結果
| 問題 |
No.2163 LCA Sum Query
|
| コンテスト | |
| ユーザー |
 hos.lyric
|
| 提出日時 | 2022-12-16 02:55:58 |
| 言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 504 ms / 6,000 ms |
| コード長 | 10,059 bytes |
| コンパイル時間 | 1,523 ms |
| コンパイル使用メモリ | 117,740 KB |
| 実行使用メモリ | 20,180 KB |
| 最終ジャッジ日時 | 2024-11-15 07:02:21 |
| 合計ジャッジ時間 | 13,531 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 40 |
ソースコード
#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using Int = long long;
template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
// T: monoid representing information of an interval.
// T() should return the identity.
// T(S s) should represent a single element of the array.
// T::push(T &l, T &r) should push the lazy update.
// T::merge(const T &l, const T &r) should merge two intervals.
template <class T> struct SegmentTreeRange {
int logN, n;
vector<T> ts;
SegmentTreeRange() {}
explicit SegmentTreeRange(int n_) {
for (logN = 0, n = 1; n < n_; ++logN, n <<= 1) {}
ts.resize(n << 1);
}
template <class S> explicit SegmentTreeRange(const vector<S> &ss) {
const int n_ = ss.size();
for (logN = 0, n = 1; n < n_; ++logN, n <<= 1) {}
ts.resize(n << 1);
for (int i = 0; i < n_; ++i) at(i) = T(ss[i]);
build();
}
T &at(int i) {
return ts[n + i];
}
void build() {
for (int u = n; --u; ) merge(u);
}
inline void push(int u) {
ts[u].push(ts[u << 1], ts[u << 1 | 1]);
}
inline void merge(int u) {
ts[u].merge(ts[u << 1], ts[u << 1 | 1]);
}
// Applies T::f(args...) to [a, b).
template <class F, class... Args>
void ch(int a, int b, F f, Args &&... args) {
assert(0 <= a); assert(a <= b); assert(b <= n);
if (a == b) return;
a += n; b += n;
for (int h = logN; h; --h) {
const int aa = a >> h, bb = b >> h;
if (aa == bb) {
if ((aa << h) != a || (bb << h) != b) push(aa);
} else {
if ((aa << h) != a) push(aa);
if ((bb << h) != b) push(bb);
}
}
for (int aa = a, bb = b; aa < bb; aa >>= 1, bb >>= 1) {
if (aa & 1) (ts[aa++].*f)(args...);
if (bb & 1) (ts[--bb].*f)(args...);
}
for (int h = 1; h <= logN; ++h) {
const int aa = a >> h, bb = b >> h;
if (aa == bb) {
if ((aa << h) != a || (bb << h) != b) merge(aa);
} else {
if ((aa << h) != a) merge(aa);
if ((bb << h) != b) merge(bb);
}
}
}
// Calculates the product for [a, b).
T get(int a, int b) {
assert(0 <= a); assert(a <= b); assert(b <= n);
if (a == b) return T();
a += n; b += n;
for (int h = logN; h; --h) {
const int aa = a >> h, bb = b >> h;
if (aa == bb) {
if ((aa << h) != a || (bb << h) != b) push(aa);
} else {
if ((aa << h) != a) push(aa);
if ((bb << h) != b) push(bb);
}
}
T prodL, prodR, t;
for (int aa = a, bb = b; aa < bb; aa >>= 1, bb >>= 1) {
if (aa & 1) { t.merge(prodL, ts[aa++]); prodL = t; }
if (bb & 1) { t.merge(ts[--bb], prodR); prodR = t; }
}
t.merge(prodL, prodR);
return t;
}
// Calculates T::f(args...) of a monoid type for [a, b).
// op(-, -) should calculate the product.
// e() should return the identity.
template <class Op, class E, class F, class... Args>
#if __cplusplus >= 201402L
auto
#else
decltype((std::declval<T>().*F())())
#endif
get(int a, int b, Op op, E e, F f, Args &&... args) {
assert(0 <= a); assert(a <= b); assert(b <= n);
if (a == b) return e();
a += n; b += n;
for (int h = logN; h; --h) {
const int aa = a >> h, bb = b >> h;
if (aa == bb) {
if ((aa << h) != a || (bb << h) != b) push(aa);
} else {
if ((aa << h) != a) push(aa);
if ((bb << h) != b) push(bb);
}
}
auto prodL = e(), prodR = e();
for (int aa = a, bb = b; aa < bb; aa >>= 1, bb >>= 1) {
if (aa & 1) prodL = op(prodL, (ts[aa++].*f)(args...));
if (bb & 1) prodR = op((ts[--bb].*f)(args...), prodR);
}
return op(prodL, prodR);
}
// Find min b s.t. T::f(args...) returns true,
// when called for the partition of [a, b) from left to right.
// Returns n + 1 if there is no such b.
template <class F, class... Args>
int findRight(int a, F f, Args &&... args) {
assert(0 <= a); assert(a <= n);
if ((T().*f)(args...)) return a;
if (a == n) return n + 1;
a += n;
for (int h = logN; h; --h) push(a >> h);
for (; ; a >>= 1) if (a & 1) {
if ((ts[a].*f)(args...)) {
for (; a < n; ) {
push(a);
if (!(ts[a <<= 1].*f)(args...)) ++a;
}
return a - n + 1;
}
++a;
if (!(a & (a - 1))) return n + 1;
}
}
// Find max a s.t. T::f(args...) returns true,
// when called for the partition of [a, b) from right to left.
// Returns -1 if there is no such a.
template <class F, class... Args>
int findLeft(int b, F f, Args &&... args) {
assert(0 <= b); assert(b <= n);
if ((T().*f)(args...)) return b;
if (b == 0) return -1;
b += n;
for (int h = logN; h; --h) push((b - 1) >> h);
for (; ; b >>= 1) if ((b & 1) || b == 2) {
if ((ts[b - 1].*f)(args...)) {
for (; b <= n; ) {
push(b - 1);
if (!(ts[(b <<= 1) - 1].*f)(args...)) --b;
}
return b - n - 1;
}
--b;
if (!(b & (b - 1))) return -1;
}
}
};
////////////////////////////////////////////////////////////////////////////////
struct Node {
Int sum0, sum1, sum2;
Int lz;
Node() : sum0(0), sum1(0), sum2(0), lz(0) {}
void push(Node &l, Node &r) {
if (lz) {
l.add(lz);
r.add(lz);
lz = 0;
}
}
void merge(const Node &l, const Node &r) {
sum0 = l.sum0 + r.sum0;
sum1 = l.sum1 + r.sum1;
sum2 = l.sum2 + r.sum2;
}
void add(Int val) {
// binom(x + val, 2) - binom(x, 2)
sum2 += sum1 * val + sum0 * val * (val - 1) / 2;
sum1 += sum0 * val;
lz += val;
}
};
int N, Q;
vector<int> A, B;
vector<vector<int>> graph;
vector<int> par, sz;
int zeit;
vector<int> dis, fin;
vector<int> head;
void dfsSz(int u) {
sz[u] = 1;
for (const int v : graph[u]) {
graph[v].erase(find(graph[v].begin(), graph[v].end(), u));
par[v] = u;
dfsSz(v);
sz[u] += sz[v];
}
}
void dfsHLD(int u) {
dis[u] = zeit++;
const int deg = graph[u].size();
if (deg > 0) {
int vm = graph[u][0];
int jm = 0;
for (int j = 1; j < deg; ++j) {
const int v = graph[u][j];
if (sz[vm] < sz[v]) {
vm = v;
jm = j;
}
}
swap(graph[u][0], graph[u][jm]);
head[vm] = head[u];
dfsHLD(vm);
for (int j = 1; j < deg; ++j) {
const int v = graph[u][j];
head[v] = v;
dfsHLD(v);
}
}
fin[u] = zeit;
}
void runHLD(int rt) {
par.assign(N, -1);
sz.resize(N);
zeit = 0;
dis.resize(N);
fin.resize(N);
head.resize(N);
dfsSz(rt);
head[rt] = rt;
dfsHLD(rt);
}
constexpr int R0 = 0;
Int tot;
vector<int> on;
SegmentTreeRange<Node> seg, segOne;
void init() {
tot = 0;
on.assign(N, 0);
seg = SegmentTreeRange<Node>(N);
segOne = SegmentTreeRange<Node>(N);
for (int u = 0; u < N; ++u) {
seg.at(dis[u]).sum0 = u - par[u];
segOne.at(dis[u]).sum0 = 1;
}
seg.build();
segOne.build();
}
void add(int u, int val) {
// cerr<<"add "<<u<<" "<<val<<endl;
tot += val;
for (int v = u; ~v; v = par[head[v]]) {
seg.ch(dis[head[v]], dis[v] + 1, &Node::add, val);
segOne.ch(dis[head[v]], dis[v] + 1, &Node::add, val);
}
}
Int solve(int r, int u) {
// cerr<<"solve "<<r<<" "<<u<<"; on = "<<on<<endl;
Int ans = 0;
if (r == R0) {
// \sum[v \in T(u)] (v - par(v)) binom(|S(v)|, 2)
ans += seg.get(dis[u], dis[u] + 1).sum2 / (u - par[u]) * (u - (-1));
ans += seg.get(dis[u] + 1, fin[u]).sum2;
} else if (r == u) {
// \sum[v \in path[R0, r]] (v - par[v]) |S(v)| (|S| - |S(v)|)
ans = solve(R0, R0);
for (int v = r; ~v; v = par[head[v]]) {
const Node res = seg.get(dis[head[v]], dis[v] + 1);
ans += tot * res.sum1;
ans -= (res.sum1 + 2 * res.sum2);
}
} else if (dis[u] <= dis[r] && dis[r] < fin[u]) {
const int deg = graph[u].size();
int lo = 0, hi = deg;
for (; lo + 1 < hi; ) {
const int mid = (lo + hi) / 2;
const int v = graph[u][mid];
((dis[v] <= dis[r]) ? lo : hi) = mid;
}
r = graph[u][lo];
ans = solve(r, r);
ans -= solve(R0, r);
{
const Node res = segOne.get(dis[r], dis[r] + 1);
ans -= (r + 1) * res.sum1 * (tot - res.sum1);
}
} else {
ans = solve(R0, u);
}
return ans;
}
int main() {
for (; ~scanf("%d%d", &N, &Q); ) {
A.resize(N - 1);
B.resize(N - 1);
for (int i = 0; i < N - 1; ++i) {
scanf("%d%d", &A[i], &B[i]);
--A[i];
--B[i];
}
graph.assign(N, {});
for (int i = 0; i < N - 1; ++i) {
graph[A[i]].push_back(B[i]);
graph[B[i]].push_back(A[i]);
}
runHLD(R0);
// cerr<<"graph = "<<graph<<endl;
// cerr<<"head = "<<head<<endl;
init();
for (; Q--; ) {
int U, R, V;
scanf("%d%d%d", &U, &R, &V);
--U;
--R;
--V;
if (on[U]) {
on[U] = 0;
add(U, -1);
} else {
on[U] = 1;
add(U, +1);
}
const Int ans = solve(R, V);
printf("%lld\n", ans);
}
#ifdef LOCAL
cerr<<"========"<<endl;
#endif
}
return 0;
}