結果
| 問題 |
No.2634 Tree Distance 3
|
| コンテスト | |
| ユーザー |
 noya2
|
| 提出日時 | 2024-02-11 18:40:11 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 1,482 ms / 3,000 ms |
| コード長 | 20,647 bytes |
| コンパイル時間 | 4,346 ms |
| コンパイル使用メモリ | 289,548 KB |
| 実行使用メモリ | 63,320 KB |
| 最終ジャッジ日時 | 2024-09-28 19:25:43 |
| 合計ジャッジ時間 | 59,505 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 69 |
ソースコード
#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
using namespace std;
#include<bits/stdc++.h>
#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp"
namespace noya2 {
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p){
os << p.first << " " << p.second;
return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p){
is >> p.first >> p.second;
return is;
}
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>
istream &operator>>(istream &is, vector<T> &v){
for (auto &x : v) is >> x;
return is;
}
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...);
}
template<typename T>
void out(const vector<vector<T>> &vv){
int s = (int)vv.size();
for (int i = 0; i < s; i++) out(vv[i]);
}
struct IoSetup {
IoSetup(){
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetup_noya2;
} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"
namespace noya2{
const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 = 998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";
void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }
} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"
namespace noya2{
unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
if (a == 0 || b == 0) return a + b;
int n = __builtin_ctzll(a); a >>= n;
int m = __builtin_ctzll(b); b >>= m;
while (a != b) {
int mm = __builtin_ctzll(a - b);
bool f = a > b;
unsigned long long c = f ? a : b;
b = f ? b : a;
a = (c - b) >> mm;
}
return a << min(n, m);
}
template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(abs(a),abs(b))); }
long long sqrt_fast(long long n) {
if (n <= 0) return 0;
long long x = sqrt(n);
while ((x + 1) * (x + 1) <= n) x++;
while (x * x > n) x--;
return x;
}
template<typename T> T floor_div(const T n, const T d) {
assert(d != 0);
return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}
template<typename T> T ceil_div(const T n, const T d) {
assert(d != 0);
return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}
template<typename T> void uniq(vector<T> &v){
sort(v.begin(),v.end());
v.erase(unique(v.begin(),v.end()),v.end());
}
template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }
template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }
template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }
} // namespace noya2
#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
#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 reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()
using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;
namespace noya2{
/* ~ (. _________ . /) */
}
using namespace noya2;
#line 2 "c.cpp"
struct csr_for_cd {
csr_for_cd (int n_ = 0) : n(n_), m((n_-1)*2), removed(n_,false) {
es.reserve(m);
start.reserve(m);
if (m == 0) build();
}
int add(int u, int v){
int eid = start.size();
es.emplace_back(u);
start.emplace_back(v);
if (eid+1 == m) build();
return eid;
}
void build(){
if (m == -2) return ;
m = start.size();
std::vector<int> nes(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++) nes[nstart[start[i]+1]++] = es[i];
swap(es,nes);
swap(start,nstart);
stop = vector<int>(start.begin()+1,start.end());
m = -2;
}
const auto operator[](int idx){
assert(m == -2);
for (int i = start[idx]; i < stop[idx]; i++){
if (removed[es[i]]) swap(es[i],es[--stop[idx]]);
}
return std::ranges::subrange(es.begin()+start[idx],es.begin()+stop[idx]);
}
void remove(int v){
removed[v] = true;
stop[v] = start[v];
}
private:
int n, m;
std::vector<bool> removed;
std::vector<int> es;
std::vector<int> start, stop;
};
struct centroid_decomposition {
centroid_decomposition () {}
centroid_decomposition (int n_) : n(n_), g(n_), sub(n_,0) {
que.push(0);
sub[0] = n;
}
void add_edge(int u, int v){
g.add(u,v);
g.add(v,u);
}
int find_centroid(){
assert(!que.empty());
int from = que.front(); que.pop();
int sz = sub[from];
int centroid = -1;
auto dfs = [&](auto sfs, int v, int f) -> void {
sub[v] = 1;
bool is_centroid = (centroid == -1);
for (int u : g[v]){
if (u == f) continue;
sfs(sfs,u,v);
if (centroid != -1) return ;
if (sub[u] > sz/2) is_centroid = false;
sub[v] += sub[u];
}
if (sz - sub[v] > sz/2) is_centroid = false;
if (is_centroid){
centroid = v;
if (f != -1){
sub[f] = sz - sub[v];
}
}
};
dfs(dfs,from,-1);
assert(centroid != -1);
return centroid;
}
void remove_centroid(int v){
for (int u : g[v]){
que.push(u);
}
g.remove(v);
}
const auto operator[](int idx) { return g[idx]; }
private:
int n;
csr_for_cd g;
queue<int> que;
vector<int> sub;
};
#line 2 "/Users/noya2/Desktop/Noya2_library/data_structure/segment_tree.hpp"
namespace noya2{
template <class S, S (*op)(S, S), S (*e)()> struct segtree {
public:
segtree() : segtree(0) {}
segtree(int n) : segtree(std::vector<S>(n, e())) {}
segtree(const std::vector<S>& v) : _n(int(v.size())) {
log = 0;
size = 1;
while (size < _n) size <<= 1, log++;
d = std::vector<S>(2 * size, e());
for (int i = 0; i < _n; i++) d[size + i] = v[i];
for (int i = size - 1; i >= 1; i--) {
update(i);
}
}
void set(int p, S x) {
assert(0 <= p && p < _n);
p += size;
d[p] = x;
for (int i = 1; i <= log; i++) update(p >> i);
}
S get(int p) {
assert(0 <= p && p < _n);
return d[p + size];
}
S prod(int l, int r) {
assert(0 <= l && l <= r && r <= _n);
S sml = e(), smr = e();
l += size;
r += size;
while (l < r) {
if (l & 1) sml = op(sml, d[l++]);
if (r & 1) smr = op(d[--r], smr);
l >>= 1;
r >>= 1;
}
return op(sml, smr);
}
S all_prod() { return d[1]; }
template <bool (*f)(S)> int max_right(int l) {
return max_right(l, [](S x) { return f(x); });
}
template <class F> int max_right(int l, F f) {
assert(0 <= l && l <= _n);
assert(f(e()));
if (l == _n) return _n;
l += size;
S sm = e();
do {
while (l % 2 == 0) l >>= 1;
if (!f(op(sm, d[l]))) {
while (l < size) {
l = (2 * l);
if (f(op(sm, d[l]))) {
sm = op(sm, d[l]);
l++;
}
}
return l - size;
}
sm = op(sm, d[l]);
l++;
} while ((l & -l) != l);
return _n;
}
template <bool (*f)(S)> int min_left(int r) {
return min_left(r, [](S x) { return f(x); });
}
template <class F> int min_left(int r, F f) {
assert(0 <= r && r <= _n);
assert(f(e()));
if (r == 0) return 0;
r += size;
S sm = e();
do {
r--;
while (r > 1 && (r % 2)) r >>= 1;
if (!f(op(d[r], sm))) {
while (r < size) {
r = (2 * r + 1);
if (f(op(d[r], sm))) {
sm = op(d[r], sm);
r--;
}
}
return r + 1 - size;
}
sm = op(d[r], sm);
} while ((r & -r) != r);
return 0;
}
private:
int _n, size, log;
std::vector<S> d;
void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
};
} // namespace noya2
#line 99 "c.cpp"
int op(int a, int b){
return max(a,b);
}
int e(){
return -iinf;
}
#line 2 "/Users/noya2/Desktop/Noya2_library/tree/heavy_light_decomposition.hpp"
#line 4 "/Users/noya2/Desktop/Noya2_library/tree/heavy_light_decomposition.hpp"
namespace noya2 {
struct hldTree {
hldTree (int n_ = 0, int root_ = 0) : n(n_), root(root_), inner_edge_id(0){
down.resize(n);
tour.resize(n);
if (n == 1) build();
}
void add_edge(int u, int v){
down[inner_edge_id] = u;
tour[inner_edge_id] = v;
if (++inner_edge_id == n-1) build();
}
void input(int indexed = 1){
for (int i = 0; i < n-1; i++){
int u, v; cin >> u >> v;
u -= indexed, v -= indexed;
add_edge(u,v);
}
}
void input_parents(int indexed = 1){
for (int i = 0; i < n-1; i++){
int p; cin >> p;
p -= indexed;
add_edge(p,i+1);
}
}
int degree(int v){
assert(0 <= v && v < n);
return start[v+1] - start[v];
}
int parent(int v){
assert(0 <= v && v < n);
if (v == root) return -1;
return es[start[v]];
}
int subtree_size(int v){
assert(0 <= v && v < n);
return sub[v];
}
int depth(int v){
assert(0 <= v && v < n);
return dep[v];
}
int la(int v, int d){
assert(0 <= v && v < n);
while (v != -1){
int u = nxt[v];
if (down[v] - d >= down[u]){
v = tour[down[v] - d];
break;
}
d -= down[v] - down[u] + 1;
v = parent(u);
}
return v;
}
int lca(int u, int v){
assert(0 <= v && v < n && 0 <= u && u < n);
while (nxt[u] != nxt[v]){
if (down[u] < down[v]) std::swap(u,v);
u = es[start[nxt[u]]];
}
return dep[u] < dep[v] ? u : v;
}
int jump(int from, int to, int d){
int l = lca(from,to);
if (d <= dep[from] - dep[l]){
return la(from,d);
}
d -= dep[from] - dep[l];
if (d <= dep[to] - dep[l]){
return la(to,dep[to]-dep[l]-d);
}
return -1;
}
int dist(int u, int v){ return dep[lca(u,v)]*(-2) + dep[u] + dep[v]; }
bool is_in_subtree(int r, int v){ return down[r] < down[v] && up[v] <= up[r]; }
bool is_in_path(int lv, int mv, int rv){ return dist(lv,mv) + dist(mv,rv) == dist(lv,rv); }
vector<int> path(int from, int to){
int l = lca(from,to);
const int sizf = dep[from]-dep[l], sizt = dep[to]-dep[l];
vector<int> pf = {from}, pt;
pf.reserve(sizf+1); pt.reserve(sizt);
for (int i = 0; i < sizf; i++){
from = parent(from);
pf.push_back(from);
}
for (int i = 0; i < sizt; i++){
pt.push_back(to);
to = parent(to);
}
pf.insert(pf.end(),pt.rbegin(),pt.rend());
return pf;
}
// dist, v1, v2
tuple<int,int,int> diameter(){
int v1 = max_element(dep.begin(),dep.end()) - dep.begin();
vector<int> dist_from_v1(n,numeric_limits<int>::max());
queue<int> que;
que.push(v1);
dist_from_v1[v1] = 0;
while (!que.empty()){
int p = que.front(); que.pop();
for (int i = start[p]; i < start[p+1]; i++){
if (dist_from_v1[es[i]] > dist_from_v1[p]+1){
dist_from_v1[es[i]] = dist_from_v1[p]+1;
que.push(es[i]);
}
}
}
int v2 = max_element(dist_from_v1.begin(),dist_from_v1.end()) - dist_from_v1.begin();
return make_tuple(dist_from_v1[v2],v1,v2);
}
template<typename F>
void path_query(int u, int v, bool vertex, const F &f){ // f is function takes (left, right) as argument, range = [left,right).
int l = lca(u,v);
for (auto &p : ascend(u,l)){
int s = p.first + 1, t = p.second; // p.first + 1 : depth(p.first) > depth(p.second), so [p.second,p.first] = [p.second,p.first+1)
s > t ? f(t,s) : f(s,t);
}
if (vertex) f(down[l],down[l]+1); // vertex is true : query is for point
for (auto &p : descend(l,v)){
int s = p.first, t = p.second + 1; // p.second +1 : depth(p.first) < depth(p.second), so [p.first,p.second] = [p.first,p.second+1)
s > t ? f(t,s) : f(s,t);
}
}
template<typename F>
void path_noncommutative_query(int u, int v, bool vertex, const F &f){ // op(l,r) != op(r,l), so prod[u->...->v] != prod[v->...->u]
int l = lca(u,v);
for (auto &p : ascend(u,l)){
int s = p.first + 1, t = p.second; // p.first + 1 : depth(p.first) > depth(p.second), so [p.second,p.first] = [p.second,p.first+1)
f(s,t); // le > ri ok
}
if (vertex) f(down[l],down[l]+1); // vertex is true : query is for point
for (auto &p : descend(l,v)){
int s = p.first, t = p.second + 1; // p.second +1 : depth(p.first) < depth(p.second), so [p.first,p.second] = [p.first,p.second+1)
f(s,t); // le > ri ok
}
}
template<typename F>
void subtree_query(int v, bool vertex, const F &f){
f(down[v] + (vertex ? 0 : 1), up[v]);
}
const auto operator[](int idx){ return std::ranges::subrange(es.begin()+start[idx],es.begin()+start[idx+1]); }
const auto operator()(int idx){ return std::ranges::subrange(es.begin()+start_skip_parent(idx),es.begin()+start[idx+1]); }
int set_id_v(int v) const {
return down[v];
}
int set_id_e(int u, int v) const {
return (dep[u] < dep[v] ? down[v] : down[u]);
}
int vertex_id(int i){
return tour[i];
}
int subtree_l(int v) const {
return down[v];
}
int subtree_r(int v) const {
return up[v];
}
private:
void build(){
es.resize((n-1)*2);
start.resize(n+2,0);
for (int i = 0; i < n-1; i++){
start[down[i]+2]++;
start[tour[i]+2]++;
}
for (int i = 1; i <= n; i++){
start[i+1] += start[i];
}
for (int i = 0; i < n-1; i++){
es[start[down[i]+1]++] = tour[i];
es[start[tour[i]+1]++] = down[i];
}
init_bfs();
init_dfs();
}
void init_bfs(){
dep.resize(n,numeric_limits<int>::max());
up.resize(n);
int l = 0, r = 0;
auto push = [&](int x){
up[r++] = x;
};
auto pop_front = [&](){
return up[l++];
};
dep[root] = 0;
push(root);
while (l < r){
int p = pop_front();
for (int i = start[p]; i < start[p+1]; i++){
auto q = es[i];
if (dep[q] > dep[p]+1){
dep[q] = dep[p]+1;
push(q);
}
else {
swap(es[start[p]],es[i]);
}
}
}
sub.resize(n,1);
for (int v : up | std::views::reverse){
const int stv = start_skip_parent(v);
for (int i = stv; i < start[v+1]; i++){
sub[v] += sub[es[i]];
if (sub[es[stv]] < sub[es[i]]) swap(es[stv],es[i]);
}
}
}
void init_dfs(){
nxt.resize(n);
nxt[root] = root;
int inner_clock = 0;
auto dfs = [&](auto sfs, int v) -> void {
down[v] = inner_clock++;
tour[down[v]] = v;
int stv = start_skip_parent(v);
if (stv < start[v+1]){
nxt[es[stv]] = nxt[v];
sfs(sfs,es[stv]);
for (int i = stv+1; i < start[v+1]; i++){
nxt[es[i]] = es[i];
sfs(sfs,es[i]);
}
}
up[v] = inner_clock;
};
dfs(dfs,root);
}
vector<pair<int,int>> ascend(int u, int v){ // [u,v), depth[u] > depth[v]
vector<pair<int,int>> res;
while (nxt[u] != nxt[v]){
res.emplace_back(down[u],down[nxt[u]]); // [s1,t1], [s2,t2], ...
u = es[start[nxt[u]]]; // parent of nxt[u]
}
if (u != v) res.emplace_back(down[u],down[v]+1); // [s,t). v is not in the range (down[] is ordered opposite direction of depth)
return res;
}
vector<pair<int,int>> descend(int u, int v){ // (u,v], depth[u] < depth[v]
if (u == v) return {};
if (nxt[u] == nxt[v]){
return {pair<int,int>(down[u]+1,down[v])}; // (s,t]. u is not in the range
}
vector<pair<int,int>> res = descend(u,es[start[nxt[v]]]); // descend(u, parent of nxt[v])
res.emplace_back(down[nxt[v]],down[v]); // [s1,t1], [s2,t2], ...
return res;
}
int start_skip_parent(int v) const { return start[v]+int(v != root); }
int n, root, inner_edge_id;
vector<int> es, start, dep, sub, down, up, tour, nxt;
};
} // namespace noya2
#line 108 "c.cpp"
void solve(){
int n; in(n);
vector<int> a(n); in(a);
centroid_decomposition g(n);
rep(i,n-1){
int u, v; in(u,v); u--, v--;
g.add_edge(u,v);
}
vector<int> ans(n,-1);
vector<int> ids(n);
rep(t_,n){
int ctr = g.find_centroid();
vector<int> vs;
auto dfs = [&](auto sfs, int v, int f) -> void {
vs.emplace_back(v);
for (int u : g[v]){
if (u == f) continue;
sfs(sfs,u,v);
}
};
dfs(dfs,ctr,-1);
int sz = vs.size();
rep(i,sz) ids[vs[i]] = i;
hldTree hld(sz);
auto init = [&](auto sfs, int v, int f) -> void {
for (int u : g[v]){
if (u == f) continue;
hld.add_edge(ids[u],ids[v]);
sfs(sfs,u,v);
}
};
init(init,ctr,-1);
vector<int> ord = vs;
sort(all(ord),[&](int u, int v){
return a[u] > a[v];
});
segtree<int,op,e> seg(sz);
for (int l = 0, r = 0; l < sz; l = r){
while (r < sz && a[ord[r]] == a[ord[l]]){
seg.set(hld.set_id_v(ids[ord[r]]),hld.depth(ids[ord[r]]));
r++;
}
repp(i,l,r){
int iv = ids[ord[i]];
if (hld.depth(iv) == 0){
chmax(ans[ord[i]],seg.all_prod());
continue;
}
int nxt = hld.jump(ids[ctr],iv,1);
chmax(ans[ord[i]],op(seg.prod(0,hld.subtree_l(nxt)),seg.prod(hld.subtree_r(nxt),sz))+hld.depth(iv));
}
}
g.remove_centroid(ctr);
}
out(ans);
}
int main(){
int t = 1; //in(t);
while (t--) { solve(); }
}