結果
| 問題 |
No.3194 Do Optimize Your Solution
|
| ユーザー |
 noya2
|
| 提出日時 | 2025-06-23 23:02:52 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
TLE
(最新)
AC
(最初)
|
| 実行時間 | - |
| コード長 | 12,380 bytes |
| コンパイル時間 | 3,884 ms |
| コンパイル使用メモリ | 303,452 KB |
| 実行使用メモリ | 62,816 KB |
| 最終ジャッジ日時 | 2025-06-27 20:51:13 |
| 合計ジャッジ時間 | 12,835 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 16 TLE * 1 |
ソースコード
#include<bits/stdc++.h>
using namespace std;
#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define all(v) (v).begin(),(v).end()
using ull = unsigned long long;
namespace noya2{
/* ~ (. _________ . /) */
}
using namespace noya2;
namespace noya2::internal {
template<class E>
struct csr {
csr () {}
csr (int _n) : n(_n) {}
csr (int _n, int m) : n(_n){
start.reserve(m);
elist.reserve(m);
}
// ACL style constructor (do not have to call build)
csr (int _n, const std::vector<std::pair<int,E>> &idx_elem) : n(_n), start(_n + 2), elist(idx_elem.size()) {
for (auto &[i, e] : idx_elem){
start[i + 2]++;
}
for (int i = 1; i < n; i++){
start[i + 2] += start[i + 1];
}
for (auto &[i, e] : idx_elem){
elist[start[i + 1]++] = e;
}
prepared = true;
}
int add(int idx, E elem){
int eid = start.size();
start.emplace_back(idx);
elist.emplace_back(elem);
return eid;
}
void build(){
if (prepared) return ;
int m = start.size();
std::vector<E> nelist(m);
std::vector<int> nstart(n + 2, 0);
for (int i = 0; i < m; i++){
nstart[start[i] + 2]++;
}
for (int i = 1; i < n; i++){
nstart[i + 2] += nstart[i + 1];
}
for (int i = 0; i < m; i++){
nelist[nstart[start[i] + 1]++] = elist[i];
}
swap(elist,nelist);
swap(start,nstart);
prepared = true;
}
const auto operator[](int idx) const {
return std::ranges::subrange(elist.begin()+start[idx],elist.begin()+start[idx+1]);
}
auto operator[](int idx){
return std::ranges::subrange(elist.begin()+start[idx],elist.begin()+start[idx+1]);
}
const auto operator()(int idx, int l, int r) const {
return std::ranges::subrange(elist.begin()+start[idx]+l,elist.begin()+start[idx]+r);
}
auto operator()(int idx, int l, int r){
return std::ranges::subrange(elist.begin()+start[idx]+l,elist.begin()+start[idx]+r);
}
size_t size() const {
return n;
}
int n;
std::vector<int> start;
std::vector<E> elist;
bool prepared = false;
};
} // namespace noya2::internal
struct simple_tree_for_yuki {
internal::csr<int> g;
simple_tree_for_yuki (int n) : g(n, (n - 1)*2) {}
template<typename Stream>
void input_edges(Stream &inputter){
for (int i = 0; i < g.n - 1; i++){
int u, v; inputter >> u >> v;
u--, v--;
g.add(u, v);
g.add(v, u);
}
g.build();
}
const auto operator[](int v) const {
return g[v];
}
auto operator[](int v){
return g[v];
}
int size() const {
return g.n;
}
};
struct hld_tree_for_yuki {
int n, root;
std::vector<int> down, nxt, sub, tour, dep;
hld_tree_for_yuki (int _n) : n(_n), root(0), down(n), nxt(n), sub(n, 1), tour(n), dep(n) {}
template<typename Stream>
void input_edges(Stream &inputter){
for (int i = 1; i < n; i++){
int u, v; inputter >> u >> v;
u--, v--;
down[u]++;
down[v]++;
nxt[u] ^= v;
nxt[v] ^= u;
}
build_from_edges();
}
ull depth(int v) const {
return dep[v];
}
int leader(int v) const {
return nxt[v] < 0 ? v : nxt[v];
}
// down[v] : degree of v
// nxt[v] : xor prod of neighbor of v
void build_from_edges(){
// use tour as queue
int back = 0;
for (int u = 0; u < n; u++){
if (u != root && down[u] == 1){
tour[back++] = u;
}
}
for (int front = 0; front < n - 1; front++){
int u = tour[front];
down[u] = -1;
int v = nxt[u]; // parent of v
nxt[v] ^= u;
if (--down[v] == 1 && v != root){
tour[back++] = v;
}
}
// check : now, tour is reverse of topological order
tour.pop_back();
// check : now, down[*] <= 1
for (int u : tour){
int v = nxt[u];
// subtree size (initialized (1,1,...,1))
sub[v] += sub[u];
// heaviest subtree of its child
if (down[v] < sub[u]){
down[v] = sub[u];
}
}
for (int u : tour){
int v = nxt[u];
// whether u is not the top of heavy path
if (down[v] == sub[u]){
sub[u] = ~sub[u];
down[v] = ~down[v];
}
}
// after appearing v as u (or v == root),
// down[v] is the visiting time of euler tour
// nxt[v] is the lowest vertex of heavy path which contains v
// (if v itself, nxt[v] is ~(parent of v))
// sub[v] + down[v] is the light child's starting time of euler tour
// note : heavy child's visiting time of euler tour is (the time of its parent) + 1
sub[root] = ~down[root] + 1;
down[root] = 0;
nxt[root] = -1;
for (int u : tour | std::views::reverse){
int v = nxt[u];
int nsub = ~down[u] + 1;
// heavy child
if (sub[u] < 0){
down[u] = down[v] + 1;
nxt[u] = (nxt[v] < 0 ? v : nxt[v]);
}
// light child
else {
down[u] = down[v] + sub[v];
sub[v] += sub[u];
nxt[u] = ~v;
}
sub[u] = nsub;
dep[u] = dep[v] + 1;
}
// tour is inverse permutation of down
tour.push_back(root);
for (int u = 0; u < n; u++){
tour[down[u]] = u;
}
}
};
namespace noya2 {
std::vector<int> centroid_decomposition(const auto &g){
int n = g.size();
if (n == 0){
return {};
}
std::vector<int> sub(n), order;
order.reserve(n);
auto subtree = [&](auto sfs, int v, int f) -> void {
sub[v] = 1;
for (int u : g[v]){
if (u == f) continue;
sfs(sfs, u, v);
sub[v] += sub[u];
}
};
subtree(subtree,0,-1);
auto fixed_root = [&](auto self, int root, int par, int cur_size) -> void {
auto dfs = [&](auto sfs, int v, int f, int sz) -> int {
int heavy = 0, child = -1;
for (int u : g[v]){
if (u == f) continue;
if (heavy < sub[u]){
heavy = sub[u];
child = u;
}
}
if (heavy > sz/2){
int ret = sfs(sfs, child, v, sz);
sub[v] -= ret;
return ret;
}
else {
order.emplace_back(v);
for (int u : g[v]){
if (u == f) continue;
self(self, u, v, sub[u]);
}
int ret = sub[v];
sub[v] = 0;
return ret;
}
};
while (cur_size > 0){
cur_size -= dfs(dfs, root, par, cur_size);
}
};
fixed_root(fixed_root, 0, -1, n);
return order;
}
} // namespace noya2
int main(){
cin.tie(0)->sync_with_stdio(0);
int n; cin >> n;
simple_tree_for_yuki a(n);
hld_tree_for_yuki b(n);
a.input_edges(cin);
b.input_edges(cin);
vector<int> spfensz(n);
rep(v,n){
int lv = b.leader(v);
spfensz[lv] = max(spfensz[lv], b.down[v] - b.down[lv] + 1);
}
vector<array<ull,2>> spfenfront(n,array<ull,2>{});
vector<array<ull,4>> spfen(n,array<ull,4>{});
ull rootdepsum = 0, rootdistsum = 0;
auto apply_from_root = [&](int v, int dist, int sgn){
ull x = 2 * sgn, y = 2 * dist * sgn;
rootdepsum += x;
rootdistsum += y;
while (true){
int lv = b.leader(v);
int start = b.down[lv];
int sz = spfensz[lv];
int r = b.down[v] + 1 - start;
int memor = r;
r++;
while (r <= sz){
int id = r - 1 + start;
spfen[id][0] += x * memor;
spfen[id][1] += -x;
spfen[id][2] += y * memor;
spfen[id][3] += -y;
r += r & -r;
}
spfenfront[start][0] += x;
spfenfront[start][1] += y;
if (lv == 0) break;
v = ~b.nxt[lv];
}
};
auto prod_from_root = [&](int v, int dist){
ull depsum = -rootdepsum, distsum = -rootdistsum;
while (true){
int lv = b.leader(v);
int start = b.down[lv];
int r = b.down[v] + 1 - start;
int memor = r;
array<ull,4> prod = {};
while (r > 0){
int id = r - 1 + start;
rep(i,4){
prod[i] += spfen[id][i];
}
r -= r & -r;
}
depsum += prod[0] + (prod[1] + spfenfront[start][0]) * memor;
distsum += prod[2] + (prod[3] + spfenfront[start][1]) * memor;
if (lv == 0) break;
v = ~b.nxt[lv];
}
return depsum * dist + distsum;
};
vector<bool> done(n,false);
ull ans = 0;
for (int ctr : centroid_decomposition(a)){
done[ctr] = true;
vector<pair<int,int>> vds = {{ctr,0}};
vector<int> start = {0,1};
auto dfs = [&](auto sfs, int v, int f, int dist) -> void {
vds.emplace_back(v,dist);
for (int u : a[v]){
if (done[u]) continue;
if (u == f) continue;
sfs(sfs,u,v,dist+1);
}
};
for (int v : a[ctr]){
if (done[v]) continue;
dfs(dfs,v,ctr,1);
start.emplace_back(vds.size());
}
// numof u, dist[u], dep[u], dist[u]*dep[u]
ull cnt = 0, distsum = 0, depsum = 0, prdsum = 0;
int csz = start.size() - 2;
// v : ctr
[&]{
// dist[u] * dep[u]
prdsum += 0;
// dist[u] * dep[v]
distsum += 0;
// dist[v] * dep[u]
depsum += b.depth(ctr);
// dist[v] * dep[v]
cnt += 1;
// dist[u] * -2dep[lca(u,v)]
// dist[v] * -2dep[lca(u,v)]
apply_from_root(ctr, 0, -1);
}();
auto proc1 = [&](int v, int dist){
// dist[u] * dep[u]
ans += prdsum;
// dist[u] * dep[v]
ans += distsum * b.depth(v);
// dist[v] * dep[u]
ans += dist * depsum;
// dist[v] * dep[v]
ans += (ull)dist * b.depth(v) * cnt;
// dist[u] * -2dep[lca(u,v)]
// dist[v] * -2dep[lca(u,v)]
ans += prod_from_root(v, dist);
};
auto proc2 = [&](int v, int dist){
// dist[u] * dep[u]
prdsum += (ull)dist * b.depth(v);
// dist[u] * dep[v]
distsum += dist;
// dist[v] * dep[u]
depsum += b.depth(v);
// dist[v] * dep[v]
cnt += 1;
// dist[u] * -2dep[lca(u,v)]
// dist[v] * -2dep[lca(u,v)]
apply_from_root(v, dist, -1);
};
auto proc3 = [&](int v, int dist){
// cancel of
// dist[u] * -2dep[lca(u,v)]
// dist[v] * -2dep[lca(u,v)]
apply_from_root(v, dist, 1);
};
rep(i,csz){
repp(j,start[i+1],start[i+2]){
auto [v, dist] = vds[j];
proc1(v,dist);
}
repp(j,start[i+1],start[i+2]){
auto [v, dist] = vds[j];
proc2(v,dist);
}
}
rep(i,csz){
repp(j,start[i+1],start[i+2]){
auto [v, dist] = vds[j];
proc3(v,dist);
}
}
[&]{
// cancel of
// dist[u] * -2dep[lca(u,v)]
// dist[v] * -2dep[lca(u,v)]
apply_from_root(ctr, 0, 1);
}();
}
ans *= 2;
cout << ans << endl;
}