結果
| 問題 | No.650 行列木クエリ |
| ユーザー |
 apricity
|
| 提出日時 | 2024-12-06 19:54:30 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 81 ms / 2,000 ms |
| コード長 | 18,045 bytes |
| コンパイル時間 | 1,904 ms |
| コンパイル使用メモリ | 156,452 KB |
| 実行使用メモリ | 22,972 KB |
| 最終ジャッジ日時 | 2024-12-06 19:54:34 |
| 合計ジャッジ時間 | 3,242 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge3 |
（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 | 1 ms
5,248 KB |
| testcase_01 | AC | 28 ms
6,236 KB |
| testcase_02 | AC | 71 ms
17,916 KB |
| testcase_03 | AC | 2 ms
5,248 KB |
| testcase_04 | AC | 31 ms
6,356 KB |
| testcase_05 | AC | 81 ms
17,916 KB |
| testcase_06 | AC | 2 ms
5,248 KB |
| testcase_07 | AC | 2 ms
5,248 KB |
| testcase_08 | AC | 28 ms
7,244 KB |
| testcase_09 | AC | 65 ms
22,972 KB |
| testcase_10 | AC | 2 ms
5,248 KB |
ソースコード
#include<iostream>
#include<string>
#include<vector>
#include<algorithm>
#include<numeric>
#include<cmath>
#include<utility>
#include<tuple>
#include<array>
#include<cstdint>
#include<cstdio>
#include<iomanip>
#include<map>
#include<set>
#include<unordered_map>
#include<unordered_set>
#include<queue>
#include<stack>
#include<deque>
#include<bitset>
#include<cctype>
#include<chrono>
#include<random>
#include<cassert>
#include<cstddef>
#include<iterator>
#include<string_view>
#include<type_traits>
#include<functional>
#ifdef LOCAL
# include "debug_print.hpp"
# define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
# define debug(...) (static_cast<void>(0))
#endif
using namespace std;
namespace io {
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (auto &x : v) is >> x;
return is;
}
template <typename T, size_t N = 0>
istream &operator>>(istream &is, array<T, N> &v) {
for (auto &x : v) is >> x;
return is;
}
template <size_t N = 0, typename T>
istream& cin_tuple_impl(istream &is, T &t) {
if constexpr (N < std::tuple_size<T>::value) {
auto &x = std::get<N>(t);
is >> x;
cin_tuple_impl<N + 1>(is, t);
}
return is;
}
template <class... T>
istream &operator>>(istream &is, tuple<T...> &t) {
return cin_tuple_impl(is, t);
}
template<typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template<typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template<typename T, size_t N>
ostream &operator<<(ostream &os, const array<T, N> &v) {
size_t n = v.size();
for (size_t i = 0; i < n; i++) {
if (i) os << " ";
os << v[i];
}
return os;
}
template <size_t N = 0, typename T>
ostream& cout_tuple_impl(ostream &os, const T &t) {
if constexpr (N < std::tuple_size<T>::value) {
if constexpr (N > 0) os << " ";
const auto &x = std::get<N>(t);
os << x;
cout_tuple_impl<N + 1>(os, t);
}
return os;
}
template <class... T>
ostream &operator<<(ostream &os, const tuple<T...> &t) {
return cout_tuple_impl(os, t);
}
void in() {}
template<typename T, class... U>
void in(T &t, U &...u) {
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template<typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
void outr() {}
template<typename T, class... U, char sep = ' '>
void outr(const T &t, const U &...u) {
cout << t;
outr(u...);
}
void __attribute__((constructor)) _c() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cout << fixed << setprecision(15);
}
} // namespace io
using io::in;
using io::out;
using io::outr;
using ll = long long;
using D = double;
using LD = long double;
using P = pair<ll, ll>;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using i128 = __int128;
using u128 = unsigned __int128;
using vi = vector<ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vector<vc<T>>;
template <class T> using vvvc = vector<vvc<T>>;
template <class T> using vvvvc = vector<vvvc<T>>;
template <class T> using vvvvvc = vector<vvvvc<T>>;
#define vv(type, name, h, ...) \
vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) \
vector<vector<vector<type>>> name( \
h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
vector<vector<vector<vector<type>>>> name( \
a, vector<vector<vector<type>>>( \
b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
template<typename T> using PQ = priority_queue<T,vector<T>>;
template<typename T> using minPQ = priority_queue<T, vector<T>, greater<T>>;
#define rep1(a) for(ll i = 0; i < a; i++)
#define rep2(i, a) for(ll i = 0; i < a; i++)
#define rep3(i, a, b) for(ll i = a; i < b; i++)
#define rep4(i, a, b, c) for(ll i = a; i < b; i += c)
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep1(a) for(ll i = (a)-1; i >= 0; i--)
#define rrep2(i, a) for(ll i = (a)-1; i >= 0; i--)
#define rrep3(i, a, b) for(ll i = (b)-1; i >= a; i--)
#define rrep4(i, a, b, c) for(ll i = (b)-1; i >= a; i -= c)
#define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)
#define for_subset(t, s) for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define ALL(v) v.begin(), v.end()
#define RALL(v) v.rbegin(), v.rend()
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() )
#define SZ(v) ll(v.size())
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(c, x) distance((c).begin(), lower_bound(ALL(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(ALL(c), (x)))
template <typename T, typename U>
T SUM(const vector<U> &v) {
T res = 0;
for(auto &&a : v) res += a;
return res;
}
template <typename T>
vector<pair<T,int>> RLE(const vector<T> &v) {
if (v.empty()) return {};
T cur = v.front();
int cnt = 1;
vector<pair<T,int>> res;
for (int i = 1; i < (int)v.size(); i++) {
if (cur == v[i]) cnt++;
else {
res.emplace_back(cur, cnt);
cnt = 1; cur = v[i];
}
}
res.emplace_back(cur, cnt);
return res;
}
template<class T, class S>
inline bool chmax(T &a, const S &b) { return (a < b ? a = b, true : false); }
template<class T, class S>
inline bool chmin(T &a, const S &b) { return (a > b ? a = b, true : false); }
void YESNO(bool flag) { out(flag ? "YES" : "NO"); }
void yesno(bool flag) { out(flag ? "Yes" : "No"); }
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_sgn(int x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(ll x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(u64 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int highbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int highbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int highbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int highbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T>
T get_bit(T x, int k) { return x >> k & 1; }
template <typename T>
T set_bit(T x, int k) { return x | T(1) << k; }
template <typename T>
T reset_bit(T x, int k) { return x & ~(T(1) << k); }
template <typename T>
T flip_bit(T x, int k) { return x ^ T(1) << k; }
template <typename T>
T popf(deque<T> &que) { T a = que.front(); que.pop_front(); return a; }
template <typename T>
T popb(deque<T> &que) { T a = que.back(); que.pop_back(); return a; }
template <typename T>
T pop(queue<T> &que) { T a = que.front(); que.pop(); return a; }
template <typename T>
T pop(stack<T> &que) { T a = que.top(); que.pop(); return a; }
template <typename T>
T pop(PQ<T> &que) { T a = que.top(); que.pop(); return a; }
template <typename T>
T pop(minPQ<T> &que) { T a = que.top(); que.pop(); return a; }
template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
if (check_ok) assert(check(ok));
while (abs(ok - ng) > 1) {
ll mid = (ok + ng) / 2;
(check(mid) ? ok : ng) = mid;
}
return ok;
}
template <typename F>
ll binary_search_real(F check, double ok, double ng, int iter = 60) {
for (int _ = 0; _ < iter; _++) {
double mid = (ok + ng) / 2;
(check(mid) ? ok : ng) = mid;
}
return (ok + ng) / 2;
}
// max x s.t. b*x <= a
ll div_floor(ll a, ll b) {
assert(b != 0);
if (b < 0) a = -a, b = -b;
return a / b - (a % b < 0);
}
// max x s.t. b*x < a
ll div_under(ll a, ll b) {
assert(b != 0);
if (b < 0) a = -a, b = -b;
return a / b - (a % b <= 0);
}
// min x s.t. b*x >= a
ll div_ceil(ll a, ll b) {
assert(b != 0);
if (b < 0) a = -a, b = -b;
return a / b + (a % b > 0);
}
// min x s.t. b*x > a
ll div_over(ll a, ll b) {
assert(b != 0);
if (b < 0) a = -a, b = -b;
return a / b + (a % b >= 0);
}
// x = a mod b (b > 0), 0 <= x < b
ll modulo(ll a, ll b) {
assert(b > 0);
ll c = a % b;
return c < 0 ? c + b : c;
}
// (q,r) s.t. a = b*q + r, 0 <= r < b (b > 0)
// div_floor(a,b), modulo(a,b)
pair<ll,ll> divmod(ll a, ll b) {
ll q = div_floor(a,b);
return {q, a - b*q};
}
template <uint32_t mod>
struct LazyMontgomeryModInt {
using mint = LazyMontgomeryModInt;
using i32 = int32_t;
using u32 = uint32_t;
using u64 = uint64_t;
static constexpr u32 get_r() {
u32 ret = mod;
for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
return ret;
}
static constexpr u32 r = get_r();
static constexpr u32 n2 = -u64(mod) % mod;
static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
static_assert(r * mod == 1, "this code has bugs.");
u32 a;
constexpr LazyMontgomeryModInt() : a(0) {}
constexpr LazyMontgomeryModInt(const int64_t &b)
: a(reduce(u64(b % mod + mod) * n2)){};
static constexpr u32 reduce(const u64 &b) {
return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
}
constexpr mint &operator+=(const mint &b) {
if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator-=(const mint &b) {
if (i32(a -= b.a) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator*=(const mint &b) {
a = reduce(u64(a) * b.a);
return *this;
}
constexpr mint &operator/=(const mint &b) {
*this *= b.inverse();
return *this;
}
constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
constexpr bool operator==(const mint &b) const {
return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
}
constexpr bool operator!=(const mint &b) const {
return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
}
constexpr mint operator-() const { return mint() - mint(*this); }
constexpr mint operator+() const { return mint(*this); }
constexpr mint pow(u64 n) const {
mint ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
constexpr mint inverse() const {
int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0;
while (y > 0) {
t = x / y;
x -= t * y, u -= t * v;
tmp = x, x = y, y = tmp;
tmp = u, u = v, v = tmp;
}
return mint{u};
}
friend ostream &operator<<(ostream &os, const mint &b) {
return os << b.get();
}
friend istream &operator>>(istream &is, mint &b) {
int64_t t;
is >> t;
b = LazyMontgomeryModInt<mod>(t);
return (is);
}
constexpr u32 get() const {
u32 ret = reduce(a);
return ret >= mod ? ret - mod : ret;
}
static constexpr u32 get_mod() { return mod; }
};
// const int mod = 998244353;
const int mod = 1000000007;
using mint = LazyMontgomeryModInt<mod>;
#define ZERO 0
#define ONE 1
#define UPD(c, a, b) (c) += (a) * (b)
template <class T>
vector<vector<T>> matrix_mul(const vector<vector<T>> &a, const vector<vector<T>> &b,
int aR = -1, int bR = -1, int bC = -1) {
assert(a.size() > 0 and b.size() > 0);
if (aR == -1) aR = a.size(), bR = b.size(), bC = b[0].size();
assert(bR == (int)a[0].size());
vector<vector<T>> c(aR, vector<T>(bC, ZERO));
for (int i = 0; i < aR; i++) for (int k = 0; k < bC; k++) {
for (int j = 0; j < bR; j++) UPD(c[i][k], a[i][j], b[j][k]);
}
return c;
}
template <class T>
vector<vector<T>> matrix_pow(vector<vector<T>> a, long long k) {
int n = a.size();
vector<vector<T>> b(n, vector<T> (n, ZERO));
for (int i = 0; i < n; i++) b[i][i] = ONE;
while (k) {
if (k & 1) b = matrix_mul<T>(b, a);
k >>= 1;
if (k) a = matrix_mul<T>(a, a);
}
return b;
}
template <class T, int N>
array<array<T, N>, N> matrix_mul(const array<array<T, N>, N> &a, const array<array<T, N>, N> &b) {
array<array<T, N>, N> c{};
for (int i = 0; i < N; i++) for (int k = 0; k < N; k++) {
T sum = ZERO;
for (int j = 0; j < N; j++) UPD(sum, a[i][j], b[j][k]);
c[i][k] = sum;
}
return c;
}
template <class T, int N>
array<array<T, N>, N> matrix_pow(array<array<T, N>, N> a, long long k) {
array<array<T, N>, N> b{};
for (int i = 0; i < N; i++) for (int j = 0; j < N; j++)
b[i][j] = ZERO;
for (int i = 0; i < N; i++) b[i][i] = ONE;
while (k) {
if (k & 1) b = matrix_mul<T, N>(b, a);
k >>= 1;
if (k) a = matrix_mul<T, N>(a, a);
}
return b;
}
#undef ZERO
#undef ONE
#undef UPD
using mat = array<array<mint,2>,2>;
struct HeavyLightDecomposition {
vector<vector<int>> g;
vector<int> head, tin, tout, depth, par;
HeavyLightDecomposition(int n_): g(n_),
head(n_), tin(n_), tout(n_), depth(n_), par(n_) {}
void add_edge(int u, int v) {
g[u].push_back(v);
g[v].push_back(u);
}
int dfs_sz(int u, int p, int d) {
depth[u] = d;
int sz_u = 1;
int max_sz_ch = 0;
for (int &v : g[u]) if (v != p) {
par[v] = u;
int sz_v = dfs_sz(v, u, d+1);
sz_u += sz_v;
if (max_sz_ch < sz_v) {
max_sz_ch = sz_v;
swap(g[u].front(), v);
}
}
return sz_u;
}
void dfs_hld(int u, int p, int &k) {
tin[u] = k++;
for (int v : g[u]) if (v != p) {
head[v] = (v == g[u].front() ? head[u] : v);
dfs_hld(v, u, k);
}
tout[u] = k;
}
void build() {
dfs_sz(0, -1, 0);
int k = 0;
/* head[0] = 0; */
dfs_hld(0, -1, k);
}
int lca(int u, int v) {
while (head[u] != head[v]) {
if (depth[head[u]] < depth[head[v]]) v = par[head[v]];
else u = par[head[u]];
}
return depth[u] < depth[v] ? u : v;
}
int distance(int u, int v) {
return depth[u] + depth[v] - 2 * depth[lca(u, v)];
}
/*
* path (u to v) -> path_u, path_v (closed intervals)
* path_u: u to lca(u,v)
* path_v: lca(u,v) to v
* path (u to v) = path_u ++ rev(path_v)
* どちらも 区間 [l,r] は l < r の順 (深さ l < r)
* path_u では euler tour の逆方向に計算する <= 非可換の時注意
* path_v では lca(u,v) to v の順に計算 <= 非可換の時注意
* exclude_lca = true の時 path に lca は含まれない <= 辺に重みがある時に使う
*/
pair<vector<pair<int, int>>, vector<pair<int, int>>>
get_path(int u, int v, bool exclude_lca = false) {
vector<pair<int, int>> path_u, path_v;
while (head[u] != head[v]) {
if (depth[head[u]] < depth[head[v]]) {
path_v.emplace_back(tin[head[v]], tin[v]);
v = par[head[v]];
}
else {
path_u.emplace_back(tin[head[u]], tin[u]);
u = par[head[u]];
}
}
if (depth[u] < depth[v]) path_v.emplace_back(tin[u] + (exclude_lca ? 1 : 0), tin[v]);
else path_u.emplace_back(tin[v] + (exclude_lca ? 1 : 0), tin[u]);
reverse(path_v.begin(), path_v.end());
return {path_u, path_v};
}
/* subtree (u) -> [tin, tout) */
pair<int, int> get_subtree(int u) {
return {tin[u], tout[u]};
}
};
/*
* 辺に重みが付く時 (ui, vi) -> wi
* 深いほうの頂点に w_i をつける
* etov[i] := depth[ui] < depth[vi] ? vi : ui
* query path (u, v) -> get_path(u, v, exclude_lca = true)
*/
#include "atcoder/segtree.hpp"
using S = mat;
S op(S a, S b) { return matrix_mul<mint,2>(a,b); }
S e() { return { { {1,0}, {0,1} } }; }
int main() {
int n; in(n);
HeavyLightDecomposition hld(n);
vector<P> edges;
rep(i,n-1){
int u,v; in(u,v);
edges.emplace_back(u,v);
hld.add_edge(u,v);
}
hld.build();
atcoder::segtree<S,op,e> seg(n);
vector<int> etov(n-1);
rep(i,n-1){
auto [u,v] = edges[i];
if(hld.depth[u] < hld.depth[v]) etov[i] = v;
else etov[i] = u;
}
int q; in(q);
while(q--){
char c; in(c);
if(c == 'x') {
int i,x00,x01,x10,x11; in(i,x00,x01,x10,x11);
seg.set(hld.tin[etov[i]], { { {x00,x01}, {x10,x11} } });
}
else{
int i,j; in(i,j);
mat res = e();
auto [pi, pj] = hld.get_path(i,j, true);
for (auto [l,r] : pj) res = matrix_mul<mint,2>(res, seg.prod(l,r+1));
out(res[0][0], res[0][1], res[1][0], res[1][1]);
}
}
}