結果
| 問題 |
No.2491 Pochi and A Warp Machine
|
| コンテスト | |
| ユーザー |
 maspy
|
| 提出日時 | 2023-11-09 03:38:54 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 540 ms / 3,000 ms |
| コード長 | 38,814 bytes |
| コンパイル時間 | 7,270 ms |
| コンパイル使用メモリ | 343,544 KB |
| 実行使用メモリ | 29,968 KB |
| 最終ジャッジ日時 | 2024-09-26 00:01:14 |
| 合計ジャッジ時間 | 24,275 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 * 3 |
| other | AC * 40 |
ソースコード
#line 1 "/home/maspy/compro/library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;
template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;
using pi = pair<ll, ll>;
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>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<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__))))
// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
#define FOR_subset(t, s) \
for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define stoi stoll
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_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
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 floor(T a, T b) {
return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
T q = floor(x, y);
return {q, x - q * y};
}
template <typename T, typename U>
T SUM(const vector<U> &A) {
T sm = 0;
for (auto &&a: A) sm += a;
return sm;
}
#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)))
#define UNIQUE(x) \
sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()
template <typename T>
T POP(deque<T> &que) {
T a = que.front();
que.pop_front();
return a;
}
template <typename T>
T POP(pq<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(pqg<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(vc<T> &que) {
T a = que.back();
que.pop_back();
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) {
auto x = (ng + ok) / 2;
(check(x) ? ok : ng) = x;
}
return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
FOR(iter) {
double x = (ok + ng) / 2;
(check(x) ? ok : ng) = x;
}
return (ok + ng) / 2;
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
return (a > b ? a = b, 1 : 0);
}
// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
vc<int> A(S.size());
FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
return A;
}
template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
int N = A.size();
vector<T> B(N + 1);
FOR(i, N) { B[i + 1] = B[i] + A[i]; }
if (off == 0) B.erase(B.begin());
return B;
}
// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
vector<int> ids(len(A));
iota(all(ids), 0);
sort(all(ids),
[&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
return ids;
}
// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
vc<T> B(len(I));
FOR(i, len(I)) B[i] = A[I[i]];
return B;
}
#endif
#line 1 "/home/maspy/compro/library/other/io.hpp"
#define FASTIO
#include <unistd.h>
// https://judge.yosupo.jp/submission/21623
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
uint32_t pil = 0, pir = 0, por = 0;
struct Pre {
char num[10000][4];
constexpr Pre() : num() {
for (int i = 0; i < 10000; i++) {
int n = i;
for (int j = 3; j >= 0; j--) {
num[i][j] = n % 10 | '0';
n /= 10;
}
}
}
} constexpr pre;
inline void load() {
memcpy(ibuf, ibuf + pil, pir - pil);
pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
pil = 0;
if (pir < SZ) ibuf[pir++] = '\n';
}
inline void flush() {
fwrite(obuf, 1, por, stdout);
por = 0;
}
void rd(char &c) {
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
}
void rd(string &x) {
x.clear();
char c;
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
do {
x += c;
if (pil == pir) load();
c = ibuf[pil++];
} while (!isspace(c));
}
template <typename T>
void rd_real(T &x) {
string s;
rd(s);
x = stod(s);
}
template <typename T>
void rd_integer(T &x) {
if (pil + 100 > pir) load();
char c;
do
c = ibuf[pil++];
while (c < '-');
bool minus = 0;
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (c == '-') { minus = 1, c = ibuf[pil++]; }
}
x = 0;
while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (minus) x = -x;
}
}
void rd(int &x) { rd_integer(x); }
void rd(ll &x) { rd_integer(x); }
void rd(i128 &x) { rd_integer(x); }
void rd(u32 &x) { rd_integer(x); }
void rd(u64 &x) { rd_integer(x); }
void rd(u128 &x) { rd_integer(x); }
void rd(double &x) { rd_real(x); }
void rd(long double &x) { rd_real(x); }
void rd(f128 &x) { rd_real(x); }
template <class T, class U>
void rd(pair<T, U> &p) {
return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
if constexpr (N < std::tuple_size<T>::value) {
auto &x = std::get<N>(t);
rd(x);
rd_tuple<N + 1>(t);
}
}
template <class... T>
void rd(tuple<T...> &tpl) {
rd_tuple(tpl);
}
template <size_t N = 0, typename T>
void rd(array<T, N> &x) {
for (auto &d: x) rd(d);
}
template <class T>
void rd(vc<T> &x) {
for (auto &d: x) rd(d);
}
void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
rd(h), read(t...);
}
void wt(const char c) {
if (por == SZ) flush();
obuf[por++] = c;
}
void wt(const string s) {
for (char c: s) wt(c);
}
void wt(const char *s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++) wt(s[i]);
}
template <typename T>
void wt_integer(T x) {
if (por > SZ - 100) flush();
if (x < 0) { obuf[por++] = '-', x = -x; }
int outi;
for (outi = 96; x >= 10000; outi -= 4) {
memcpy(out + outi, pre.num[x % 10000], 4);
x /= 10000;
}
if (x >= 1000) {
memcpy(obuf + por, pre.num[x], 4);
por += 4;
} else if (x >= 100) {
memcpy(obuf + por, pre.num[x] + 1, 3);
por += 3;
} else if (x >= 10) {
int q = (x * 103) >> 10;
obuf[por] = q | '0';
obuf[por + 1] = (x - q * 10) | '0';
por += 2;
} else
obuf[por++] = x | '0';
memcpy(obuf + por, out + outi + 4, 96 - outi);
por += 96 - outi;
}
template <typename T>
void wt_real(T x) {
ostringstream oss;
oss << fixed << setprecision(15) << double(x);
string s = oss.str();
wt(s);
}
void wt(int x) { wt_integer(x); }
void wt(ll x) { wt_integer(x); }
void wt(i128 x) { wt_integer(x); }
void wt(u32 x) { wt_integer(x); }
void wt(u64 x) { wt_integer(x); }
void wt(u128 x) { wt_integer(x); }
void wt(double x) { wt_real(x); }
void wt(long double x) { wt_real(x); }
void wt(f128 x) { wt_real(x); }
template <class T, class U>
void wt(const pair<T, U> val) {
wt(val.first);
wt(' ');
wt(val.second);
}
template <size_t N = 0, typename T>
void wt_tuple(const T t) {
if constexpr (N < std::tuple_size<T>::value) {
if constexpr (N > 0) { wt(' '); }
const auto x = std::get<N>(t);
wt(x);
wt_tuple<N + 1>(t);
}
}
template <class... T>
void wt(tuple<T...> tpl) {
wt_tuple(tpl);
}
template <class T, size_t S>
void wt(const array<T, S> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt(' ');
wt(val[i]);
}
}
template <class T>
void wt(const vector<T> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt(' ');
wt(val[i]);
}
}
void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
wt(head);
if (sizeof...(Tail)) wt(' ');
print(forward<Tail>(tail)...);
}
// gcc expansion. called automaticall after main.
void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio
using fastio::read;
using fastio::print;
using fastio::flush;
#define INT(...) \
int __VA_ARGS__; \
read(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
read(__VA_ARGS__)
#define U32(...) \
u32 __VA_ARGS__; \
read(__VA_ARGS__)
#define U64(...) \
u64 __VA_ARGS__; \
read(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
read(__VA_ARGS__)
#define CHAR(...) \
char __VA_ARGS__; \
read(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
read(__VA_ARGS__)
#define VEC(type, name, size) \
vector<type> name(size); \
read(name)
#define VV(type, name, h, w) \
vector<vector<type>> name(h, vector<type>(w)); \
read(name)
void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 3 "main.cpp"
#line 2 "/home/maspy/compro/library/graph/tree.hpp"
#line 2 "/home/maspy/compro/library/graph/base.hpp"
template <typename T>
struct Edge {
int frm, to;
T cost;
int id;
};
template <typename T = int, bool directed = false>
struct Graph {
static constexpr bool is_directed = directed;
int N, M;
using cost_type = T;
using edge_type = Edge<T>;
vector<edge_type> edges;
vector<int> indptr;
vector<edge_type> csr_edges;
vc<int> vc_deg, vc_indeg, vc_outdeg;
bool prepared;
class OutgoingEdges {
public:
OutgoingEdges(const Graph* G, int l, int r) : G(G), l(l), r(r) {}
const edge_type* begin() const {
if (l == r) { return 0; }
return &G->csr_edges[l];
}
const edge_type* end() const {
if (l == r) { return 0; }
return &G->csr_edges[r];
}
private:
const Graph* G;
int l, r;
};
bool is_prepared() { return prepared; }
Graph() : N(0), M(0), prepared(0) {}
Graph(int N) : N(N), M(0), prepared(0) {}
void build(int n) {
N = n, M = 0;
prepared = 0;
edges.clear();
indptr.clear();
csr_edges.clear();
vc_deg.clear();
vc_indeg.clear();
vc_outdeg.clear();
}
void add(int frm, int to, T cost = 1, int i = -1) {
assert(!prepared);
assert(0 <= frm && 0 <= to && to < N);
if (i == -1) i = M;
auto e = edge_type({frm, to, cost, i});
edges.eb(e);
++M;
}
#ifdef FASTIO
// wt, off
void read_tree(bool wt = false, int off = 1) { read_graph(N - 1, wt, off); }
void read_graph(int M, bool wt = false, int off = 1) {
for (int m = 0; m < M; ++m) {
INT(a, b);
a -= off, b -= off;
if (!wt) {
add(a, b);
} else {
T c;
read(c);
add(a, b, c);
}
}
build();
}
#endif
void build() {
assert(!prepared);
prepared = true;
indptr.assign(N + 1, 0);
for (auto&& e: edges) {
indptr[e.frm + 1]++;
if (!directed) indptr[e.to + 1]++;
}
for (int v = 0; v < N; ++v) { indptr[v + 1] += indptr[v]; }
auto counter = indptr;
csr_edges.resize(indptr.back() + 1);
for (auto&& e: edges) {
csr_edges[counter[e.frm]++] = e;
if (!directed)
csr_edges[counter[e.to]++] = edge_type({e.to, e.frm, e.cost, e.id});
}
}
OutgoingEdges operator[](int v) const {
assert(prepared);
return {this, indptr[v], indptr[v + 1]};
}
vc<int> deg_array() {
if (vc_deg.empty()) calc_deg();
return vc_deg;
}
pair<vc<int>, vc<int>> deg_array_inout() {
if (vc_indeg.empty()) calc_deg_inout();
return {vc_indeg, vc_outdeg};
}
int deg(int v) {
if (vc_deg.empty()) calc_deg();
return vc_deg[v];
}
int in_deg(int v) {
if (vc_indeg.empty()) calc_deg_inout();
return vc_indeg[v];
}
int out_deg(int v) {
if (vc_outdeg.empty()) calc_deg_inout();
return vc_outdeg[v];
}
#ifdef FASTIO
void debug() {
print("Graph");
if (!prepared) {
print("frm to cost id");
for (auto&& e: edges) print(e.frm, e.to, e.cost, e.id);
} else {
print("indptr", indptr);
print("frm to cost id");
FOR(v, N) for (auto&& e: (*this)[v]) print(e.frm, e.to, e.cost, e.id);
}
}
#endif
vc<int> new_idx;
vc<bool> used_e;
// G における頂点 V[i] が、新しいグラフで i になるようにする
// {G, es}
Graph<T, directed> rearrange(vc<int> V, bool keep_eid = 0) {
if (len(new_idx) != N) new_idx.assign(N, -1);
if (len(used_e) != M) used_e.assign(M, 0);
int n = len(V);
FOR(i, n) new_idx[V[i]] = i;
Graph<T, directed> G(n);
vc<int> history;
FOR(i, n) {
for (auto&& e: (*this)[V[i]]) {
if (used_e[e.id]) continue;
int a = e.frm, b = e.to;
if (new_idx[a] != -1 && new_idx[b] != -1) {
history.eb(e.id);
used_e[e.id] = 1;
int eid = (keep_eid ? e.id : -1);
G.add(new_idx[a], new_idx[b], e.cost, eid);
}
}
}
FOR(i, n) new_idx[V[i]] = -1;
for (auto&& eid: history) used_e[eid] = 0;
G.build();
return G;
}
private:
void calc_deg() {
assert(vc_deg.empty());
vc_deg.resize(N);
for (auto&& e: edges) vc_deg[e.frm]++, vc_deg[e.to]++;
}
void calc_deg_inout() {
assert(vc_indeg.empty());
vc_indeg.resize(N);
vc_outdeg.resize(N);
for (auto&& e: edges) { vc_indeg[e.to]++, vc_outdeg[e.frm]++; }
}
};
#line 4 "/home/maspy/compro/library/graph/tree.hpp"
// HLD euler tour をとっていろいろ。
template <typename GT>
struct Tree {
using Graph_type = GT;
GT &G;
using WT = typename GT::cost_type;
int N;
vector<int> LID, RID, head, V, parent, VtoE;
vc<int> depth;
vc<WT> depth_weighted;
Tree(GT &G, int r = 0, bool hld = 1) : G(G) { build(r, hld); }
void build(int r = 0, bool hld = 1) {
if (r == -1) return; // build を遅延したいとき
N = G.N;
LID.assign(N, -1), RID.assign(N, -1), head.assign(N, r);
V.assign(N, -1), parent.assign(N, -1), VtoE.assign(N, -1);
depth.assign(N, -1), depth_weighted.assign(N, 0);
assert(G.is_prepared());
int t1 = 0;
dfs_sz(r, -1, hld);
dfs_hld(r, t1);
}
void dfs_sz(int v, int p, bool hld) {
auto &sz = RID;
parent[v] = p;
depth[v] = (p == -1 ? 0 : depth[p] + 1);
sz[v] = 1;
int l = G.indptr[v], r = G.indptr[v + 1];
auto &csr = G.csr_edges;
// 使う辺があれば先頭にする
for (int i = r - 2; i >= l; --i) {
if (hld && depth[csr[i + 1].to] == -1) swap(csr[i], csr[i + 1]);
}
int hld_sz = 0;
for (int i = l; i < r; ++i) {
auto e = csr[i];
if (depth[e.to] != -1) continue;
depth_weighted[e.to] = depth_weighted[v] + e.cost;
VtoE[e.to] = e.id;
dfs_sz(e.to, v, hld);
sz[v] += sz[e.to];
if (hld && chmax(hld_sz, sz[e.to]) && l < i) { swap(csr[l], csr[i]); }
}
}
void dfs_hld(int v, int ×) {
LID[v] = times++;
RID[v] += LID[v];
V[LID[v]] = v;
bool heavy = true;
for (auto &&e: G[v]) {
if (depth[e.to] <= depth[v]) continue;
head[e.to] = (heavy ? head[v] : e.to);
heavy = false;
dfs_hld(e.to, times);
}
}
vc<int> heavy_path_at(int v) {
vc<int> P = {v};
while (1) {
int a = P.back();
for (auto &&e: G[a]) {
if (e.to != parent[a] && head[e.to] == v) {
P.eb(e.to);
break;
}
}
if (P.back() == a) break;
}
return P;
}
int heavy_child(int v) {
int k = LID[v] + 1;
if (k == N) return -1;
int w = V[k];
return (parent[w] == v ? w : -1);
}
int e_to_v(int eid) {
auto e = G.edges[eid];
return (parent[e.frm] == e.to ? e.frm : e.to);
}
int v_to_e(int v) { return VtoE[v]; }
int ELID(int v) { return 2 * LID[v] - depth[v]; }
int ERID(int v) { return 2 * RID[v] - depth[v] - 1; }
// 目標地点へ進む個数が k
int LA(int v, int k) {
assert(k <= depth[v]);
while (1) {
int u = head[v];
if (LID[v] - k >= LID[u]) return V[LID[v] - k];
k -= LID[v] - LID[u] + 1;
v = parent[u];
}
}
int la(int u, int v) { return LA(u, v); }
int LCA(int u, int v) {
for (;; v = parent[head[v]]) {
if (LID[u] > LID[v]) swap(u, v);
if (head[u] == head[v]) return u;
}
}
// root を根とした場合の lca
int LCA_root(int u, int v, int root) {
return LCA(u, v) ^ LCA(u, root) ^ LCA(v, root);
}
int lca(int u, int v) { return LCA(u, v); }
int lca_root(int u, int v, int root) { return LCA_root(u, v, root); }
int subtree_size(int v, int root = -1) {
if (root == -1) return RID[v] - LID[v];
if (v == root) return N;
int x = jump(v, root, 1);
if (in_subtree(v, x)) return RID[v] - LID[v];
return N - RID[x] + LID[x];
}
int dist(int a, int b) {
int c = LCA(a, b);
return depth[a] + depth[b] - 2 * depth[c];
}
WT dist_weighted(int a, int b) {
int c = LCA(a, b);
return depth_weighted[a] + depth_weighted[b] - WT(2) * depth_weighted[c];
}
// a is in b
bool in_subtree(int a, int b) { return LID[b] <= LID[a] && LID[a] < RID[b]; }
int jump(int a, int b, ll k) {
if (k == 1) {
if (a == b) return -1;
return (in_subtree(b, a) ? LA(b, depth[b] - depth[a] - 1) : parent[a]);
}
int c = LCA(a, b);
int d_ac = depth[a] - depth[c];
int d_bc = depth[b] - depth[c];
if (k > d_ac + d_bc) return -1;
if (k <= d_ac) return LA(a, k);
return LA(b, d_ac + d_bc - k);
}
vc<int> collect_child(int v) {
vc<int> res;
for (auto &&e: G[v])
if (e.to != parent[v]) res.eb(e.to);
return res;
}
vc<pair<int, int>> get_path_decomposition(int u, int v, bool edge) {
// [始点, 終点] の"閉"区間列。
vc<pair<int, int>> up, down;
while (1) {
if (head[u] == head[v]) break;
if (LID[u] < LID[v]) {
down.eb(LID[head[v]], LID[v]);
v = parent[head[v]];
} else {
up.eb(LID[u], LID[head[u]]);
u = parent[head[u]];
}
}
if (LID[u] < LID[v]) down.eb(LID[u] + edge, LID[v]);
elif (LID[v] + edge <= LID[u]) up.eb(LID[u], LID[v] + edge);
reverse(all(down));
up.insert(up.end(), all(down));
return up;
}
vc<int> restore_path(int u, int v) {
vc<int> P;
for (auto &&[a, b]: get_path_decomposition(u, v, 0)) {
if (a <= b) {
FOR(i, a, b + 1) P.eb(V[i]);
} else {
FOR_R(i, b, a + 1) P.eb(V[i]);
}
}
return P;
}
};
#line 2 "/home/maspy/compro/library/ds/segtree/dual_segtree.hpp"
template <typename Monoid>
struct Dual_SegTree {
using MA = Monoid;
using A = typename MA::value_type;
int n, log, size;
vc<A> laz;
Dual_SegTree() : Dual_SegTree(0) {}
Dual_SegTree(int n) { build(n); }
void build(int m) {
n = m;
log = 1;
while ((1 << log) < n) ++log;
size = 1 << log;
laz.assign(size << 1, MA::unit());
}
A get(int p) {
assert(0 <= p && p < n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
return laz[p];
}
vc<A> get_all() {
FOR(i, size) push(i);
return {laz.begin() + size, laz.begin() + size + n};
}
void apply(int l, int r, const A& a) {
assert(0 <= l && l <= r && r <= n);
if (l == r) return;
l += size, r += size;
if (!MA::commute) {
for (int i = log; i >= 1; i--) {
if (((l >> i) << i) != l) push(l >> i);
if (((r >> i) << i) != r) push((r - 1) >> i);
}
}
while (l < r) {
if (l & 1) all_apply(l++, a);
if (r & 1) all_apply(--r, a);
l >>= 1, r >>= 1;
}
}
private:
void push(int k) {
if (laz[k] == MA::unit()) return;
all_apply(2 * k, laz[k]), all_apply(2 * k + 1, laz[k]);
laz[k] = MA::unit();
}
void all_apply(int k, A a) { laz[k] = MA::op(laz[k], a); }
};
#line 3 "/home/maspy/compro/library/graph/ds/dual_tree_monoid.hpp"
template <typename TREE, typename Monoid, bool edge>
struct Dual_Tree_Monoid {
using MX = Monoid;
using X = typename MX::value_type;
TREE &tree;
int N;
Dual_SegTree<MX> seg;
Dual_Tree_Monoid(TREE &tree) : tree(tree), N(tree.N), seg(tree.N) {}
X get(int i) {
int v = i;
if (edge) {
auto &&e = tree.G.edges[i];
v = (tree.parent[e.frm] == e.to ? e.frm : e.to);
}
return seg.get(tree.LID[v]);
}
vc<X> get_all() {
vc<X> tmp = seg.get_all();
vc<X> res;
FOR(i, N) {
if (edge && i == N - 1) break;
int v = i;
if (edge) {
auto &&e = tree.G.edges[i];
v = (tree.parent[e.frm] == e.to ? e.frm : e.to);
}
res.eb(tmp[tree.LID[v]]);
}
return res;
}
void apply_path(int u, int v, X x) {
auto pd = tree.get_path_decomposition(u, v, edge);
for (auto &&[a, b]: pd) {
(a <= b ? seg.apply(a, b + 1, x) : seg.apply(b, a + 1, x));
}
return;
}
void apply_subtree(int u, X x) {
int l = tree.LID[u], r = tree.RID[u];
return seg.apply(l + edge, r, x);
}
};
#line 3 "/home/maspy/compro/library/graph/shortest_path/bfs01.hpp"
template <typename T, typename GT>
pair<vc<T>, vc<int>> bfs01(GT& G, int v) {
assert(G.is_prepared());
int N = G.N;
vc<T> dist(N, infty<T>);
vc<int> par(N, -1);
deque<int> que;
dist[v] = 0;
que.push_front(v);
while (!que.empty()) {
auto v = que.front();
que.pop_front();
for (auto&& e: G[v]) {
if (dist[e.to] == infty<T> || dist[e.to] > dist[e.frm] + e.cost) {
dist[e.to] = dist[e.frm] + e.cost;
par[e.to] = e.frm;
if (e.cost == 0)
que.push_front(e.to);
else
que.push_back(e.to);
}
}
}
return {dist, par};
}
// 多点スタート。[dist, par, root]
template <typename T, typename GT>
tuple<vc<T>, vc<int>, vc<int>> bfs01(GT& G, vc<int> vs) {
assert(G.is_prepared());
int N = G.N;
vc<T> dist(N, infty<T>);
vc<int> par(N, -1);
vc<int> root(N, -1);
deque<int> que;
for (auto&& v: vs) {
dist[v] = 0;
root[v] = v;
que.push_front(v);
}
while (!que.empty()) {
auto v = que.front();
que.pop_front();
for (auto&& e: G[v]) {
if (dist[e.to] == infty<T> || dist[e.to] > dist[e.frm] + e.cost) {
dist[e.to] = dist[e.frm] + e.cost;
root[e.to] = root[e.frm];
par[e.to] = e.frm;
if (e.cost == 0)
que.push_front(e.to);
else
que.push_back(e.to);
}
}
}
return {dist, par, root};
}
#line 3 "/home/maspy/compro/library/graph/centroid_decomposition.hpp"
template <typename F>
void centroid_decomposition_0_dfs(vc<int>& par, vc<int>& vs, F f) {
const int N = len(par);
assert(N >= 1);
int c = -1;
vc<int> sz(N, 1);
FOR_R(i, N) {
if (sz[i] >= ceil<int>(N, 2)) {
c = i;
break;
}
sz[par[i]] += sz[i];
}
vc<int> color(N);
vc<int> V = {c};
int nc = 1;
FOR(v, 1, N) {
if (par[v] == c) { V.eb(v), color[v] = nc++; }
}
if (c > 0) {
for (int a = par[c]; a != -1; a = par[a]) { color[a] = nc, V.eb(a); }
++nc;
}
FOR(i, N) {
if (i != c && color[i] == 0) color[i] = color[par[i]], V.eb(i);
}
vc<int> indptr(nc + 1);
FOR(i, N) indptr[1 + color[i]]++;
FOR(i, nc) indptr[i + 1] += indptr[i];
vc<int> counter = indptr;
vc<int> ord(N);
for (auto& v: V) { ord[counter[color[v]]++] = v; }
vc<int> new_idx(N);
FOR(i, N) new_idx[ord[i]] = i;
vc<int> name(N);
FOR(i, N) name[new_idx[i]] = vs[i];
{
vc<int> tmp(N, -1);
FOR(i, 1, N) {
int a = new_idx[i], b = new_idx[par[i]];
if (a > b) swap(a, b);
tmp[b] = a;
}
swap(par, tmp);
}
f(par, name, indptr);
FOR(k, 1, nc) {
int L = indptr[k], R = indptr[k + 1];
vc<int> par1(R - L, -1);
vc<int> name1(R - L, -1);
name1[0] = name[0];
FOR(i, L, R) name1[i - L] = name[i];
FOR(i, L, R) { par1[i - L] = max(par[i] - L, -1); }
centroid_decomposition_0_dfs(par1, name1, f);
}
}
/*
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1/3 CD のみ扱う
centroid_decomposition_1：長さ 2 以上のパス全体
*/
template <typename F>
void centroid_decomposition_1_dfs(vc<int>& par, vc<int> vs, F f) {
const int N = len(par);
assert(N > 1);
if (N == 2) { return; }
int c = -1;
vc<int> sz(N, 1);
FOR_R(i, N) {
if (sz[i] >= ceil<int>(N, 2)) {
c = i;
break;
}
sz[par[i]] += sz[i];
}
vc<int> color(N, -1);
int take = 0;
vc<int> ord(N, -1);
ord[c] = 0;
int p = 1;
FOR(v, 1, N) {
if (par[v] == c && take + sz[v] <= floor<int>(N - 1, 2)) {
color[v] = 0, ord[v] = p++, take += sz[v];
}
}
FOR(i, 1, N) {
if (color[par[i]] == 0) color[i] = 0, ord[i] = p++;
}
int n0 = p - 1;
for (int a = par[c]; a != -1; a = par[a]) { color[a] = 1, ord[a] = p++; }
FOR(i, N) {
if (i != c && color[i] == -1) color[i] = 1, ord[i] = p++;
}
assert(p == N);
int n1 = N - 1 - n0;
vc<int> par0(n0 + 1, -1), par1(n1 + 1, -1), par2(N, -1);
vc<int> V0(n0 + 1), V1(n1 + 1), V2(N);
FOR(v, N) {
int i = ord[v];
V2[i] = vs[v];
if (color[v] != 1) { V0[i] = vs[v]; }
if (color[v] != 0) { V1[max(i - n0, 0)] = vs[v]; }
}
FOR(v, 1, N) {
int a = ord[v], b = ord[par[v]];
if (a > b) swap(a, b);
par2[b] = a;
if (color[v] != 1 && color[par[v]] != 1) par0[b] = a;
if (color[v] != 0 && color[par[v]] != 0)
par1[max(b - n0, 0)] = max(a - n0, 0);
}
f(par2, V2, n0, n1);
centroid_decomposition_1_dfs(par0, V0, f);
centroid_decomposition_1_dfs(par1, V1, f);
}
/*
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1/3 CD のみ扱う
centroid_decomposition_1：長さ 2 以上のパス全体
*/
template <typename F>
void centroid_decomposition_2_dfs(vc<int>& par, vc<int>& vs, vc<int>& real,
F f) {
const int N = len(par);
assert(N > 1);
if (N == 2) {
if (real[0] && real[1]) {
vc<int> color = {0, 1};
f(par, vs, color);
}
return;
}
int c = -1;
vc<int> sz(N, 1);
FOR_R(i, N) {
if (sz[i] >= ceil<int>(N, 2)) {
c = i;
break;
}
sz[par[i]] += sz[i];
}
vc<int> color(N, -1);
int take = 0;
vc<int> ord(N, -1);
ord[c] = 0;
int p = 1;
FOR(v, 1, N) {
if (par[v] == c && take + sz[v] <= floor<int>(N - 1, 2)) {
color[v] = 0, ord[v] = p++, take += sz[v];
}
}
FOR(i, 1, N) {
if (color[par[i]] == 0) color[i] = 0, ord[i] = p++;
}
int n0 = p - 1;
for (int a = par[c]; a != -1; a = par[a]) { color[a] = 1, ord[a] = p++; }
FOR(i, N) {
if (i != c && color[i] == -1) color[i] = 1, ord[i] = p++;
}
assert(p == N);
int n1 = N - 1 - n0;
vc<int> par0(n0 + 1, -1), par1(n1 + 1, -1), par2(N, -1);
vc<int> V0(n0 + 1), V1(n1 + 1), V2(N);
vc<int> rea0(n0 + 1), rea1(n1 + 1), rea2(N);
FOR(v, N) {
int i = ord[v];
V2[i] = vs[v], rea2[i] = real[v];
if (color[v] != 1) { V0[i] = vs[v], rea0[i] = real[v]; }
if (color[v] != 0) {
V1[max(i - n0, 0)] = vs[v], rea1[max(i - n0, 0)] = real[v];
}
}
FOR(v, 1, N) {
int a = ord[v], b = ord[par[v]];
if (a > b) swap(a, b);
par2[b] = a;
if (color[v] != 1 && color[par[v]] != 1) par0[b] = a;
if (color[v] != 0 && color[par[v]] != 0)
par1[max(b - n0, 0)] = max(a - n0, 0);
}
if (real[c]) {
color.assign(N, -1);
color[0] = 0;
FOR(i, 1, N) color[i] = rea2[i] ? 1 : -1;
f(par2, V2, color);
rea0[0] = rea1[0] = rea2[0] = 0;
}
color.assign(N, -1);
FOR(i, 1, N) if (rea2[i]) color[i] = (i <= n0 ? 0 : 1);
f(par2, V2, color);
centroid_decomposition_2_dfs(par0, V0, rea0, f);
centroid_decomposition_2_dfs(par1, V1, rea1, f);
}
// f(par, V, color)
// V: label in original tree, dfs order
// color in [-1,0,1], color=-1: virtual
template <int MODE, typename GT, typename F>
void centroid_decomposition(GT& G, F f) {
const int N = G.N;
if (N == 1) return;
vc<int> V(N), par(N, -1);
int l = 0, r = 0;
V[r++] = 0;
while (l < r) {
int v = V[l++];
for (auto& e: G[v]) {
if (e.to != par[v]) V[r++] = e.to, par[e.to] = v;
}
}
assert(r == N);
vc<int> new_idx(N);
FOR(i, N) new_idx[V[i]] = i;
vc<int> tmp(N, -1);
FOR(i, 1, N) {
int j = par[i];
tmp[new_idx[i]] = new_idx[j];
}
swap(par, tmp);
static_assert(MODE == 0 || MODE == 1 || MODE == 2);
if constexpr (MODE == 0) { centroid_decomposition_0_dfs(par, V, f); }
elif constexpr(MODE == 1) { centroid_decomposition_1_dfs(par, V, f); }
else {
vc<int> real(N, 1);
centroid_decomposition_2_dfs(par, V, real, f);
}
}
#line 2 "/home/maspy/compro/library/alg/monoid/add.hpp"
template <typename X>
struct Monoid_Add {
using value_type = X;
static constexpr X op(const X &x, const X &y) noexcept { return x + y; }
static constexpr X inverse(const X &x) noexcept { return -x; }
static constexpr X power(const X &x, ll n) noexcept { return X(n) * x; }
static constexpr X unit() { return X(0); }
static constexpr bool commute = true;
};
#line 3 "/home/maspy/compro/library/ds/fenwicktree/fenwicktree.hpp"
template <typename Monoid>
struct FenwickTree {
using G = Monoid;
using E = typename G::value_type;
int n;
vector<E> dat;
E total;
FenwickTree() {}
FenwickTree(int n) { build(n); }
template <typename F>
FenwickTree(int n, F f) {
build(n, f);
}
FenwickTree(const vc<E>& v) { build(v); }
void build(int m) {
n = m;
dat.assign(m, G::unit());
total = G::unit();
}
void build(const vc<E>& v) {
build(len(v), [&](int i) -> E { return v[i]; });
}
template <typename F>
void build(int m, F f) {
n = m;
dat.clear();
dat.reserve(n);
total = G::unit();
FOR(i, n) { dat.eb(f(i)); }
for (int i = 1; i <= n; ++i) {
int j = i + (i & -i);
if (j <= n) dat[j - 1] = G::op(dat[i - 1], dat[j - 1]);
}
total = prefix_sum(m);
}
E prod_all() { return total; }
E sum_all() { return total; }
E sum(int k) { return prefix_sum(k); }
E prod(int k) { return prefix_prod(k); }
E prefix_sum(int k) { return prefix_prod(k); }
E prefix_prod(int k) {
chmin(k, n);
E ret = G::unit();
for (; k > 0; k -= k & -k) ret = G::op(ret, dat[k - 1]);
return ret;
}
E sum(int L, int R) { return prod(L, R); }
E prod(int L, int R) {
chmax(L, 0), chmin(R, n);
if (L == 0) return prefix_prod(R);
assert(0 <= L && L <= R && R <= n);
E pos = G::unit(), neg = G::unit();
while (L < R) { pos = G::op(pos, dat[R - 1]), R -= R & -R; }
while (R < L) { neg = G::op(neg, dat[L - 1]), L -= L & -L; }
return G::op(pos, G::inverse(neg));
}
void add(int k, E x) { multiply(k, x); }
void multiply(int k, E x) {
static_assert(G::commute);
total = G::op(total, x);
for (++k; k <= n; k += k & -k) dat[k - 1] = G::op(dat[k - 1], x);
}
template <class F>
int max_right(const F check) {
assert(check(G::unit()));
int i = 0;
E s = G::unit();
int k = 1;
while (2 * k <= n) k *= 2;
while (k) {
if (i + k - 1 < len(dat)) {
E t = G::op(s, dat[i + k - 1]);
if (check(t)) { i += k, s = t; }
}
k >>= 1;
}
return i;
}
// check(i, x)
template <class F>
int max_right_with_index(const F check) {
assert(check(0, G::unit()));
int i = 0;
E s = G::unit();
int k = 1;
while (2 * k <= n) k *= 2;
while (k) {
if (i + k - 1 < len(dat)) {
E t = G::op(s, dat[i + k - 1]);
if (check(i + k, t)) { i += k, s = t; }
}
k >>= 1;
}
return i;
}
int kth(E k) {
return max_right([&k](E x) -> bool { return x <= k; });
}
};
#line 2 "/home/maspy/compro/library/ds/offline_query/rectangle_add_point_sum.hpp"
template <typename AbelGroup, typename XY, bool SMALL_X = false>
struct Rectangle_Add_Point_Sum {
using G = typename AbelGroup::value_type;
vector<tuple<XY, XY, XY, G>> rect;
vector<tuple<int, XY, XY>> point;
Rectangle_Add_Point_Sum() {}
void add_query(XY x1, XY x2, XY y1, XY y2, G g) {
rect.eb(y1, x1, x2, g), rect.eb(y2, x2, x1, g);
}
void sum_query(XY x, XY y) { point.eb(len(point), x, y); }
vector<G> calc() {
int N = rect.size(), Q = point.size();
if (N == 0 || Q == 0) return vector<G>(Q, AbelGroup::unit());
// X 方向の座圧
int NX = 0;
if (!SMALL_X) {
sort(all(point),
[&](auto &x, auto &y) -> bool { return get<1>(x) < get<1>(y); });
vc<XY> keyX;
keyX.reserve(Q);
for (auto &&[i, a, b]: point) {
if (len(keyX) == 0 || keyX.back() != a) { keyX.eb(a); }
a = len(keyX) - 1;
}
for (auto &&[y, x1, x2, g]: rect) x1 = LB(keyX, x1), x2 = LB(keyX, x2);
NX = len(keyX);
}
if (SMALL_X) {
XY mx = infty<XY>;
for (auto &&[i, x, y]: point) chmin(mx, x);
for (auto &&[i, x, y]: point) x -= mx, chmax(NX, x + 1);
for (auto &&[y, x1, x2, g]: rect) {
x1 -= mx, x2 -= mx;
x1 = max(0, min<int>(x1, NX)), x2 = max(0, min<int>(x2, NX));
}
}
sort(all(point),
[&](auto &x, auto &y) -> bool { return get<2>(x) < get<2>(y); });
sort(all(rect),
[&](auto &x, auto &y) -> bool { return get<0>(x) < get<0>(y); });
FenwickTree<AbelGroup> bit(NX);
vc<G> res(Q, AbelGroup::unit());
int j = 0;
FOR(i, Q) {
auto [q, x, y] = point[i];
while (j < N && get<0>(rect[j]) <= y) {
auto [yy, x1, x2, g] = rect[j++];
bit.add(x1, g), bit.add(x2, AbelGroup::inverse(g));
}
res[q] = bit.sum(x + 1);
}
return res;
}
};
#line 2 "/home/maspy/compro/library/alg/monoid/add_pair.hpp"
template <typename E>
struct Monoid_Add_Pair {
using value_type = pair<E, E>;
using X = value_type;
static constexpr X op(const X &x, const X &y) {
return {x.fi + y.fi, x.se + y.se};
}
static constexpr X inverse(const X &x) { return {-x.fi, -x.se}; }
static constexpr X unit() { return {0, 0}; }
static constexpr bool commute = true;
};
#line 8 "main.cpp"
void solve() {
INT(N);
Graph<int, 0> G(N);
G.read_tree();
Tree<decltype(G)> tree(G);
vc<int> D(N);
FOR(i, 1, N) D[i] = tree.dist(i - 1, i);
ll base = SUM<ll>(D);
vi ANS(N, base);
/*
i -> i+1, 距離 d[i+1]
やること
i+1 からの距離が e かつ番号が i 以下の点に対して
max(0, d - 1 - e) を引くことができる
rectangle add rectangle sum
*/
FOR(i, 1, N) {
for (auto& e: G[i]) {
if (e.to < i) { ANS[e.to] -= max(0, D[i] - 1 - 1); }
}
}
auto f = [&](vc<int>& par, vc<int>& V, int n1, int n2) -> void {
int n = 1 + n1 + n2;
vc<int> dep(n);
FOR(i, 1, n) dep[i] += dep[par[i]] + 1;
auto F = [&](int L1, int R1, int L2, int R2) -> void {
// dep range, index range
Rectangle_Add_Point_Sum<Monoid_Add_Pair<ll>, int, true> X;
FOR(i, L1, R1) {
int v = V[i];
if (v == 0) continue;
int d = D[v];
if (d <= 2) continue;
// 距離が d-2 以下
int d1 = 1, d2 = d - 2 - dep[i];
if (d1 > d2) continue;
// 足すもの：(d - 1 - dep[i]) - x
X.add_query(d1, d2 + 1, 0, v, {d - 1 - dep[i], -1});
}
FOR(i, L2, R2) { X.sum_query(dep[i], V[i]); }
auto res = X.calc();
FOR(i, L2, R2) {
auto [a, b] = res[i - L2];
ANS[V[i]] -= a + b * dep[i];
}
};
F(1, 1 + n1, 1 + n1, 1 + n1 + n2);
F(1 + n1, 1 + n1 + n2, 1, 1 + n1);
};
centroid_decomposition<1, decltype(G)>(G, f);
for (auto& x: ANS) print(x);
}
signed main() {
int T = 1;
// INT(T);
FOR(T) solve();
return 0;
}