結果
| 問題 |
No.650 行列木クエリ
|
| コンテスト | |
| ユーザー |
 outline
|
| 提出日時 | 2022-11-08 14:45:36 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 83 ms / 2,000 ms |
| コード長 | 9,760 bytes |
| コンパイル時間 | 1,880 ms |
| コンパイル使用メモリ | 156,628 KB |
| 最終ジャッジ日時 | 2025-02-08 19:12:45 |
|
ジャッジサーバーID （参考情報） |
judge4 / judge3 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 10 |
ソースコード
#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
#include <queue>
#include <string>
#include <map>
#include <set>
#include <stack>
#include <tuple>
#include <deque>
#include <array>
#include <numeric>
#include <bitset>
#include <iomanip>
#include <cassert>
#include <chrono>
#include <random>
#include <limits>
#include <iterator>
#include <functional>
#include <sstream>
#include <fstream>
#include <complex>
#include <cstring>
#include <unordered_map>
#include <unordered_set>
#include <memory>
using namespace std;
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,tune=native")
// #pragma GCC target("avx512f,avx512dq,avx512cd,avx512bw,avx512vl")
using ll = long long;
constexpr int INF = 1001001001;
constexpr int mod = 1000000007;
// constexpr int mod = 998244353;
template<class T>
inline bool chmax(T& x, T y){
if(x < y){
x = y;
return true;
}
return false;
}
template<class T>
inline bool chmin(T& x, T y){
if(x > y){
x = y;
return true;
}
return false;
}
constexpr int dx[] = {1, 0, -1, 0, 1, 1, -1, -1};
constexpr int dy[] = {0, 1, 0, -1, 1, -1, 1, -1};
struct mint {
int x;
mint() : x(0) {}
mint(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
mint& operator+=(const mint& p){
if((x += p.x) >= mod) x -= mod;
return *this;
}
mint& operator-=(const mint& p){
if((x -= p.x) < 0) x += mod;
return *this;
}
mint& operator*=(const mint& p){
x = (int)(1LL * x * p.x % mod);
return *this;
}
mint& operator/=(const mint& p){
*this *= p.inverse();
return *this;
}
mint operator-() const { return mint(-x); }
mint operator+(const mint& p) const { return mint(*this) += p; }
mint operator-(const mint& p) const { return mint(*this) -= p; }
mint operator*(const mint& p) const { return mint(*this) *= p; }
mint operator/(const mint& p) const { return mint(*this) /= p; }
bool operator==(const mint& p) const { return x == p.x; }
bool operator!=(const mint& p) const { return x != p.x; }
mint pow(int64_t n) const {
mint res = 1, mul = x;
while(n > 0){
if(n & 1) res *= mul;
mul *= mul;
n >>= 1;
}
return res;
}
// x^(a^b)
// warning : x と mod は互いに素
// x != 0 かつ x % mod == 0 かつ a > 0 はこれを呼び出さずに 0 を返すように処理
mint pow2(int64_t a, int64_t b) const {
if(b == 0) return *this;
if((a %= mod - 1) == 0) return mint(1);
int64_t n = 1;
while(b > 0){
if(b & 1) (n *= a) %= mod - 1;
(a *= a) %= mod - 1;
b >>= 1;
}
return pow(n);
}
mint inverse() const { return pow(mod - 2); }
friend ostream& operator<<(ostream& os, const mint& p){
return os << p.x;
}
friend istream& operator>>(istream& is, mint& p){
int64_t val;
is >> val;
p = mint(val);
return is;
}
};
struct HeavyLightDecomposition {
using Graph = vector<vector<int>>;
int V;
Graph& g;
vector<int> subtree_size, head, in, out, par, inverse;
HeavyLightDecomposition(Graph& g_) :
V(g_.size()), g(g_), subtree_size(V), head(V), in(V), out(V), par(V), inverse(V) {}
void calc_subtree_size(int cur, int p){
if(g[cur].size() && g[cur][0] == p){
swap(g[cur][0], g[cur].back());
}
subtree_size[cur] = 1;
par[cur] = p;
for(auto& child : g[cur]){
if(child == p) continue;
calc_subtree_size(child, cur);
subtree_size[cur] += subtree_size[child];
if(subtree_size[g[cur][0]] < subtree_size[child]){
swap(g[cur][0], child);
}
}
}
void dfs(int cur, int p, int& times){
in[cur] = times++;
inverse[in[cur]] = cur;
for(auto& child : g[cur]){
if(child == p) continue;
head[child] = (g[cur][0] == child ? head[cur] : child);
dfs(child, cur, times);
}
out[cur] = times;
}
void build(int root = 0){
calc_subtree_size(root, -1);
int t = 0;
dfs(root, -1, t);
}
int get(int v, int k){
for(;;){
int u = head[v];
if(in[v] - k >= in[u]){ // u, v in same group
return inverse[in[v] - k];
}
k -= in[v] - in[u] + 1;
v = par[u];
}
}
int lca(int u, int v){
for(;; v = par[head[v]]){
if(in[u] > in[v]) swap(u, v);
if(head[u] == head[v]) return u;
}
}
// path
vector<pair<int, int>> get_sections(int u, int v, bool is_edge = false){
vector<pair<int, int>> res;
for(;; v = par[head[v]]){
if(in[u] > in[v]) swap(u, v);
if(head[u] == head[v]) break;
res.emplace_back(in[head[v]], in[v] + 1);
}
res.emplace_back(in[u] + is_edge, in[v] + 1);
return res;
}
// subtree
pair<int, int> get_section(int v, bool is_edge = false){
return {in[v] + is_edge, out[v]};
}
int operator[](const int& v) const {
return in[v];
}
int edge(int u, int v){
return in[in[u] > in[v] ? u : v];
}
};
template<typename Monoid>
struct SegmentTree{
using F = function<Monoid(Monoid, Monoid)>;
int sz;
vector<Monoid> seg;
const F f;
const Monoid M1;
SegmentTree(const F f, const Monoid& M1) : f(f), M1(M1) {}
SegmentTree(int n, const F f, const Monoid &M1) : f(f), M1(M1) {
sz = 1;
while(sz < n) sz <<= 1;
seg.assign(2 * sz, M1);
}
void resize(int n){
sz = 1;
while(sz < n) sz <<= 1;
seg.assign(2 * sz, M1);
}
void set(int k, const Monoid &x){
seg[k + sz] = x;
}
void build(){
for(int k = sz - 1; k > 0; --k){
seg[k] = f(seg[k << 1], seg[k << 1 | 1]);
}
}
void update(int k, const Monoid &x){
k += sz;
seg[k] = x;
while(k >>= 1){
seg[k] = f(seg[k << 1], seg[k << 1 | 1]);
}
}
Monoid query(int a, int b){
Monoid L = M1, R = M1;
for(a += sz, b += sz; a < b; a >>= 1, b >>= 1){
if(a & 1) L = f(L, seg[a++]);
if(b & 1) R = f(seg[--b], R);
}
return f(L, R);
}
Monoid operator[](const int &k) const{
return seg[k + sz];
}
// (type = true) : find_last
// (type = false) : find_first
template<typename C>
int find_subtree(int a, const C &check, Monoid &M, bool type){
while(a < sz){
Monoid nxt = type ? f(seg[a << 1 | type], M) : f(M, seg[a << 1 | type]);
if(check(nxt)) a = a << 1 | type;
else M = nxt, a = 2 * a + 1 - type;
}
return a - sz;
}
template<typename C>
int find_first(int a, const C &check){
Monoid L = M1;
if(a <= 0){
if(check(f(L, seg[1]))) return find_subtree(1, check, L, false);
return -1;
}
int b = sz;
for(a += sz, b += sz; a < b; a >>= 1, b >>= 1){
if(a & 1){
Monoid nxt = f(L, seg[a]);
if(check(nxt)) return find_subtree(a, check, L, false);
L = nxt;
++a;
}
}
return -1;
}
template<typename C>
int find_last(int b, const C &check){
Monoid R = M1;
if(b >= sz){
if(check(f(seg[1], R))) return find_subtree(1, check, R, true);
return -1;
}
int a = sz;
for(b += sz; a < b; a >>= 1, b >>= 1){
if(b & 1){
Monoid nxt = f(seg[--b], R);
if(check(nxt)) return find_subtree(b, check, R, true);
R = nxt;
}
}
return -1;
}
};
int main(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
int N;
cin >> N;
vector<int> a(N), b(N);
vector<vector<int>> g(N);
for(int i = 0; i < N - 1; ++i){
cin >> a[i] >> b[i];
g[a[i]].emplace_back(b[i]);
g[b[i]].emplace_back(a[i]);
}
HeavyLightDecomposition hld(g);
hld.build();
using S = array<array<mint, 2>, 2>;
auto op = [&](S l, S r) -> S {
S res = {0, 0,
0, 0};
for(int k = 0; k < 2; ++k){
for(int i = 0; i < 2; ++i){
for(int j = 0; j < 2; ++j){
res[i][j] += l[i][k] * r[k][j];
}
}
}
return res;
};
S E = {1, 0,
0, 1};
SegmentTree<S> seg(N, op, E);
int Q;
cin >> Q;
for(int q = 0; q < Q; ++q){
char c; cin >> c;
if(c == 'x'){
int i;
cin >> i;
S x;
for(int i = 0; i < 2; ++i){
for(int j = 0; j < 2; ++j){
cin >> x[i][j];
}
}
seg.update(hld.edge(a[i], b[i]), x);
}
else{
int i, j;
cin >> i >> j;
auto sections = hld.get_sections(i, j, true);
sort(begin(sections), end(sections));
S ans = E;
for(auto& [l, r] : sections){
ans = op(ans, seg.query(l, r));
}
cout << ans[0][0] << ' ' << ans[0][1] << ' ';
cout << ans[1][0] << ' ' << ans[1][1] << '\n';
}
}
return 0;
}