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test/mytest/wavelet_matrix.test.cpp
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- Last update: 2024-04-04 00:56:26+09:00
- Problem: https://judge.yosupo.jp/problem/aplusb
Depends on
- alg/monoid/add.hpp
- ds/bit_vector.hpp
- ds/wavelet_matrix/wavelet_matrix.hpp
- my_template.hpp
- random/base.hpp
Code
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#include "my_template.hpp"
#include "ds/wavelet_matrix/wavelet_matrix.hpp"
#include "random/base.hpp"
void test_compress() {
int N = RNG(0, 64);
int MAX = RNG(2, 1 << 10);
vc<int> A(N);
vc<int> X(N);
FOR(i, N) X[i] = RNG(MAX);
FOR(i, N) A[i] = RNG(MAX);
Wavelet_Matrix<int, true> WM(A, X);
int Q = 100;
FOR(Q) {
int L = RNG(0, max(1, N));
int R = RNG(0, max(1, N + 1));
if (L > R) swap(L, R);
int lo = RNG(0, MAX);
int hi = RNG(0, MAX);
if (lo > hi) swap(lo, hi);
++hi;
vc<int> B = {A.begin() + L, A.begin() + R};
vc<int> Y = {X.begin() + L, X.begin() + R};
int t = RNG(0, 5);
if (t == 0) { // count
int cnt = 0;
for (auto&& x: B)
if (lo <= x && x < hi) cnt += 1;
assert(WM.count(L, R, lo, hi) == cnt);
}
if (t == 1) { // sm
int sm = 0;
int k1 = RNG(R - L + 1);
int k2 = RNG(R - L + 1);
if (k1 > k2) swap(k1, k2);
auto I = argsort(B);
FOR(i, k1, k2) sm += Y[I[i]];
assert(WM.sum(L, R, k1, k2) == sm);
}
if (t == 2) { // kth
if (L == R) continue;
int k = RNG(R - L);
sort(all(B));
assert(WM.kth(L, R, k) == B[k]);
}
if (t == 3) { // max_right
int a = RNG(0, 10);
int b = RNG(0, 10);
int c = RNG(0, a * (R - L) + b * MAX * (R - L) + 1);
auto check
= [&](int cnt, int sm) -> bool { return a * cnt + b * sm <= c; };
auto p = WM.max_right(check, L, R);
int k = binary_search(
[&](int k) -> bool {
int sm = WM.sum(L, R, 0, k);
return check(k, sm);
},
0, R - L + 1);
int sm = WM.sum(L, R, 0, k);
assert(p.fi == k && p.se == sm);
}
if (t == 4) { // k-th value and sum
int k = RNG(0, R - L + 1);
B.eb(infty<int>);
auto I = argsort(B);
int val = B[I[k]];
int sm = 0;
FOR(i, k) sm += Y[I[i]];
auto p = WM.kth_value_and_sum(L, R, k);
assert(p.fi == val && p.se == sm);
}
}
}
void test_not_compress() {
int N = RNG(0, 64);
int log = RNG(1, 7);
int MAX = 1 << log;
vc<int> A(N);
vc<int> X(N);
FOR(i, N) X[i] = RNG(0, MAX);
FOR(i, N) A[i] = RNG(MAX);
Wavelet_Matrix<int, false> WM(A, X, log);
int Q = 100;
FOR(Q) {
int L = RNG(0, max(1, N));
int R = RNG(0, max(1, N + 1));
if (L > R) swap(L, R);
int lo = RNG(0, MAX);
int hi = RNG(0, MAX);
int xor_val = RNG(0, MAX);
if (lo > hi) swap(lo, hi);
++hi;
vc<int> B = {A.begin() + L, A.begin() + R};
vc<int> Y = {X.begin() + L, X.begin() + R};
for (auto&& x: B) x ^= xor_val;
int t = RNG(0, 5);
if (t == 0) { // count
int cnt = 0;
for (auto&& x: B) {
if (lo <= x && x < hi) cnt += 1;
}
assert(WM.count(L, R, lo, hi, xor_val) == cnt);
}
if (t == 1) { // sm
int sm = 0;
int k1 = RNG(R - L + 1);
int k2 = RNG(R - L + 1);
if (k1 > k2) swap(k1, k2);
auto I = argsort(B);
FOR(i, k1, k2) sm += Y[I[i]];
assert(WM.sum(L, R, k1, k2, xor_val) == sm);
}
if (t == 2) { // kth
if (L == R) continue;
int k = RNG(R - L);
sort(all(B));
assert(WM.kth(L, R, k, xor_val) == B[k]);
}
if (t == 3) { // max_right
int a = RNG(0, 10);
int b = RNG(0, 10);
int c = RNG(0, a * (R - L) + b * MAX * (R - L) + 1);
auto check
= [&](int cnt, int sm) -> bool { return a * cnt + b * sm <= c; };
auto p = WM.max_right(check, L, R, xor_val);
int k = binary_search(
[&](int k) -> bool {
int sm = WM.sum(L, R, 0, k, xor_val);
return check(k, sm);
},
0, R - L + 1);
int sm = WM.sum(L, R, 0, k, xor_val);
assert(k == p.fi && sm == p.se);
}
if (t == 4) { // k-th value and sum
int k = RNG(0, R - L + 1);
B.eb(infty<int>);
auto I = argsort(B);
int val = B[I[k]];
int sm = 0;
FOR(i, k) sm += Y[I[i]];
auto p = WM.kth_value_and_sum(L, R, k, xor_val);
assert(p.fi == val && p.se == sm);
}
}
}
void solve() {
int a, b;
cin >> a >> b;
cout << a + b << "\n";
}
signed main() {
FOR(1000) test_compress();
FOR(1000) test_not_compress();
solve();
return 0;
}#line 1 "test/mytest/wavelet_matrix.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 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 "ds/bit_vector.hpp"
struct Bit_Vector {
vc<pair<u32, u32>> dat;
Bit_Vector(int n) { dat.assign((n + 63) >> 5, {0, 0}); }
void set(int i) { dat[i >> 5].fi |= u32(1) << (i & 31); }
void build() {
FOR(i, len(dat) - 1) dat[i + 1].se = dat[i].se + popcnt(dat[i].fi);
}
// [0, k) 内の 1 の個数
int rank(int k, bool f = 1) {
auto [a, b] = dat[k >> 5];
int ret = b + popcnt(a & ((u32(1) << (k & 31)) - 1));
return (f ? ret : k - ret);
}
};
#line 2 "alg/monoid/add.hpp"
template <typename E>
struct Monoid_Add {
using X = E;
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 "ds/wavelet_matrix/wavelet_matrix.hpp"
// 座圧するかどうかを COMPRESS で指定する
// xor 的な使い方をする場合には、コンストラクタで log を渡すこと
template <typename T, bool COMPRESS, typename Monoid = Monoid_Add<T>>
struct Wavelet_Matrix {
using MX = Monoid;
using X = typename MX::value_type;
static_assert(MX::commute);
int N, lg;
vector<int> mid;
vector<Bit_Vector> bv;
vc<T> key;
bool set_log;
vvc<X> cumsum;
Wavelet_Matrix() {}
// 和を使わないなら、SUM_data は空でよい
Wavelet_Matrix(vc<T> A, vc<X> SUM_data = {}, int log = -1) {
build(A, SUM_data, log);
}
void build(vc<T> A, vc<X> SUM_data = {}, int log = -1) {
N = len(A), lg = log, set_log = (log != -1);
if (N == 0) {
lg = 0;
return;
}
bool MAKE_SUM = !(SUM_data.empty());
vc<X>& S = SUM_data;
if (COMPRESS) {
assert(!set_log);
key.reserve(N);
vc<int> I = argsort(A);
for (auto&& i: I) {
if (key.empty() || key.back() != A[i]) key.eb(A[i]);
A[i] = len(key) - 1;
}
key.shrink_to_fit();
}
if (lg == -1) lg = __lg(max<ll>(MAX(A), 1)) + 1;
mid.resize(lg);
bv.assign(lg, Bit_Vector(N));
if (MAKE_SUM) cumsum.assign(1 + lg, vc<X>(N + 1, MX::unit()));
S.resize(N);
vc<T> A0(N), A1(N);
vc<X> S0(N), S1(N);
FOR_R(d, -1, lg) {
int p0 = 0, p1 = 0;
if (MAKE_SUM) {
FOR(i, N) { cumsum[d + 1][i + 1] = MX::op(cumsum[d + 1][i], S[i]); }
}
if (d == -1) break;
FOR(i, N) {
bool f = (A[i] >> d & 1);
if (!f) {
if (MAKE_SUM) S0[p0] = S[i];
A0[p0++] = A[i];
}
if (f) {
if (MAKE_SUM) S1[p1] = S[i];
bv[d].set(i), A1[p1++] = A[i];
}
}
mid[d] = p0;
bv[d].build();
swap(A, A0), swap(S, S0);
FOR(i, p1) A[p0 + i] = A1[i], S[p0 + i] = S1[i];
}
}
// xor した結果で [a, b) に収まるものを数える
int count(int L, int R, T a, T b, T xor_val = 0) {
return prefix_count(L, R, b, xor_val) - prefix_count(L, R, a, xor_val);
}
int count(vc<pair<int, int>> segments, T a, T b, T xor_val = 0) {
int res = 0;
for (auto&& [L, R]: segments) res += count(L, R, a, b, xor_val);
return res;
}
// xor した結果で、[L, R) の中で k>=0 番目と prefix sum
pair<T, X> kth_value_and_sum(int L, int R, int k, T xor_val = 0) {
assert(0 <= k && k <= R - L);
if (L == R) return {infty<T>, MX::unit()};
if (k == R - L) { return {infty<T>, sum_all(L, R)}; }
if (xor_val != 0) assert(set_log);
assert(!cumsum.empty());
int cnt = 0;
X sm = MX::unit();
T ret = 0;
for (int d = lg - 1; d >= 0; --d) {
bool f = (xor_val >> d) & 1;
int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
int c = (f ? (R - L) - (r0 - l0) : (r0 - l0));
if (cnt + c > k) {
if (!f) L = l0, R = r0;
if (f) L += mid[d] - l0, R += mid[d] - r0;
} else {
X s = (f ? get(d, L + mid[d] - l0, R + mid[d] - r0) : get(d, l0, r0));
cnt += c, ret |= T(1) << d, sm = MX::op(sm, s);
if (!f) L += mid[d] - l0, R += mid[d] - r0;
if (f) L = l0, R = r0;
}
}
sm = MX::op(sm, get(0, L, L + k - cnt));
if (COMPRESS) ret = key[ret];
return {ret, sm};
}
// xor した結果で、[L, R) の中で k>=0 番目と prefix sum
pair<T, X> kth_value_and_sum(vc<pair<int, int>> segments, int k,
T xor_val = 0) {
assert(!cumsum.empty());
if (xor_val != 0) assert(set_log);
int total_len = 0;
for (auto&& [L, R]: segments) total_len += R - L;
assert(0 <= k && k <= total_len);
if (k == total_len) { return {infty<T>, sum_all(segments)}; }
int cnt = 0;
X sm = MX::unit();
T ret = 0;
for (int d = lg - 1; d >= 0; --d) {
bool f = (xor_val >> d) & 1;
int c = 0;
for (auto&& [L, R]: segments) {
int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
c += (f ? (R - L) - (r0 - l0) : (r0 - l0));
}
if (cnt + c > k) {
for (auto&& [L, R]: segments) {
int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
if (!f) L = l0, R = r0;
if (f) L += mid[d] - l0, R += mid[d] - r0;
}
} else {
cnt += c, ret |= T(1) << d;
for (auto&& [L, R]: segments) {
int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
X s = (f ? get(d, L + mid[d] - l0, R + mid[d] - r0) : get(d, l0, r0));
sm = MX::op(sm, s);
if (!f) L += mid[d] - l0, R += mid[d] - r0;
if (f) L = l0, R = r0;
}
}
}
for (auto&& [L, R]: segments) {
int t = min(R - L, k - cnt);
sm = MX::op(sm, get(0, L, L + t));
cnt += t;
}
if (COMPRESS) ret = key[ret];
return {ret, sm};
}
// xor した結果で、[L, R) の中で k>=0 番目
T kth(int L, int R, int k, T xor_val = 0) {
if (xor_val != 0) assert(set_log);
assert(0 <= k && k < R - L);
int cnt = 0;
T ret = 0;
for (int d = lg - 1; d >= 0; --d) {
bool f = (xor_val >> d) & 1;
int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
int c = (f ? (R - L) - (r0 - l0) : (r0 - l0));
if (cnt + c > k) {
if (!f) L = l0, R = r0;
if (f) L += mid[d] - l0, R += mid[d] - r0;
} else {
cnt += c, ret |= T(1) << d;
if (!f) L += mid[d] - l0, R += mid[d] - r0;
if (f) L = l0, R = r0;
}
}
if (COMPRESS) ret = key[ret];
return ret;
}
T kth(vc<pair<int, int>> segments, int k, T xor_val = 0) {
int total_len = 0;
for (auto&& [L, R]: segments) total_len += R - L;
assert(0 <= k && k < total_len);
int cnt = 0;
T ret = 0;
for (int d = lg - 1; d >= 0; --d) {
bool f = (xor_val >> d) & 1;
int c = 0;
for (auto&& [L, R]: segments) {
int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
c += (f ? (R - L) - (r0 - l0) : (r0 - l0));
}
if (cnt + c > k) {
for (auto&& [L, R]: segments) {
int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
if (!f) L = l0, R = r0;
if (f) L += mid[d] - l0, R += mid[d] - r0;
}
} else {
cnt += c, ret |= T(1) << d;
for (auto&& [L, R]: segments) {
int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
if (!f) L += mid[d] - l0, R += mid[d] - r0;
if (f) L = l0, R = r0;
}
}
}
if (COMPRESS) ret = key[ret];
return ret;
}
// xor した結果で、[L, R) の中で中央値。
// LOWER = true：下側中央値、false：上側中央値
T median(bool UPPER, int L, int R, T xor_val = 0) {
int n = R - L;
int k = (UPPER ? n / 2 : (n - 1) / 2);
return kth(L, R, k, xor_val);
}
T median(bool UPPER, vc<pair<int, int>> segments, T xor_val = 0) {
int n = 0;
for (auto&& [L, R]: segments) n += R - L;
int k = (UPPER ? n / 2 : (n - 1) / 2);
return kth(segments, k, xor_val);
}
// xor した結果で [k1, k2) 番目であるところの SUM_data の和
X sum(int L, int R, int k1, int k2, T xor_val = 0) {
assert(0 <= k1 && k1 <= k2 && k2 <= R - L);
if (k1 == k2) return MX::unit();
X add = prefix_sum(L, R, k2, xor_val);
X sub = prefix_sum(L, R, k1, xor_val);
return MX::op(add, MX::inverse(sub));
}
X sum_all(int L, int R) { return get(lg, L, R); }
X sum_all(vc<pair<int, int>> segments) {
X sm = MX::unit();
for (auto&& [L, R]: segments) { sm = MX::op(sm, get(lg, L, R)); }
return sm;
}
// check(cnt, prefix sum) が true となるような最大の (cnt, sum)
template <typename F>
pair<int, X> max_right(F check, int L, int R, T xor_val = 0) {
assert(check(0, MX::unit()));
if (xor_val != 0) assert(set_log);
if (L == R) return {R - L, MX::unit()};
if (check(R - L, get(lg, L, R))) return {R - L, get(lg, L, R)};
int cnt = 0;
X sm = MX::unit();
for (int d = lg - 1; d >= 0; --d) {
bool f = (xor_val >> d) & 1;
int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
int c = (f ? (R - L) - (r0 - l0) : (r0 - l0));
X s = (f ? get(d, L + mid[d] - l0, R + mid[d] - r0) : get(d, l0, r0));
if (check(cnt + c, MX::op(sm, s))) {
cnt += c, sm = MX::op(sm, s);
if (f) L = l0, R = r0;
if (!f) L += mid[d] - l0, R += mid[d] - r0;
} else {
if (!f) L = l0, R = r0;
if (f) L += mid[d] - l0, R += mid[d] - r0;
}
}
int k = binary_search(
[&](int k) -> bool {
return check(cnt + k, MX::op(sm, get(0, L, L + k)));
},
0, R - L);
cnt += k;
sm = MX::op(sm, get(0, L, L + k));
return {cnt, sm};
}
private:
inline X get(int d, int L, int R) {
assert(!cumsum.empty());
return MX::op(MX::inverse(cumsum[d][L]), cumsum[d][R]);
}
// xor した結果で [0, x) に収まるものを数える
int prefix_count(int L, int R, T x, T xor_val = 0) {
if (xor_val != 0) assert(set_log);
x = (COMPRESS ? LB(key, x) : x);
if (x == 0) return 0;
if (x >= (1 << lg)) return R - L;
int cnt = 0;
FOR_R(d, lg) {
bool add = (x >> d) & 1;
bool f = ((xor_val) >> d) & 1;
int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
int kf = (f ? (R - L) - (r0 - l0) : (r0 - l0));
if (add) {
cnt += kf;
if (f) { L = l0, R = r0; }
if (!f) { L += mid[d] - l0, R += mid[d] - r0; }
} else {
if (!f) L = l0, R = r0;
if (f) L += mid[d] - l0, R += mid[d] - r0;
}
}
return cnt;
}
// xor した結果で [0, k) 番目のものの和
X prefix_sum(int L, int R, int k, T xor_val = 0) {
return kth_value_and_sum(L, R, k, xor_val).se;
}
// xor した結果で [0, k) 番目のものの和
X prefix_sum(vc<pair<int, int>> segments, int k, T xor_val = 0) {
return kth_value_and_sum(segments, k, xor_val).se;
}
};
#line 2 "random/base.hpp"
u64 RNG_64() {
static uint64_t x_
= uint64_t(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 5 "test/mytest/wavelet_matrix.test.cpp"
void test_compress() {
int N = RNG(0, 64);
int MAX = RNG(2, 1 << 10);
vc<int> A(N);
vc<int> X(N);
FOR(i, N) X[i] = RNG(MAX);
FOR(i, N) A[i] = RNG(MAX);
Wavelet_Matrix<int, true> WM(A, X);
int Q = 100;
FOR(Q) {
int L = RNG(0, max(1, N));
int R = RNG(0, max(1, N + 1));
if (L > R) swap(L, R);
int lo = RNG(0, MAX);
int hi = RNG(0, MAX);
if (lo > hi) swap(lo, hi);
++hi;
vc<int> B = {A.begin() + L, A.begin() + R};
vc<int> Y = {X.begin() + L, X.begin() + R};
int t = RNG(0, 5);
if (t == 0) { // count
int cnt = 0;
for (auto&& x: B)
if (lo <= x && x < hi) cnt += 1;
assert(WM.count(L, R, lo, hi) == cnt);
}
if (t == 1) { // sm
int sm = 0;
int k1 = RNG(R - L + 1);
int k2 = RNG(R - L + 1);
if (k1 > k2) swap(k1, k2);
auto I = argsort(B);
FOR(i, k1, k2) sm += Y[I[i]];
assert(WM.sum(L, R, k1, k2) == sm);
}
if (t == 2) { // kth
if (L == R) continue;
int k = RNG(R - L);
sort(all(B));
assert(WM.kth(L, R, k) == B[k]);
}
if (t == 3) { // max_right
int a = RNG(0, 10);
int b = RNG(0, 10);
int c = RNG(0, a * (R - L) + b * MAX * (R - L) + 1);
auto check
= [&](int cnt, int sm) -> bool { return a * cnt + b * sm <= c; };
auto p = WM.max_right(check, L, R);
int k = binary_search(
[&](int k) -> bool {
int sm = WM.sum(L, R, 0, k);
return check(k, sm);
},
0, R - L + 1);
int sm = WM.sum(L, R, 0, k);
assert(p.fi == k && p.se == sm);
}
if (t == 4) { // k-th value and sum
int k = RNG(0, R - L + 1);
B.eb(infty<int>);
auto I = argsort(B);
int val = B[I[k]];
int sm = 0;
FOR(i, k) sm += Y[I[i]];
auto p = WM.kth_value_and_sum(L, R, k);
assert(p.fi == val && p.se == sm);
}
}
}
void test_not_compress() {
int N = RNG(0, 64);
int log = RNG(1, 7);
int MAX = 1 << log;
vc<int> A(N);
vc<int> X(N);
FOR(i, N) X[i] = RNG(0, MAX);
FOR(i, N) A[i] = RNG(MAX);
Wavelet_Matrix<int, false> WM(A, X, log);
int Q = 100;
FOR(Q) {
int L = RNG(0, max(1, N));
int R = RNG(0, max(1, N + 1));
if (L > R) swap(L, R);
int lo = RNG(0, MAX);
int hi = RNG(0, MAX);
int xor_val = RNG(0, MAX);
if (lo > hi) swap(lo, hi);
++hi;
vc<int> B = {A.begin() + L, A.begin() + R};
vc<int> Y = {X.begin() + L, X.begin() + R};
for (auto&& x: B) x ^= xor_val;
int t = RNG(0, 5);
if (t == 0) { // count
int cnt = 0;
for (auto&& x: B) {
if (lo <= x && x < hi) cnt += 1;
}
assert(WM.count(L, R, lo, hi, xor_val) == cnt);
}
if (t == 1) { // sm
int sm = 0;
int k1 = RNG(R - L + 1);
int k2 = RNG(R - L + 1);
if (k1 > k2) swap(k1, k2);
auto I = argsort(B);
FOR(i, k1, k2) sm += Y[I[i]];
assert(WM.sum(L, R, k1, k2, xor_val) == sm);
}
if (t == 2) { // kth
if (L == R) continue;
int k = RNG(R - L);
sort(all(B));
assert(WM.kth(L, R, k, xor_val) == B[k]);
}
if (t == 3) { // max_right
int a = RNG(0, 10);
int b = RNG(0, 10);
int c = RNG(0, a * (R - L) + b * MAX * (R - L) + 1);
auto check
= [&](int cnt, int sm) -> bool { return a * cnt + b * sm <= c; };
auto p = WM.max_right(check, L, R, xor_val);
int k = binary_search(
[&](int k) -> bool {
int sm = WM.sum(L, R, 0, k, xor_val);
return check(k, sm);
},
0, R - L + 1);
int sm = WM.sum(L, R, 0, k, xor_val);
assert(k == p.fi && sm == p.se);
}
if (t == 4) { // k-th value and sum
int k = RNG(0, R - L + 1);
B.eb(infty<int>);
auto I = argsort(B);
int val = B[I[k]];
int sm = 0;
FOR(i, k) sm += Y[I[i]];
auto p = WM.kth_value_and_sum(L, R, k, xor_val);
assert(p.fi == val && p.se == sm);
}
}
}
void solve() {
int a, b;
cin >> a >> b;
cout << a + b << "\n";
}
signed main() {
FOR(1000) test_compress();
FOR(1000) test_not_compress();
solve();
return 0;
}