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test/1_mytest/rolling_hash_on_tree.test.cpp
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- Last update: 2025-07-03 18:22:07+09:00
- Problem: https://judge.yosupo.jp/problem/aplusb
Depends on
- ds/hashmap.hpp
- ds/unionfind/unionfind.hpp
- graph/base.hpp
- graph/ds/rolling_hash_on_tree.hpp
- graph/tree.hpp
- mod/modint61.hpp
- my_template.hpp
- random/base.hpp
- random/random_graph.hpp
- random/shuffle.hpp
Code
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#include "my_template.hpp"
#include "graph/ds/rolling_hash_on_tree.hpp"
#include "random/random_graph.hpp"
void test_edge() {
ll N = RNG(1, 20);
auto edges = random_tree(N);
Graph<int, 0> G(N);
for (auto& [a, b]: edges) {
int x = RNG(0, 3);
G.add(a, b, x);
}
G.build();
Tree<decltype(G)> tree(G);
using mint = modint61;
mint base = RNG_64();
Rolling_Hash_On_Tree<decltype(tree), true> RH(
tree, [&](int i) -> int { return G.edges[i].cost; }, base);
vvv(int, dat, N, N, 0);
FOR(a, N) FOR(b, N) {
vc<int> P = tree.restore_path(a, b);
vc<int> S;
FOR(i, len(P) - 1) {
int eid = tree.get_eid(P[i], P[i + 1]);
S.eb(G.edges[eid].cost);
}
dat[a][b] = S;
}
FOR(a, N) FOR(b, N) {
mint h = 0;
for (auto& x: dat[a][b]) { h = h * base + x; }
assert(h == RH.get(a, b));
}
FOR(a, N) FOR(b, N) FOR(c, N) FOR(d, N) {
vc<int> A = dat[a][b], B = dat[c][d];
int lcp = 0;
while (lcp < len(A) && lcp < len(B) && A[lcp] == B[lcp]) ++lcp;
auto [k, ch] = RH.lcp_and_comp(a, b, c, d);
assert(k == lcp);
if (ch == '<') assert(A < B);
if (ch == '=') assert(A == B);
if (ch == '>') assert(A > B);
}
}
void test_vertex() {
ll N = RNG(1, 20);
auto edges = random_tree(N);
Graph<int, 0> G(N);
for (auto& [a, b]: edges) { G.add(a, b); }
vc<int> A(N);
FOR(i, N) A[i] = RNG(0, 3);
G.build();
Tree<decltype(G)> tree(G);
using mint = modint61;
mint base = RNG_64();
Rolling_Hash_On_Tree<decltype(tree), false> RH(
tree, [&](int i) -> int { return A[i]; }, base);
vvv(int, dat, N, N, 0);
FOR(a, N) FOR(b, N) {
vc<int> P = tree.restore_path(a, b);
vc<int> S;
for (auto& v: P) S.eb(A[v]);
dat[a][b] = S;
}
FOR(a, N) FOR(b, N) {
mint h = 0;
for (auto& x: dat[a][b]) { h = h * base + x; }
assert(h == RH.get(a, b));
}
FOR(a, N) FOR(b, N) FOR(c, N) FOR(d, N) {
vc<int> A = dat[a][b], B = dat[c][d];
int lcp = 0;
while (lcp < len(A) && lcp < len(B) && A[lcp] == B[lcp]) ++lcp;
auto [k, ch] = RH.lcp_and_comp(a, b, c, d);
assert(k == lcp);
if (ch == '<') assert(A < B);
if (ch == '=') assert(A == B);
if (ch == '>') assert(A > B);
}
}
void solve() {
int a, b;
cin >> a >> b;
cout << a + b << "\n";
}
signed main() {
FOR(300) test_edge();
FOR(300) test_vertex();
solve();
}#line 1 "test/1_mytest/rolling_hash_on_tree.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
// https://codeforces.com/blog/entry/126772?#comment-1154880
#include <bits/allocator.h>
#pragma GCC optimize("Ofast,unroll-loops")
#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_max = priority_queue<T>;
template <class T>
using pq_min = 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 U &A) {
return std::accumulate(A.begin(), A.end(), T{});
}
#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_min<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(pq_max<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 4 "test/1_mytest/rolling_hash_on_tree.test.cpp"
#line 2 "random/base.hpp"
u64 RNG_64() {
static u64 x_ = u64(chrono::duration_cast<chrono::nanoseconds>(chrono::high_resolution_clock::now().time_since_epoch()).count()) * 10150724397891781847ULL;
x_ ^= x_ << 7;
return x_ ^= x_ >> 9;
}
u64 RNG(u64 lim) { return RNG_64() % lim; }
ll RNG(ll l, ll r) { return l + RNG_64() % (r - l); }
#line 2 "graph/tree.hpp"
#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() {
#ifdef LOCAL
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
}
#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 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);
}
vc<int> memo_tail;
int tail(int v) {
if (memo_tail.empty()) {
memo_tail.assign(N, -1);
FOR_R(i, N) {
int v = V[i];
int w = heavy_child(v);
memo_tail[v] = (w == -1 ? v : memo_tail[w]);
}
}
return memo_tail[v];
}
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_subtree(int v) { return {V.begin() + LID[v], V.begin() + RID[v]}; }
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 2 "mod/modint61.hpp"
struct modint61 {
static constexpr u64 mod = (1ULL << 61) - 1;
u64 val;
constexpr modint61() : val(0ULL) {}
constexpr modint61(u32 x) : val(x) {}
constexpr modint61(u64 x) : val(x % mod) {}
constexpr modint61(int x) : val((x < 0) ? (x + static_cast<ll>(mod)) : x) {}
constexpr modint61(ll x) : val(((x %= static_cast<ll>(mod)) < 0) ? (x + static_cast<ll>(mod)) : x) {}
static constexpr u64 get_mod() { return mod; }
modint61 &operator+=(const modint61 &a) {
val = ((val += a.val) >= mod) ? (val - mod) : val;
return *this;
}
modint61 &operator-=(const modint61 &a) {
val = ((val -= a.val) >= mod) ? (val + mod) : val;
return *this;
}
modint61 &operator*=(const modint61 &a) {
const unsigned __int128 y = static_cast<unsigned __int128>(val) * a.val;
val = (y >> 61) + (y & mod);
val = (val >= mod) ? (val - mod) : val;
return *this;
}
modint61 operator-() const { return modint61(val ? mod - val : u64(0)); }
modint61 &operator/=(const modint61 &a) { return (*this *= a.inverse()); }
modint61 operator+(const modint61 &p) const { return modint61(*this) += p; }
modint61 operator-(const modint61 &p) const { return modint61(*this) -= p; }
modint61 operator*(const modint61 &p) const { return modint61(*this) *= p; }
modint61 operator/(const modint61 &p) const { return modint61(*this) /= p; }
bool operator<(const modint61 &other) const { return val < other.val; }
bool operator==(const modint61 &p) const { return val == p.val; }
bool operator!=(const modint61 &p) const { return val != p.val; }
modint61 inverse() const {
ll a = val, b = mod, u = 1, v = 0, t;
while (b > 0) {
t = a / b;
swap(a -= t * b, b), swap(u -= t * v, v);
}
return modint61(u);
}
modint61 pow(ll n) const {
assert(n >= 0);
modint61 ret(1), mul(val);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul, n >>= 1;
}
return ret;
}
};
#ifdef FASTIO
void rd(modint61 &x) {
fastio::rd(x.val);
assert(0 <= x.val && x.val < modint61::mod);
}
void wt(modint61 x) { fastio::wt(x.val); }
#endif
#line 4 "graph/ds/rolling_hash_on_tree.hpp"
// 木の辺に文字がちょうどひとつ書いてある (static)
template <typename TREE, bool EDGE>
struct Rolling_Hash_On_Tree {
using mint = modint61;
TREE& tree;
int N;
mint base;
// edge に文字があると思って
// dp1: [root,v]
// dp2: [v,root]
vc<int> dat;
vc<mint> dp1, dp2;
vc<mint> pow, ipow;
template <typename F>
Rolling_Hash_On_Tree(TREE& tree, F f, mint base_ = 0)
: tree(tree), N(tree.N), base(base_) {
if (base == mint(0)) base = RNG(mint::get_mod());
build(f);
}
template <typename F>
void build(F f) {
dat.resize(N);
if constexpr (EDGE) {
FOR(i, N - 1) { dat[tree.e_to_v(i)] = f(i); }
} else {
FOR(i, N) { dat[i] = f(i); }
}
pow.resize(N + 1), ipow.resize(N + 1);
pow[0] = 1, pow[1] = base;
ipow[0] = 1, ipow[1] = base.inverse();
FOR(i, 2, N + 1) pow[i] = pow[i - 1] * pow[1];
FOR(i, 2, N + 1) ipow[i] = ipow[i - 1] * ipow[1];
int root = tree.V[0];
dp1.resize(N), dp2.resize(N);
dp1[root] = dp2[root] = dat[0];
FOR(i, 1, N) {
int v = tree.V[i];
int d = tree.depth[v], p = tree.parent[v];
dp1[v] = base * dp1[p] + dat[v];
dp2[v] = dp2[p] + pow[d] * dat[v];
}
}
mint get(int a, int b) {
int c = tree.lca(a, b);
mint x1 = get_du(a, c), x2 = get_ud(c, b);
int n2 = tree.depth[b] - tree.depth[c];
if constexpr (!EDGE) { x1 = x1 * base + dat[c]; }
return x1 * pow[n2] + x2;
}
int lcp(int s1, int t1, int s2, int t2) {
return lcp_and_comp(s1, t1, s2, t2).fi;
}
// <=>
char comp(int s1, int t1, int s2, int t2) {
return lcp_and_comp(s1, t1, s2, t2).se;
}
pair<int, char> lcp_and_comp(int s1, int t1, int s2, int t2) {
int lcp = 0;
// heavy path の頂点列
auto path1 = tree.get_path_decomposition(s1, t1, EDGE);
auto path2 = tree.get_path_decomposition(s2, t2, EDGE);
reverse(all(path1));
reverse(all(path2));
while (len(path1) && len(path2)) {
int a, b, c, d;
tie(a, b) = POP(path1), tie(c, d) = POP(path2);
ll n1 = abs(a - b) + 1, n2 = abs(c - d) + 1;
ll n = min(n1, n2);
if (n < n1) {
if (a <= b) { path1.eb(a + n, b), b = a + n - 1; }
if (a > b) { path1.eb(a - n, b), b = a - n + 1; }
}
if (n < n2) {
if (c <= d) { path2.eb(c + n, d), d = c + n - 1; }
if (c > d) { path2.eb(c - n, d), d = c - n + 1; }
}
mint x1 = from_hld_pair(a, b), x2 = from_hld_pair(c, d);
if (x1 == x2) {
lcp += n;
continue;
}
auto check = [&](ll n) -> bool {
if (n == 0) return 1;
mint x1 = (a <= b ? from_hld_pair(a, a + n - 1)
: from_hld_pair(a, a - n + 1));
mint x2 = (c <= d ? from_hld_pair(c, c + n - 1)
: from_hld_pair(c, c - n + 1));
return x1 == x2;
};
ll k = binary_search(check, 0, n);
lcp += k;
a = (a <= b ? a + k : a - k);
c = (c <= d ? c + k : c - k);
a = tree.V[a], c = tree.V[c];
if (dat[a] < dat[c]) return {lcp, '<'};
if (dat[a] == dat[c]) return {lcp, '='};
if (dat[a] > dat[c]) return {lcp, '>'};
}
if (!path1.empty()) return {lcp, '>'};
if (!path2.empty()) return {lcp, '<'};
return {lcp, '='};
}
private:
mint get_ud(int a, int b) {
return (a == -1 ? dp1[b]
: dp1[b] - dp1[a] * pow[tree.depth[b] - tree.depth[a]]);
}
mint get_du(int a, int b) {
return (b == -1 ? dp2[a] : (dp2[a] - dp2[b]) * ipow[tree.depth[b] + 1]);
}
mint from_hld_pair(int a, int b) {
if (a <= b) { return get_ud(tree.parent[tree.V[a]], tree.V[b]); }
return get_du(tree.V[a], tree.parent[tree.V[b]]);
}
};
#line 2 "random/shuffle.hpp"
template <typename T>
void shuffle(vc<T>& A) {
FOR(i, len(A)) {
int j = RNG(0, i + 1);
if (i != j) swap(A[i], A[j]);
}
}
#line 2 "ds/unionfind/unionfind.hpp"
struct UnionFind {
int n, n_comp;
vc<int> dat; // par or (-size)
UnionFind(int n = 0) { build(n); }
void build(int m) {
n = m, n_comp = m;
dat.assign(n, -1);
}
void reset() { build(n); }
int operator[](int x) {
while (dat[x] >= 0) {
int pp = dat[dat[x]];
if (pp < 0) { return dat[x]; }
x = dat[x] = pp;
}
return x;
}
ll size(int x) {
x = (*this)[x];
return -dat[x];
}
bool merge(int x, int y) {
x = (*this)[x], y = (*this)[y];
if (x == y) return false;
if (-dat[x] < -dat[y]) swap(x, y);
dat[x] += dat[y], dat[y] = x, n_comp--;
return true;
}
vc<int> get_all() {
vc<int> A(n);
FOR(i, n) A[i] = (*this)[i];
return A;
}
};
#line 5 "random/random_graph.hpp"
void random_relabel(int N, vc<pair<int, int>>& G) {
shuffle(G);
vc<int> A(N);
FOR(i, N) A[i] = i;
shuffle(A);
for (auto& [a, b]: G) a = A[a], b = A[b];
}
template <int DIRECTED>
vc<pair<int, int>> random_graph(int n, bool simple) {
vc<pair<int, int>> G, cand;
FOR(a, n) FOR(b, n) {
if (simple && a == b) continue;
if (!DIRECTED && a > b) continue;
cand.eb(a, b);
}
int m = RNG(0, len(cand) + 1);
set<int> ss;
FOR(m) {
while (1) {
int i = RNG(0, len(cand));
if (simple && ss.count(i)) continue;
ss.insert(i);
auto [a, b] = cand[i];
G.eb(a, b);
break;
}
}
random_relabel(n, G);
return G;
}
vc<pair<int, int>> random_tree(int n) {
vc<pair<int, int>> G;
FOR(i, 1, n) { G.eb(RNG(0, i), i); }
random_relabel(n, G);
return G;
}
// EDGE = true: 各辺が唯一のサイクル（関節点でサイクルまたは辺）
// EDGE = false： 各頂点が唯一のサイクル（橋でサイクルまたは辺）
vc<pair<int, int>> random_cactus(int N, bool EDGE) {
if (!EDGE) {
// n 頂点を 1 または 3 以上に分割
vvc<int> A;
int n = RNG(1, N + 1);
vc<int> S(n, 1);
int rest = N - n;
while (rest > 0) {
int k = RNG(0, n);
if (S[k] == 1) {
if (rest == 1) {
S.eb(1), rest = 0;
} else {
S[k] += 2, rest -= 2;
}
} else {
S[k]++, rest--;
}
}
n = len(S);
int p = 0;
FOR(i, n) {
vc<int> C;
FOR(v, p, p + S[i]) C.eb(v);
A.eb(C);
p += S[i];
}
int m = len(A);
auto H = random_tree(m);
vc<pair<int, int>> G;
FOR(i, m) {
vc<int>& V = A[i];
if (len(V) == 1) continue;
FOR(k, len(V)) { G.eb(V[k], V[(1 + k) % len(V)]); }
}
for (auto& [c1, c2]: H) {
int a = A[c1][RNG(0, len(A[c1]))];
int b = A[c2][RNG(0, len(A[c2]))];
G.eb(a, b);
}
random_relabel(N, G);
return G;
}
assert(EDGE);
if (N == 1) return {};
int n = RNG(1, N);
vc<int> S(n, 2);
int rest = N - 1 - n;
while (rest > 0) {
int k = RNG(0, n);
S[k]++, --rest;
}
vvc<int> A;
int p = 0;
FOR(i, n) {
vc<int> C;
FOR(v, p, p + S[i]) C.eb(v);
A.eb(C);
p += S[i];
}
assert(p == N + n - 1);
UnionFind uf(p);
auto H = random_tree(n);
for (auto& [c1, c2]: H) {
int a = A[c1][RNG(0, len(A[c1]))];
int b = A[c2][RNG(0, len(A[c2]))];
uf.merge(a, b);
}
vc<int> new_idx(p);
int x = 0;
FOR(i, p) if (uf[i] == i) new_idx[i] = x++;
assert(x == N);
FOR(i, p) new_idx[i] = new_idx[uf[i]];
vc<pair<int, int>> G;
FOR(i, n) {
vc<int>& V = A[i];
for (auto& v: V) v = new_idx[v];
if (len(V) == 2) {
G.eb(V[0], V[1]);
} else {
FOR(k, len(V)) { G.eb(V[k], V[(1 + k) % len(V)]); }
}
}
random_relabel(N, G);
return G;
}
// |child| = 0 or 2 or (1 if can1), ラベルはトポロジカル
// return: par
vc<int> random_binary_tree(int N, bool can_1) {
if (can_1) {
vc<int> S;
S.eb(0), S.eb(0);
vc<int> par(N, -1);
FOR(v, 1, N) {
int k = RNG(0, len(S));
swap(S[k], S.back());
par[v] = POP(S);
S.eb(v), S.eb(v);
}
return par;
}
// 0 or 2
assert(N % 2 == 1);
vc<int> par(N, -1);
vc<int> S;
FOR(v, N / 2, N) S.eb(v);
int nxt = N / 2 - 1;
while (len(S) >= 2) {
shuffle(S);
int a = POP(S), b = POP(S);
par[a] = par[b] = nxt;
S.eb(nxt), --nxt;
}
return par;
}
#line 7 "test/1_mytest/rolling_hash_on_tree.test.cpp"
void test_edge() {
ll N = RNG(1, 20);
auto edges = random_tree(N);
Graph<int, 0> G(N);
for (auto& [a, b]: edges) {
int x = RNG(0, 3);
G.add(a, b, x);
}
G.build();
Tree<decltype(G)> tree(G);
using mint = modint61;
mint base = RNG_64();
Rolling_Hash_On_Tree<decltype(tree), true> RH(
tree, [&](int i) -> int { return G.edges[i].cost; }, base);
vvv(int, dat, N, N, 0);
FOR(a, N) FOR(b, N) {
vc<int> P = tree.restore_path(a, b);
vc<int> S;
FOR(i, len(P) - 1) {
int eid = tree.get_eid(P[i], P[i + 1]);
S.eb(G.edges[eid].cost);
}
dat[a][b] = S;
}
FOR(a, N) FOR(b, N) {
mint h = 0;
for (auto& x: dat[a][b]) { h = h * base + x; }
assert(h == RH.get(a, b));
}
FOR(a, N) FOR(b, N) FOR(c, N) FOR(d, N) {
vc<int> A = dat[a][b], B = dat[c][d];
int lcp = 0;
while (lcp < len(A) && lcp < len(B) && A[lcp] == B[lcp]) ++lcp;
auto [k, ch] = RH.lcp_and_comp(a, b, c, d);
assert(k == lcp);
if (ch == '<') assert(A < B);
if (ch == '=') assert(A == B);
if (ch == '>') assert(A > B);
}
}
void test_vertex() {
ll N = RNG(1, 20);
auto edges = random_tree(N);
Graph<int, 0> G(N);
for (auto& [a, b]: edges) { G.add(a, b); }
vc<int> A(N);
FOR(i, N) A[i] = RNG(0, 3);
G.build();
Tree<decltype(G)> tree(G);
using mint = modint61;
mint base = RNG_64();
Rolling_Hash_On_Tree<decltype(tree), false> RH(
tree, [&](int i) -> int { return A[i]; }, base);
vvv(int, dat, N, N, 0);
FOR(a, N) FOR(b, N) {
vc<int> P = tree.restore_path(a, b);
vc<int> S;
for (auto& v: P) S.eb(A[v]);
dat[a][b] = S;
}
FOR(a, N) FOR(b, N) {
mint h = 0;
for (auto& x: dat[a][b]) { h = h * base + x; }
assert(h == RH.get(a, b));
}
FOR(a, N) FOR(b, N) FOR(c, N) FOR(d, N) {
vc<int> A = dat[a][b], B = dat[c][d];
int lcp = 0;
while (lcp < len(A) && lcp < len(B) && A[lcp] == B[lcp]) ++lcp;
auto [k, ch] = RH.lcp_and_comp(a, b, c, d);
assert(k == lcp);
if (ch == '<') assert(A < B);
if (ch == '=') assert(A == B);
if (ch == '>') assert(A > B);
}
}
void solve() {
int a, b;
cin >> a >> b;
cout << a + b << "\n";
}
signed main() {
FOR(300) test_edge();
FOR(300) test_vertex();
solve();
}