結果

問題 No.650 行列木クエリ
ユーザー heno239heno239
提出日時 2023-04-02 18:26:41
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 140 ms / 2,000 ms
コード長 12,550 bytes
コンパイル時間 4,102 ms
コンパイル使用メモリ 208,680 KB
実行使用メモリ 41,340 KB
最終ジャッジ日時 2023-10-25 05:09:23
合計ジャッジ時間 5,793 ms
ジャッジサーバーID
（参考情報） 		judge12 / judge11
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 8 ms
11,996 KB
testcase_01 AC 39 ms
19,000 KB
testcase_02 AC 138 ms
41,340 KB
testcase_03 AC 8 ms
11,996 KB
testcase_04 AC 42 ms
19,016 KB
testcase_05 AC 140 ms
41,216 KB
testcase_06 AC 7 ms
11,992 KB
testcase_07 AC 8 ms
11,992 KB
testcase_08 AC 42 ms
17,424 KB
testcase_09 AC 86 ms
37,956 KB
testcase_10 AC 7 ms
11,992 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

diff # 

#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<unordered_set>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
#include<array>
#include<chrono>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
//ll mod = 1;
//constexpr ll mod = 998244353;
constexpr ll mod = 1000000007;
const ll INF = mod * mod;
typedef pair<int, int>P;

#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;

template<typename T>
void chmin(T& a, T b) {
	a = min(a, b);
}
template<typename T>
void chmax(T& a, T b) {
	a = max(a, b);
}
template<typename T>
vector<T> vmerge(vector<T>& a, vector<T>& b) {
	vector<T> res;
	int ida = 0, idb = 0;
	while (ida < a.size() || idb < b.size()) {
		if (idb == b.size()) {
			res.push_back(a[ida]); ida++;
		}
		else if (ida == a.size()) {
			res.push_back(b[idb]); idb++;
		}
		else {
			if (a[ida] < b[idb]) {
				res.push_back(a[ida]); ida++;
			}
			else {
				res.push_back(b[idb]); idb++;
			}
		}
	}
	return res;
}
template<typename T>
void cinarray(vector<T>& v) {
	rep(i, v.size())cin >> v[i];
}
template<typename T>
void coutarray(vector<T>& v) {
	rep(i, v.size()) {
		if (i > 0)cout << " "; cout << v[i];
	}
	cout << "\n";
}
ll mod_pow(ll x, ll n, ll m = mod) {
	if (n < 0) {
		ll res = mod_pow(x, -n, m);
		return mod_pow(res, m - 2, m);
	}
	if (abs(x) >= m)x %= m;
	if (x < 0)x += m;
	//if (x == 0)return 0;
	ll res = 1;
	while (n) {
		if (n & 1)res = res * x % m;
		x = x * x % m; n >>= 1;
	}
	return res;
}
//mod should be <2^31
struct modint {
	int n;
	modint() :n(0) { ; }
	modint(ll m) {
		if (m < 0 || mod <= m) {
			m %= mod; if (m < 0)m += mod;
		}
		n = m;
	}
	operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
bool operator<(modint a, modint b) { return a.n < b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= (int)mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += (int)mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, ll n) {
	if (n == 0)return modint(1);
	modint res = (a * a) ^ (n / 2);
	if (n % 2)res = res * a;
	return res;
}

ll inv(ll a, ll p) {
	return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }
modint operator/=(modint& a, modint b) { a = a / b; return a; }
const int max_n = 1 << 20;
modint fact[max_n], factinv[max_n];
void init_f() {
	fact[0] = modint(1);
	for (int i = 0; i < max_n - 1; i++) {
		fact[i + 1] = fact[i] * modint(i + 1);
	}
	factinv[max_n - 1] = modint(1) / fact[max_n - 1];
	for (int i = max_n - 2; i >= 0; i--) {
		factinv[i] = factinv[i + 1] * modint(i + 1);
	}
}
modint comb(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[b] * factinv[a - b];
}
modint combP(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[a - b];
}

ll gcd(ll a, ll b) {
	a = abs(a); b = abs(b);
	if (a < b)swap(a, b);
	while (b) {
		ll r = a % b; a = b; b = r;
	}
	return a;
}
using ld = long double;
//typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-10;
const ld pi = acosl(-1.0);
template<typename T>
void addv(vector<T>& v, int loc, T val) {
	if (loc >= v.size())v.resize(loc + 1, 0);
	v[loc] += val;
}
/*const int mn = 2000005;
bool isp[mn];
vector<int> ps;
void init() {
	fill(isp + 2, isp + mn, true);
	for (int i = 2; i < mn; i++) {
		if (!isp[i])continue;
		ps.push_back(i);
		for (int j = 2 * i; j < mn; j += i) {
			isp[j] = false;
		}
	}
}*/

//[,val)
template<typename T>
auto prev_itr(set<T>& st, T val) {
	auto res = st.lower_bound(val);
	if (res == st.begin())return st.end();
	res--; return res;
}

//[val,)
template<typename T>
auto next_itr(set<T>& st, T val) {
	auto res = st.lower_bound(val);
	return res;
}
using mP = pair<modint, modint>;
mP operator+(mP a, mP b) {
	return { a.first + b.first,a.second + b.second };
}
mP operator+=(mP& a, mP b) {
	a = a + b; return a;
}
mP operator-(mP a, mP b) {
	return { a.first - b.first,a.second - b.second };
}
mP operator-=(mP& a, mP b) {
	a = a - b; return a;
}
LP operator+(LP a, LP b) {
	return { a.first + b.first,a.second + b.second };
}
LP operator+=(LP& a, LP b) {
	a = a + b; return a;
}
LP operator-(LP a, LP b) {
	return { a.first - b.first,a.second - b.second };
}
LP operator-=(LP& a, LP b) {
	a = a - b; return a;
}

mt19937 mt(time(0));

const string drul = "DRUL";
string senw = "SENW";
//DRUL,or SENW
//int dx[4] = { 1,0,-1,0 };
//int dy[4] = { 0,1,0,-1 };

//-----------------------------------------

template<typename T>
struct SegT {
private:
	int sz; vector<T> node;
	T init_c;
	function<T(T, T)> f;
public:
	SegT() { ; }
	SegT(vector<T> v, T _init_c, function<T(T, T)> _f) {
		init_c = _init_c; f = _f;
		int n = v.size();
		sz = 1;
		while (sz < n)sz *= 2;
		node.resize(2 * sz - 1, init_c);
		rep(i, n) {
			node[i + sz - 1] = v[i];
		}
		per(i, sz - 1) {
			node[i] = f(node[2 * i + 1], node[2 * i + 2]);
		}
	}
	SegT(int n, T _init_c, function<T(T, T)> _f) {
		init_c = _init_c; f = _f;
		sz = 1;
		while (sz < n)sz *= 2;
		node.resize(2 * sz - 1, init_c);
	}
	void update(int k, T a) {
		k += sz - 1;
		node[k] = a;
		while (k > 0) {
			k = (k - 1) / 2;
			node[k] = f(node[k * 2 + 1], node[k * 2 + 2]);
		}
	}
	T query(int a, int b, int k = 0, int l = 0, int r = -1) {
		if (r < 0)r = sz;
		if (r <= a || b <= l)return init_c;
		else if (a <= l && r <= b)return node[k];
		else {
			T vl = query(a, b, k * 2 + 1, l, (l + r) / 2);
			T vr = query(a, b, k * 2 + 2, (l + r) / 2, r);
			return f(vl, vr);
		}
	}
	//k以上でf(x,node[y+sz-1])をtrueにするような最小のy
	int searchloc(int le, T x, function<bool(T, T)> comp) {
		int  k = le + sz - 1;
		if (comp(x, node[k]))return le;
		x = f(x, node[k]);
		while (k > 0) {
			int mem = k;
			k = (k - 1) / 2;
			if (2 * k + 1 == mem) {
				if (comp(x, node[2 * k + 2])) {
					k = 2 * k + 2; break;
				}
				x = f(x, node[2 * k + 2]);
			}
		}
		if (k == 0)return sz;
		while (k < sz - 1) {
			if (comp(x, node[2 * k + 1])) {
				k = 2 * k + 1;
			}
			else {
				x = f(x, node[2 * k + 1]);
				k = 2 * k + 2;
			}
		}
		return k - (sz - 1);
	}
};

using ar = array<modint, 2>;
using mat = array<ar, 2>;
mat e = { ar{1,0},ar{0,1} };
mat f(mat a, mat b) {
	mat res; rep(i, 2)rep(j, 2)res[i][j] = 0;
	rep(i, 2)rep(k, 2)rep(j, 2)res[i][j] += a[i][k] * b[k][j];
	return res;
}
struct edge {
	int to, id;
};
using edges = vector<edge>;
using Graph = vector<edges>;
struct HLDecomposition {
	struct Chain {
		int depth;
		P parent;//chain number,index
		vector<P> child;//child chain number,parent index
		vector<int> mapfrom;
		SegT<mat> stree;

		Chain() { ; }
		Chain(int n) :stree(n,e,f) { ; }
	};
	Graph baseG;
	vector<Chain> chains;
	vector<P> mapto;//raw index->chain number &index
	vector<vector<int>> mapfrom;//chain number & index ->raw index

	HLDecomposition() { ; }
	HLDecomposition(const Graph& g) {
		baseG = g;
		const int n = baseG.size();
		mapto = vector<P>(n, P{ -1,-1 });
		mapfrom.clear();
		vector<int> sz(n, 0);
		int start = 0;
		//int start = -1;
		//rep(i, n)if (baseG[i].size() <= 1) { start = i; break; }
		//assert(start != -1);
		size_check_bfs(start, sz);
		decomposition(start, start, 0, 0, 0, sz);
	}
	int depth(int t) {
		return chains[mapto[t].first].depth;
	}

private:
	void size_check_bfs(int start, vector<int>& sz) {
		const int n = baseG.size();
		queue<P> que;
		que.push({ start,start });
		int cnt = 0; vector<int> ord(n, -1);
		while (!que.empty()) {
			int from, parent;
			tie(from, parent) = que.front(); que.pop();
			ord[cnt++] = from;
			for (edge e : baseG[from]) {
				if (e.to == parent)continue;
				que.push({ e.to,from });
			}
		}
		//assert(cnt == n);
		reverse(all(ord));
		rep(i, n) {
			int from = ord[i];
			sz[from] = 1; for (edge e : baseG[from])sz[from] += sz[e.to];
		}
	}
	int decomposition(int from, int parent, int depth, int pnumber, int pindex, const vector<int>& sz) {
		vector<int> seq;
		bfs(from, parent, seq, sz);
		const int c = chains.size();
		chains.push_back(Chain((int)seq.size()));
		//chains.push_back(Chain());
		chains[c].depth = depth;
		chains[c].parent = { pnumber,pindex };
		rep(i, seq.size()) {
			mapto[seq[i]] = { c,i };
			chains[c].mapfrom.push_back(seq[i]);
		}
		mapfrom.push_back(chains[c].mapfrom);
		rep(i, seq.size()) {
			for (edge e : baseG[seq[i]]) {
				if (mapto[e.to].first != -1)continue;
				int nc = decomposition(e.to, seq[i], depth + 1, c, i, sz);
				chains[c].child.push_back({ nc,i });
			}
		}
		return c;
	}
	void bfs(int from, int parent, vector<int>& seq, const vector<int>& sz) {
		for (;;) {
			seq.push_back(from);
			int best = -1, next = -1;
			for (edge e : baseG[from]) {
				if (e.to == parent)continue;
				if (best < sz[e.to]) {
					best = sz[e.to]; next = e.to;
				}
			}
			if (next == -1)break;
			parent = from; from = next;
		}
	}
	vector<pair<int, P>> all_edge(int u, int v) {
		vector<pair<int, P>> res;
		if (depth(u) > depth(v))swap(u, v);
		while (depth(v) > depth(u)) {
			res.push_back({ mapto[v].first,{ 0,mapto[v].second + 1 } });
			P par = chains[mapto[v].first].parent;
			v = mapfrom[par.first][par.second];
		}
		while (mapto[v].first != mapto[u].first) {
			res.push_back({ mapto[v].first,{ 0,mapto[v].second + 1 } });
			P par = chains[mapto[v].first].parent;
			v = mapfrom[par.first][par.second];
			res.push_back({ mapto[u].first,{ 0,mapto[u].second + 1 } });
			par = chains[mapto[u].first].parent;
			u = mapfrom[par.first][par.second];
		}
		P p = minmax(mapto[v].second, mapto[u].second);
		res.push_back({ mapto[v].first,{ p.first + 1,p.second + 1 } });
		return res;
	}
	vector<pair<int, P>> all_vertice(int u, int v) {
		vector<pair<int, P>> res;
		if (depth(u) > depth(v))swap(u, v);
		while (depth(v) > depth(u)) {
			res.push_back({ mapto[v].first,{ 0,mapto[v].second + 1 } });
			P par = chains[mapto[v].first].parent;
			v = mapfrom[par.first][par.second];
		}
		while (mapto[v].first != mapto[u].first) {
			res.push_back({ mapto[v].first,{ 0,mapto[v].second + 1 } });
			P par = chains[mapto[v].first].parent;
			v = mapfrom[par.first][par.second];
			res.push_back({ mapto[u].first,{ 0,mapto[u].second + 1 } });
			par = chains[mapto[u].first].parent;
			u = mapfrom[par.first][par.second];
		}
		P p = minmax(mapto[v].second, mapto[u].second);
		res.push_back({ mapto[v].first,{ p.first,p.second + 1 } });
		return res;
	}

public:

	void update(int v, mat a) {
		int id = mapto[v].first;
		int loc = mapto[v].second;
		chains[id].stree.update(loc, a);
	}
	void query(int u, int v) {
		mat res = e;
		auto es = all_edge(u, v);
		for (auto pp : es) {
			int id = pp.first;
			int le = pp.second.first;
			int ri = pp.second.second;
			mat nex = chains[id].stree.query(le, ri);
			res = f(nex, res);
		}
		rep(i, 4) {
			if (i > 0)cout << " ";
			cout << res[i / 2][i % 2];
		}cout << "\n";
	}

};
void solve() {
	int n; cin >> n;
	Graph g(n);
	rep(i, n - 1) {
		int a, b; cin >> a >> b;
		g[a].push_back({ b,i });
		g[b].push_back({ a,i });
	}
	HLDecomposition hld(g);
	vector<int> trans(n-1);
	function<void(int, int)> dfs = [&](int id, int fr) {
		for (edge e : g[id])if (e.to != fr) {
			trans[e.id] = e.to;
			dfs(e.to, id);
		}
	}; dfs(0, -1);
	int q; cin >> q;
	rep(i, q) {
		char typ; cin >> typ;
		if (typ == 'x') {
			int id; mat a;
			cin >> id;
			rep(i, 2)rep(j, 2) {
				int x; cin >> x; a[i][j] = x;
			}
			hld.update(trans[id], a);
		}
		else {
			int u, v; cin >> u >> v;
			hld.query(u, v);
		}
	}
}



signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(8);
	//init_f();
	//init();
	//while(true)
	//expr();
	//int t; cin >> t; rep(i, t)
	solve();
	return 0;
}
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