結果
| 問題 |
No.3194 Do Optimize Your Solution
|
| コンテスト | |
| ユーザー |
 hos.lyric
|
| 提出日時 | 2025-06-27 23:18:37 |
| 言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 2,500 ms / 3,000 ms |
| コード長 | 15,229 bytes |
| コンパイル時間 | 3,787 ms |
| コンパイル使用メモリ | 196,836 KB |
| 実行使用メモリ | 107,392 KB |
| 最終ジャッジ日時 | 2025-06-27 23:19:27 |
| 合計ジャッジ時間 | 35,661 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 17 |
コンパイルメッセージ
main.cpp: In function ‘int main()’:
main.cpp:406:14: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
406 | scanf("%d%d", &A[h][i], &B[h][i]);
| ~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~
ソースコード
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <chrono>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#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; }
#define COLOR(s) ("\x1b[" s "m")
// build: O(n log(n)) time/space
// operator(): O(1) time
struct Lca {
int n, rt;
vector<vector<int>> graph;
vector<int> par, dep, su;
int usLen;
vector<int> us;
vector<int> buffer;
vector<int *> mn;
Lca() : n(0), rt(-1), usLen(0) {}
explicit Lca(int n_) : n(n_), rt(-1), graph(n), usLen(0) {}
void ae(int u, int v) {
assert(0 <= u); assert(u < n);
assert(0 <= v); assert(v < n);
graph[u].push_back(v);
graph[v].push_back(u);
}
void dfs(int u, int p) {
us[su[u] = usLen++] = u;
for (const int v : graph[u]) if (p != v) {
par[v] = u;
dep[v] = dep[u] + 1;
dfs(v, u);
us[usLen++] = u;
}
}
void build(int rt_) {
assert(0 <= rt_); assert(rt_ < n);
rt = rt_;
par.assign(n, -1);
dep.assign(n, -1);
su.assign(n, -1);
usLen = 0;
us.assign(2 * n - 1, -1);
dep[rt] = 0;
dfs(rt, -1);
assert(usLen == 2 * n - 1);
const int l = (31 - __builtin_clz(usLen)) + 1;
buffer.resize(l * usLen);
mn.resize(l);
for (int e = 0; e < l; ++e) mn[e] = buffer.data() + e * usLen;
for (int j = 0; j < usLen; ++j) mn[0][j] = us[j];
for (int e = 0; e < l - 1; ++e) for (int i = 0; i + (1 << (e + 1)) <= usLen; ++i) {
mn[e + 1][i] = shallower(mn[e][i], mn[e][i + (1 << e)]);
}
}
int shallower(int u, int v) const {
return (dep[u] <= dep[v]) ? u : v;
}
int operator()(int u, int v) const {
int j0 = su[u], j1 = su[v];
if (j0 > j1) swap(j0, j1);
++j1;
const int e = 31 - __builtin_clz(j1 - j0);
return shallower(mn[e][j0], mn[e][j1 - (1 << e)]);
}
int dist(int u, int v) const {
return dep[u] + dep[v] - 2 * dep[operator()(u, v)];
}
};
////////////////////////////////////////////////////////////////////////////////
struct Hld {
int n, rt;
// needs to be tree
// vertex lists
// modified in build(rt) (parent removed, heavy child first)
vector<vector<int>> graph;
vector<int> sz, par, dep;
int zeit;
vector<int> dis, fin, sid;
// head vertex (minimum depth) in heavy path
vector<int> head;
Hld() : n(0), rt(-1), zeit(0) {}
explicit Hld(int n_) : n(n_), rt(-1), graph(n), zeit(0) {}
void ae(int u, int v) {
assert(0 <= u); assert(u < n);
assert(0 <= v); assert(v < n);
graph[u].push_back(v);
graph[v].push_back(u);
}
void dfsSz(int u) {
sz[u] = 1;
for (const int v : graph[u]) {
auto it = std::find(graph[v].begin(), graph[v].end(), u);
if (it != graph[v].end()) graph[v].erase(it);
par[v] = u;
dep[v] = dep[u] + 1;
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 build(int rt_) {
assert(0 <= rt_); assert(rt_ < n);
rt = rt_;
sz.assign(n, 0);
par.assign(n, -1);
dep.assign(n, -1);
dep[rt] = 0;
dfsSz(rt);
zeit = 0;
dis.assign(n, -1);
fin.assign(n, -1);
head.assign(n, -1);
head[rt] = rt;
dfsHld(rt);
assert(zeit == n);
sid.assign(n, -1);
for (int u = 0; u < n; ++u) sid[dis[u]] = u;
}
friend ostream &operator<<(ostream &os, const Hld &hld) {
const int maxDep = *max_element(hld.dep.begin(), hld.dep.end());
vector<string> ss(2 * maxDep + 1);
int pos = 0, maxPos = 0;
for (int j = 0; j < hld.n; ++j) {
const int u = hld.sid[j];
const int d = hld.dep[u];
if (hld.head[u] == u) {
if (j != 0) {
pos = maxPos + 1;
ss[2 * d - 1].resize(pos, '-');
ss[2 * d - 1] += '+';
}
} else {
ss[2 * d - 1].resize(pos, ' ');
ss[2 * d - 1] += '|';
}
ss[2 * d].resize(pos, ' ');
ss[2 * d] += std::to_string(u);
if (maxPos < static_cast<int>(ss[2 * d].size())) {
maxPos = ss[2 * d].size();
}
}
for (int d = 0; d <= 2 * maxDep; ++d) os << ss[d] << '\n';
return os;
}
bool contains(int u, int v) const {
return (dis[u] <= dis[v] && dis[v] < fin[u]);
}
int lca(int u, int v) const {
assert(0 <= u); assert(u < n);
assert(0 <= v); assert(v < n);
for (; head[u] != head[v]; ) (dis[u] > dis[v]) ? (u = par[head[u]]) : (v = par[head[v]]);
return (dis[u] > dis[v]) ? v : u;
}
int jumpUp(int u, int d) const {
assert(0 <= u); assert(u < n);
assert(d >= 0);
if (dep[u] < d) return -1;
const int tar = dep[u] - d;
for (u = head[u]; ; u = head[par[u]]) {
if (dep[u] <= tar) return sid[dis[u] + (tar - dep[u])];
}
}
int jump(int u, int v, int d) const {
assert(0 <= u); assert(u < n);
assert(0 <= v); assert(v < n);
assert(d >= 0);
const int l = lca(u, v);
const int du = dep[u] - dep[l], dv = dep[v] - dep[l];
if (d <= du) {
return jumpUp(u, d);
} else if (d <= du + dv) {
return jumpUp(v, du + dv - d);
} else {
return -1;
}
}
// [u, v) or [u, v]
template <class F> void doPathUp(int u, int v, bool inclusive, F f) const {
assert(contains(v, u));
for (; head[u] != head[v]; u = par[head[u]]) f(dis[head[u]], dis[u] + 1);
if (inclusive) {
f(dis[v], dis[u] + 1);
} else {
if (v != u) f(dis[v] + 1, dis[u] + 1);
}
}
// not path order, include lca(u, v) or not
template <class F> void doPath(int u, int v, bool inclusive, F f) const {
const int l = lca(u, v);
doPathUp(u, l, false, f);
doPathUp(v, l, inclusive, f);
}
// (vs, ps): compressed tree
// vs: DFS order (sorted by dis)
// vs[ps[x]]: the parent of vs[x]
// ids[vs[x]] = x, not set for non-tree vertex
vector<int> ids;
// pair<vector<int>, vector<int>> compress(vector<int> us) {
pair<vector<int>, vector<int>> compress(vector<int> us, const Lca &lcaFast) {
// O(n) first time
ids.resize(n, -1);
std::sort(us.begin(), us.end(), [&](int u, int v) -> bool {
return (dis[u] < dis[v]);
});
us.erase(std::unique(us.begin(), us.end()), us.end());
int usLen = us.size();
assert(usLen >= 1);
// for (int x = 1; x < usLen; ++x) us.push_back(lca(us[x - 1], us[x]));
for (int x = 1; x < usLen; ++x) us.push_back(lcaFast(us[x - 1], us[x]));
std::sort(us.begin(), us.end(), [&](int u, int v) -> bool {
return (dis[u] < dis[v]);
});
us.erase(std::unique(us.begin(), us.end()), us.end());
usLen = us.size();
for (int x = 0; x < usLen; ++x) ids[us[x]] = x;
vector<int> ps(usLen, -1);
// for (int x = 1; x < usLen; ++x) ps[x] = ids[lca(us[x - 1], us[x])];
for (int x = 1; x < usLen; ++x) ps[x] = ids[lcaFast(us[x - 1], us[x])];
return make_pair(us, ps);
}
};
////////////////////////////////////////////////////////////////////////////////
struct Tree {
int n;
// vector<vector<pair<int, int>>> graph;
vector<pair<int, pair<int, int>>> edges;
// explicit Tree(int n_) : n(n_), graph(n) {}
explicit Tree(int n_) : n(n_), edges() {
edges.reserve(n - 1);
}
void ae(int u, int v, int c) {
// graph[u].emplace_back(c, v);
// graph[v].emplace_back(c, u);
edges.emplace_back(c, make_pair(u, v));
}
vector<int> pt;
vector<pair<int, int>> zu;
void build() {
pt.assign(n + 1, 0);
for (int i = 0; i < n - 1; ++i) {
const int u = edges[i].second.first;
const int v = edges[i].second.second;
++pt[u];
++pt[v];
}
for (int u = 0; u < n; ++u) pt[u + 1] += pt[u];
zu.resize(2 * (n - 1));
for (int i = n - 1; --i >= 0; ) {
const int c = edges[i].first;
const int u = edges[i].second.first;
const int v = edges[i].second.second;
zu[--pt[u]] = make_pair(c, v);
zu[--pt[v]] = make_pair(c, u);
}
}
template <class F> void decomp(F f) {
sz.assign(n, 0);
dfsSz(0, -1);
del.assign(n, 0);
solveRec(0, f);
}
vector<int> sz, del;
void dfsSz(int u, int p) {
sz[u] = 1;
// for (const auto &e : graph[u]) { const int v = e.second; if (p != v) {
for (int j = pt[u]; j < pt[u + 1]; ++j) { const auto &e = zu[j]; const int v = e.second; if (p != v) {
dfsSz(v, u);
sz[u] += sz[v];
}}
}
template <class F> void solveRec(int u, F f) {
for (; ; ) {
int vm = -1;
// for (const auto &e : graph[u]) { const int v = e.second; if (!del[v]) {
for (int j = pt[u]; j < pt[u + 1]; ++j) { const auto &e = zu[j]; const int v = e.second; if (!del[v]) {
if (!~vm || sz[vm] < sz[v]) {
vm = v;
}
}}
if (!~vm || 2 * sz[vm] <= sz[u]) {
solveSubtree(u, f);
del[u] = 1;
// for (const auto &e : graph[u]) { const int v = e.second; if (!del[v]) {
for (int j = pt[u]; j < pt[u + 1]; ++j) { const auto &e = zu[j]; const int v = e.second; if (!del[v]) {
solveRec(v, f);
}}
break;
} else {
sz[u] -= sz[vm];
sz[vm] += sz[u];
u = vm;
}
}
}
template <class F> void solveSubtree(int r, F f) {
int allLen = 0;
vector<pair<int, int>> all(sz[r]);
all[allLen++] = make_pair(0, r);
// for (const auto &e1 : graph[r]) { const int r1 = e1.second; if (!del[r1]) {
for (int j1 = pt[r]; j1 < pt[r + 1]; ++j1) { const auto &e1 = zu[j1]; const int r1 = e1.second; if (!del[r1]) {
int queLen = 0;
// vector<pair<int, int>> que(sz[r1]);
auto *que = all.data() + allLen;
que[queLen++] = e1;
for (int k = 0; k < sz[r1]; ++k) {
const int d = que[k].first;
const int u = que[k].second;
// for (const auto &e : graph[u]) { const int v = e.second; if (!del[v] && sz[u] > sz[v]) {
for (int j = pt[u]; j < pt[u + 1]; ++j) { const auto &e = zu[j]; const int v = e.second; if (!del[v] && sz[u] > sz[v]) {
que[queLen++] = make_pair(d + e.first, v);
}}
}
// f(-1, que);
f(-1, que, que + queLen);
// for (int k = 0; k < sz[r1]; ++k) all[allLen++] = que[k];
allLen += queLen;
}}
// f(+1, all);
f(+1, all.data(), all.data() + allLen);
}
};
int N;
vector<int> A[2], B[2];
int main() {
for (; ~scanf("%d", &N); ) {
for (int h = 0; h < 2; ++h) {
A[h].resize(N - 1);
B[h].resize(N - 1);
for (int i = 0; i < N - 1; ++i) {
scanf("%d%d", &A[h][i], &B[h][i]);
--A[h][i];
--B[h][i];
}
}
Hld hld[2];
Lca lca[2];
#ifdef LOCAL
for (int h = 0; h < 2; ++h) {
#else
for (int h = 1; h < 2; ++h) {
#endif
hld[h] = Hld(N);
for (int i = 0; i < N - 1; ++i) hld[h].ae(A[h][i], B[h][i]);
hld[h].build(0);
// cerr<<hld[h]<<endl;
lca[h] = Lca(N);
for (int i = 0; i < N - 1; ++i) lca[h].ae(A[h][i], B[h][i]);
lca[h].build(0);
}
unsigned long long ans = 0;
vector<int> gs(N);
vector<unsigned long long> dp0(N), dp1(N);
Tree T0(N);
for (int i = 0; i < N - 1; ++i) T0.ae(A[0][i], B[0][i], 1);
T0.build();
// T0.decomp([&](int s0, const vector<pair<int, int>> &fs) -> void {
T0.decomp([&](int s0, const pair<int, int> *fL, const pair<int, int> *fR) -> void {
const vector<pair<int, int>> fs(fL, fR);
// cerr<<"s0 = "<<s0<<", fs = "<<fs<<endl;
const int fsLen = fs.size();
//*
if (fsLen <= 50) {
unsigned long long here = 0;
for (int k = 0; k < fsLen; ++k) for (int l = k + 1; l < fsLen; ++l) {
const int u = fs[k].second;
const int v = fs[l].second;
here += (unsigned long long)(fs[k].first + fs[l].first) * lca[1].dist(u, v);
}
ans += s0 * here;
return;
}
//*/
vector<int> us(fsLen);
for (int k = 0; k < fsLen; ++k) us[k] = fs[k].second;
const auto vsps = hld[1].compress(us, lca[1]); // bottleneck
const auto &vs = vsps.first;
const auto &ps = vsps.second;
const int n = vs.size();
// damasareta! O(N log(N)) here
// vector<int> gs(n, 0);
fill(gs.begin(), gs.begin() + n, 0);
for (int y = 1; y < n; ++y) {
const int x = ps[y];
gs[y] = gs[x] + (hld[1].dep[vs[y]] - hld[1].dep[vs[x]]);
}
// vector<unsigned long long> dp0(n, 0), dp1(n, 0);
fill(dp0.begin(), dp0.begin() + n, 0);
fill(dp1.begin(), dp1.begin() + n, 0);
unsigned long long sum = 0, sumF = 0, sumG = 0, sumFG = 0;
for (int k = 0; k < fsLen; ++k) {
const int f = fs[k].first;
const int x = hld[1].ids[fs[k].second];
dp0[x] += 1;
dp1[x] += f;
sum += 1;
sumF += f;
sumG += gs[x];
sumFG += (unsigned long long)f * gs[x];
}
for (int y = n; --y; ) {
const int x = ps[y];
dp0[x] += dp0[y];
dp1[x] += dp1[y];
}
unsigned long long here = 0;
here += sum * sumFG;
here += sumF * sumG;
for (int y = 1; y < n; ++y) {
const int x = ps[y];
here -= 2 * (gs[y] - gs[x]) * dp0[y] * dp1[y];
}
ans += s0 * here;
});
ans *= 2;
printf("%llu\n", ans);
#ifdef LOCAL
if(N<=1000){
unsigned long long brt=0;
for(int u=0;u<N;++u)for(int v=0;v<N;++v){
unsigned long long d[2];
for(int h=0;h<2;++h){
const int l=hld[h].lca(u,v);
d[h]=hld[h].dep[u]+hld[h].dep[v]-2*hld[h].dep[l];
}
brt+=d[0]*d[1];
}
if(brt!=ans){
cerr<<N<<endl;
for(int h=0;h<2;++h)for(int i=0;i<N-1;++i)cerr<<(A[h][i]+1)<<" "<<(B[h][i]+1)<<endl;
cerr<<"brt = "<<brt<<endl;
cerr<<"ans = "<<ans<<endl;
assert(false);
}
}
#endif
}
return 0;
}