int>> edge(N-1);
	for(int i = 0; i < N-1; ++i) {
		int u,v; cin >> u >> v;
		tree.makeEdge(u,v);
		tree.makeEdge(v,u);
		edge[i] = {u,v};
	}
	tree.makeDepth(0);
	tree.makeChild();
	tree.makeParent();
	tree.makeSize();
	tree.heavyLightDecomposition();
    SegmentTree<nodeMatrixPointUpdate<matrix>> seg(N);
    nodeMatrixPointUpdate<matrix> Op;
    int Q; cin >> Q;
    for(int i = 0; i < Q; ++i) {
        char c; cin >> c;
        if(c == 'x'){
            int j; cin >> j;
            modint a,b,c,d; cin >> a >> b >> c >> d;
            matrix x = {a,b,c,d};
            int l = edge[j].first, r = edge[j].second;
            l = tree.hldorder[l],r = tree.hldorder[r];
            if(l > r) swap(l,r);
            seg.update(r,x);
        }
        else{
            int l,r; cin >> l >> r;
            auto vp = tree.path(l,r);
            matrix ans = E;
            for(auto p:vp){
                if(p.first != tree.hldorder[l]) ans = Op.funcNode(ans,seg.get(p.first,p.first+1));
                ans = Op.funcNode(ans,seg.get(p.first+1,p.second+1));
            }
            cout << ans[0] << " " << ans[1] << " " << ans[2] << " " << ans[3] << endl;
        }
    }
	return 0;
}