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test/1_mytest/QOJ5445.test.cpp
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- Last update: 2025-01-04 13:02:14+09:00
- Problem: https://judge.yosupo.jp/problem/aplusb
Depends on
ds/hashmap.hpp
- graph/base.hpp
- graph/tree.hpp
- graph/tree_dp/rerooting_dp.hpp
- linalg/xor/mat_inv.hpp
- linalg/xor/transpose.hpp
- linalg/xor/vector_space.hpp
- my_template.hpp
Code
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#include "my_template.hpp"
#include "graph/base.hpp"
#include "graph/tree.hpp"
#include "graph/tree_dp/rerooting_dp.hpp"
#include "linalg/xor/vector_space.hpp"
#include "linalg/xor/mat_inv.hpp"
#include "linalg/xor/transpose.hpp"
const int LOG = 64;
vc<u64> solve_QOJ_5445(int N, vc<int> par, vvc<u64> dat) {
using SP = Vector_Space<u64>;
Graph<bool, 0> G(N);
FOR(v, 1, N) { G.add(par[v - 1] - 1, v); }
G.build();
Tree<decltype(G)> tree(G);
vc<SP> dual(N);
FOR(v, N) {
SP x;
for (auto&& e: dat[v]) x.add_element(e);
dual[v] = x.orthogonal_space(LOG);
}
/*
木 dp の状態
・深さ d のときに dual space に a が追加される (d,a) というイベントの列
・高々 64
*/
using P = pair<int, u64>;
using Data = vc<P>;
Data unit = {};
auto fee = [&](Data x, Data y) -> Data {
// merge sort
Data z;
auto V = SP{};
auto add = [&](P& dat) -> void {
if (len(V) == LOG) return;
if (V.add_element(dat.se)) z.eb(dat.fi, V.dat.back());
};
int p = 0, q = 0;
while (p < len(x) || q < len(y)) {
if (len(V) == LOG) break;
if (p == len(x)) { add(y[q++]); }
elif (q == len(y)) { add(x[p++]); }
else {
if (x[p].fi < y[q].fi) {
add(x[p++]);
} else {
add(y[q++]);
}
}
}
return z;
};
auto fev = [&](Data x, int v) -> Data {
Data y;
for (auto&& a: dual[v].dat) y.eb(0, a);
auto V = dual[v];
for (auto&& [d, a]: x) {
if (len(V) == LOG) break;
if (V.add_element(a)) y.eb(d, V.dat.back());
}
return y;
};
// e は v に入る有向辺
auto fve = [&](Data x, auto e) -> Data {
for (auto&& [d, a]: x) ++d;
return x;
};
Rerooting_dp<decltype(tree), Data> dp(tree, fee, fev, fve, unit);
vc<u64> ANS(N);
FOR(v, N) {
auto event = dp[v];
// full space にしておく
vc<int> done(LOG);
for (auto&& [d, a]: event) done[topbit(a)] = 1;
FOR(i, LOG) if (!done[i]) event.eb(N, u64(1) << i);
assert(len(event) == LOG);
vc<u64> mat(LOG);
FOR(i, LOG) mat[i] = event[i].se;
mat = mat_inv<u64>(mat);
mat = transpose<u64>(LOG, LOG, mat);
FOR(j, LOG) { event[j].se = mat[j]; }
event.insert(event.begin(), {0, u64(0)});
SP X{};
FOR_R(i, 1, 1 + LOG) {
u64 x = event[i].se;
X.add_element(x);
int t1 = event[i - 1].fi, t2 = event[i].fi;
if (t1 < t2) {
u64 ans = X.get_max(0);
ANS[v] += ans * u64(t2 - t1);
}
}
}
return ANS;
}
void test_QOJ_5445() {
int N = 5;
vc<int> par = {1, 2, 2, 3};
vvc<u64> dat(N);
dat[0] = {83, 75, 58};
dat[1] = {125, 124, 58, 16};
dat[2] = {39, 125, 71, 112};
dat[3] = {69, 66, 5};
dat[4] = {48, 73, 69, 6};
auto ANS = solve_QOJ_5445(N, par, dat);
assert(ANS == vc<u64>({171, 125, 183, 142, 243}));
}
void solve() {
int a, b;
cin >> a >> b;
cout << a + b << "\n";
}
signed main() {
test_QOJ_5445();
solve();
return 0;
}#line 1 "test/1_mytest/QOJ5445.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#line 1 "my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
// https://codeforces.com/blog/entry/96344
#pragma GCC optimize("Ofast,unroll-loops")
// いまの CF だとこれ入れると動かない？
// #pragma GCC target("avx2,popcnt")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;
template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'010'000'000;
template <>
constexpr ll infty<ll> = 2'020'000'000'000'000'000;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000;
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 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_sgn(int x) { return (__builtin_parity(unsigned(x)) & 1 ? -1 : 1); }
int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(ll x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
int popcnt_sgn(u64 x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
// (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 kth_bit(int k) {
return T(1) << k;
}
template <typename T>
bool has_kth_bit(T x, int k) {
return x >> k & 1;
}
template <typename UINT>
struct all_bit {
struct iter {
UINT s;
iter(UINT s) : s(s) {}
int operator*() const { return lowbit(s); }
iter &operator++() {
s &= s - 1;
return *this;
}
bool operator!=(const iter) const { return s != 0; }
};
UINT s;
all_bit(UINT s) : s(s) {}
iter begin() const { return iter(s); }
iter end() const { return iter(0); }
};
template <typename UINT>
struct all_subset {
static_assert(is_unsigned<UINT>::value);
struct iter {
UINT s, t;
bool ed;
iter(UINT s) : s(s), t(s), ed(0) {}
int operator*() const { return s ^ t; }
iter &operator++() {
(t == 0 ? ed = 1 : t = (t - 1) & s);
return *this;
}
bool operator!=(const iter) const { return !ed; }
};
UINT s;
all_subset(UINT s) : s(s) {}
iter begin() const { return iter(s); }
iter end() const { return iter(0); }
};
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;
}
template <typename T, typename... Vectors>
void concat(vc<T> &first, const Vectors &... others) {
vc<T> &res = first;
(res.insert(res.end(), others.begin(), others.end()), ...);
}
#endif
#line 3 "test/1_mytest/QOJ5445.test.cpp"
#line 2 "ds/hashmap.hpp"
// u64 -> Val
template <typename Val>
struct HashMap {
// n は入れたいものの個数で ok
HashMap(u32 n = 0) { build(n); }
void build(u32 n) {
u32 k = 8;
while (k < n * 2) k *= 2;
cap = k / 2, mask = k - 1;
key.resize(k), val.resize(k), used.assign(k, 0);
}
// size を保ったまま. size=0 にするときは build すること.
void clear() {
used.assign(len(used), 0);
cap = (mask + 1) / 2;
}
int size() { return len(used) / 2 - cap; }
int index(const u64& k) {
int i = 0;
for (i = hash(k); used[i] && key[i] != k; i = (i + 1) & mask) {}
return i;
}
Val& operator[](const u64& k) {
if (cap == 0) extend();
int i = index(k);
if (!used[i]) { used[i] = 1, key[i] = k, val[i] = Val{}, --cap; }
return val[i];
}
Val get(const u64& k, Val default_value) {
int i = index(k);
return (used[i] ? val[i] : default_value);
}
bool count(const u64& k) {
int i = index(k);
return used[i] && key[i] == k;
}
// f(key, val)
template <typename F>
void enumerate_all(F f) {
FOR(i, len(used)) if (used[i]) f(key[i], val[i]);
}
private:
u32 cap, mask;
vc<u64> key;
vc<Val> val;
vc<bool> used;
u64 hash(u64 x) {
static const u64 FIXED_RANDOM = std::chrono::steady_clock::now().time_since_epoch().count();
x += FIXED_RANDOM;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return (x ^ (x >> 31)) & mask;
}
void extend() {
vc<pair<u64, Val>> dat;
dat.reserve(len(used) / 2 - cap);
FOR(i, len(used)) {
if (used[i]) dat.eb(key[i], val[i]);
}
build(2 * len(dat));
for (auto& [a, b]: dat) (*this)[a] = b;
}
};
#line 3 "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}
// sum(deg(v)) の計算量になっていて、
// 新しいグラフの n+m より大きい可能性があるので注意
Graph<T, directed> rearrange(vc<int> V, bool keep_eid = 0) {
if (len(new_idx) != N) new_idx.assign(N, -1);
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 (len(used_e) <= e.id) used_e.resize(e.id + 1);
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;
}
Graph<T, true> to_directed_tree(int root = -1) {
if (root == -1) root = 0;
assert(!is_directed && prepared && M == N - 1);
Graph<T, true> G1(N);
vc<int> par(N, -1);
auto dfs = [&](auto& dfs, int v) -> void {
for (auto& e: (*this)[v]) {
if (e.to == par[v]) continue;
par[e.to] = v, dfs(dfs, e.to);
}
};
dfs(dfs, root);
for (auto& e: edges) {
int a = e.frm, b = e.to;
if (par[a] == b) swap(a, b);
assert(par[b] == a);
G1.add(a, b, e.cost);
}
G1.build();
return G1;
}
HashMap<int> MP_FOR_EID;
int get_eid(u64 a, u64 b) {
if (len(MP_FOR_EID) == 0) {
MP_FOR_EID.build(N - 1);
for (auto& e: edges) {
u64 a = e.frm, b = e.to;
u64 k = to_eid_key(a, b);
MP_FOR_EID[k] = e.id;
}
}
return MP_FOR_EID.get(to_eid_key(a, b), -1);
}
u64 to_eid_key(u64 a, u64 b) {
if (!directed && a > b) swap(a, b);
return N * a + b;
}
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 2 "graph/tree.hpp"
#line 4 "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 get_eid(int u, int v) {
if (parent[u] != v) swap(u, v);
assert(parent[u] == v);
return VtoE[u];
}
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;
}
}
int meet(int a, int b, int c) { return LCA(a, b) ^ LCA(a, c) ^ LCA(b, c); }
int lca(int u, int v) { return LCA(u, v); }
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<int> collect_light(int v) {
vc<int> res;
bool skip = true;
for (auto &&e: G[v])
if (e.to != parent[v]) {
if (!skip) res.eb(e.to);
skip = false;
}
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;
}
// 辺の列の情報 (frm,to,str)
// str = "heavy_up", "heavy_down", "light_up", "light_down"
vc<tuple<int, int, string>> get_path_decomposition_detail(int u, int v) {
vc<tuple<int, int, string>> up, down;
while (1) {
if (head[u] == head[v]) break;
if (LID[u] < LID[v]) {
if (v != head[v]) down.eb(head[v], v, "heavy_down"), v = head[v];
down.eb(parent[v], v, "light_down"), v = parent[v];
} else {
if (u != head[u]) up.eb(u, head[u], "heavy_up"), u = head[u];
up.eb(u, parent[u], "light_up"), u = parent[u];
}
}
if (LID[u] < LID[v]) down.eb(u, v, "heavy_down");
elif (LID[v] < LID[u]) up.eb(u, v, "heavy_up");
reverse(all(down));
concat(up, 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;
}
// path [a,b] と [c,d] の交わり. 空ならば {-1,-1}.
// https://codeforces.com/problemset/problem/500/G
pair<int, int> path_intersection(int a, int b, int c, int d) {
int ab = lca(a, b), ac = lca(a, c), ad = lca(a, d);
int bc = lca(b, c), bd = lca(b, d), cd = lca(c, d);
int x = ab ^ ac ^ bc, y = ab ^ ad ^ bd; // meet(a,b,c), meet(a,b,d)
if (x != y) return {x, y};
int z = ac ^ ad ^ cd;
if (x != z) x = -1;
return {x, x};
}
// uv path 上で check(v) を満たす最後の v
// なければ （つまり check(v) が ng ）-1
template <class F>
int max_path(F check, int u, int v) {
if (!check(u)) return -1;
auto pd = get_path_decomposition(u, v, false);
for (auto [a, b]: pd) {
if (!check(V[a])) return u;
if (check(V[b])) {
u = V[b];
continue;
}
int c = binary_search([&](int c) -> bool { return check(V[c]); }, a, b, 0);
return V[c];
}
return u;
}
};
#line 4 "graph/tree_dp/rerooting_dp.hpp"
template <typename TREE, typename Data>
struct Rerooting_dp {
static_assert(!TREE::Graph_type::is_directed);
TREE& tree;
vc<Data> dp_1; // 辺 pv に対して、部分木 v
vc<Data> dp_2; // 辺 pv に対して、部分木 p
vc<Data> dp; // full tree
template <typename F1, typename F2, typename F3>
Rerooting_dp(TREE& tree, F1 f_ee, F2 f_ev, F3 f_ve, const Data unit) : tree(tree) {
build(f_ee, f_ev, f_ve, unit);
}
// v を根としたときの full tree
Data operator[](int v) { return dp[v]; }
// root を根としたときの部分木 v
Data get(int v, int root) {
if (root == v) return dp[v];
if (!tree.in_subtree(root, v)) { return dp_1[v]; }
int w = tree.jump(v, root, 1);
return dp_2[w];
}
template <typename F1, typename F2, typename F3>
void build(F1 f_ee, F2 f_ev, F3 f_ve, const Data unit) {
int N = tree.N;
// dp1: subtree
dp_1.assign(N, unit);
FOR_R(i, N) {
int v = tree.V[i];
for (auto&& e: tree.G[v]) {
if (e.to == tree.parent[v]) continue;
dp_1[v] = f_ee(dp_1[v], f_ve(dp_1[e.to], e));
}
dp_1[v] = f_ev(dp_1[v], v);
}
// dp2[v]: subtree of p, rooted at v
dp_2.assign(N, unit);
// dp[v]: fulltree, rooted at v
dp.assign(N, unit);
FOR(i, N) {
int p = tree.V[i];
vc<int> ch;
vc<Data> ch_data;
Data x = unit;
for (auto&& e: tree.G[p]) {
if (e.to == tree.parent[p]) {
x = f_ve(dp_2[p], e);
} else {
ch.eb(e.to);
ch_data.eb(f_ve(dp_1[e.to], e));
}
}
int n = len(ch);
if (!n) {
dp[p] = f_ev(x, p);
continue;
}
vc<Data> prod_left(n, x);
FOR(i, n - 1) prod_left[i + 1] = f_ee(prod_left[i], ch_data[i]);
Data prod_right = unit;
FOR_R(i, n) {
dp_2[ch[i]] = f_ev(f_ee(prod_left[i], prod_right), p);
prod_right = f_ee(prod_right, ch_data[i]);
}
dp[p] = f_ev(f_ee(x, prod_right), p);
}
}
};
#line 7 "test/1_mytest/QOJ5445.test.cpp"
#line 2 "linalg/xor/transpose.hpp"
// n x m 行列の transpose。O((n+m)log(n+m)) 時間。
// https://github.com/dsnet/matrix-transpose
template <typename UINT>
vc<UINT> transpose(int n, int m, vc<UINT>& A, bool keep_A = 1) {
assert(max(n, m) <= numeric_limits<UINT>::digits);
assert(len(A) == n);
vc<UINT> tmp;
if (keep_A) tmp = A;
int LOG = 0;
while ((1 << LOG) < max(n, m)) ++LOG;
A.resize(1 << LOG);
int width = 1 << LOG;
UINT mask = 1;
FOR(i, LOG) mask = mask | (mask << (1 << i));
FOR(t, LOG) {
width >>= 1;
mask = mask ^ (mask >> width);
FOR(i, 1 << t) {
FOR(j, width) {
UINT* x = &A[width * (2 * i + 0) + j];
UINT* y = &A[width * (2 * i + 1) + j];
*x = ((*y << width) & mask) ^ *x;
*y = ((*x & mask) >> width) ^ *y;
*x = ((*y << width) & mask) ^ *x;
}
}
}
A.resize(m);
if (!keep_A) return A;
swap(A, tmp);
return tmp;
}
#line 2 "linalg/xor/vector_space.hpp"
template <typename UINT>
struct Vector_Space {
#define SP Vector_Space
vc<UINT> dat;
Vector_Space() {}
Vector_Space(vc<UINT> dat, bool is_reduced = false) : dat(dat) {
if (!is_reduced) reduce();
}
int size() { return dat.size(); }
int dim() { return dat.size(); }
bool add_element(UINT v) {
for (auto&& e: dat) {
if (e == 0 || v == 0) break;
chmin(v, v ^ e);
}
if (v) {
dat.eb(v);
return true;
}
return false;
}
bool contain(UINT v) {
for (auto&& w: dat) {
if (v == 0) break;
chmin(v, v ^ w);
}
return v == 0;
}
UINT get_max(UINT xor_val = 0) {
UINT res = xor_val;
for (auto&& x: dat) chmax(res, res ^ x);
return res;
}
UINT get_min(UINT xor_val) {
UINT res = xor_val;
for (auto&& x: dat) chmin(res, res ^ x);
return res;
}
static SP merge(SP x, SP y) {
if (len(x) < len(y)) swap(x, y);
for (auto v: y.dat) { x.add_element(v); }
return x;
}
static SP intersection(SP& x, SP& y) {
// とりあえず
static_assert(is_same_v<UINT, u32>);
vc<u64> xx;
for (auto& v: x.dat) xx.eb(v | static_cast<u64>(v) << 32);
Vector_Space<u64> z(xx, true);
for (auto& v: y.dat) z.add_element(static_cast<u64>(v) << 32);
vc<u32> xy;
for (auto& v: z.dat) {
if (v <= u32(-1)) xy.eb(v);
}
return SP(xy, true);
}
SP orthogonal_space(int max_dim) {
normalize();
int m = max_dim;
// pivot[k] == k となるように行の順番を変える
vc<u64> tmp(m);
FOR(i, len(dat)) tmp[topbit(dat[i])] = dat[i];
tmp = transpose(m, m, tmp, 0);
SP res;
FOR(j, m) {
if (tmp[j] >> j & 1) continue;
res.add_element(tmp[j] | UINT(1) << j);
}
return res;
}
void normalize(bool dec = true) {
int n = len(dat);
// 三角化
FOR(j, n) FOR(i, j) chmin(dat[i], dat[i] ^ dat[j]);
sort(all(dat));
if (dec) reverse(all(dat));
}
private:
void reduce() {
SP y;
for (auto&& e: dat) y.add_element(e);
(*this) = y;
}
#undef SP
};
#line 1 "linalg/xor/mat_inv.hpp"
// 行ベクトルを整数型で表現
template <typename UINT>
vc<UINT> mat_inv(vc<UINT> A) {
const int N = len(A);
vc<UINT> B(N);
FOR(i, N) B[i] = u64(1) << i;
FOR(i, N) FOR(j, N) if (j != i) {
if (chmin(A[i], A[i] ^ A[j])) B[i] ^= B[j];
}
vc<UINT> res(N);
FOR(i, N) res[topbit(A[i])] = B[i];
return res;
}
#line 11 "test/1_mytest/QOJ5445.test.cpp"
const int LOG = 64;
vc<u64> solve_QOJ_5445(int N, vc<int> par, vvc<u64> dat) {
using SP = Vector_Space<u64>;
Graph<bool, 0> G(N);
FOR(v, 1, N) { G.add(par[v - 1] - 1, v); }
G.build();
Tree<decltype(G)> tree(G);
vc<SP> dual(N);
FOR(v, N) {
SP x;
for (auto&& e: dat[v]) x.add_element(e);
dual[v] = x.orthogonal_space(LOG);
}
/*
木 dp の状態
・深さ d のときに dual space に a が追加される (d,a) というイベントの列
・高々 64
*/
using P = pair<int, u64>;
using Data = vc<P>;
Data unit = {};
auto fee = [&](Data x, Data y) -> Data {
// merge sort
Data z;
auto V = SP{};
auto add = [&](P& dat) -> void {
if (len(V) == LOG) return;
if (V.add_element(dat.se)) z.eb(dat.fi, V.dat.back());
};
int p = 0, q = 0;
while (p < len(x) || q < len(y)) {
if (len(V) == LOG) break;
if (p == len(x)) { add(y[q++]); }
elif (q == len(y)) { add(x[p++]); }
else {
if (x[p].fi < y[q].fi) {
add(x[p++]);
} else {
add(y[q++]);
}
}
}
return z;
};
auto fev = [&](Data x, int v) -> Data {
Data y;
for (auto&& a: dual[v].dat) y.eb(0, a);
auto V = dual[v];
for (auto&& [d, a]: x) {
if (len(V) == LOG) break;
if (V.add_element(a)) y.eb(d, V.dat.back());
}
return y;
};
// e は v に入る有向辺
auto fve = [&](Data x, auto e) -> Data {
for (auto&& [d, a]: x) ++d;
return x;
};
Rerooting_dp<decltype(tree), Data> dp(tree, fee, fev, fve, unit);
vc<u64> ANS(N);
FOR(v, N) {
auto event = dp[v];
// full space にしておく
vc<int> done(LOG);
for (auto&& [d, a]: event) done[topbit(a)] = 1;
FOR(i, LOG) if (!done[i]) event.eb(N, u64(1) << i);
assert(len(event) == LOG);
vc<u64> mat(LOG);
FOR(i, LOG) mat[i] = event[i].se;
mat = mat_inv<u64>(mat);
mat = transpose<u64>(LOG, LOG, mat);
FOR(j, LOG) { event[j].se = mat[j]; }
event.insert(event.begin(), {0, u64(0)});
SP X{};
FOR_R(i, 1, 1 + LOG) {
u64 x = event[i].se;
X.add_element(x);
int t1 = event[i - 1].fi, t2 = event[i].fi;
if (t1 < t2) {
u64 ans = X.get_max(0);
ANS[v] += ans * u64(t2 - t1);
}
}
}
return ANS;
}
void test_QOJ_5445() {
int N = 5;
vc<int> par = {1, 2, 2, 3};
vvc<u64> dat(N);
dat[0] = {83, 75, 58};
dat[1] = {125, 124, 58, 16};
dat[2] = {39, 125, 71, 112};
dat[3] = {69, 66, 5};
dat[4] = {48, 73, 69, 6};
auto ANS = solve_QOJ_5445(N, par, dat);
assert(ANS == vc<u64>({171, 125, 183, 142, 243}));
}
void solve() {
int a, b;
cin >> a >> b;
cout << a + b << "\n";
}
signed main() {
test_QOJ_5445();
solve();
return 0;
}