competitive-programming-library
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Wavelet Matrix
(data-structure/WaveletMatrix.hpp)
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- Last update: 2023-06-25 16:21:20+09:00
- Include:
#include "data-structure/WaveletMatrix.hpp"
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#pragma once
#include "../basic/template.hpp"
#include "SuccinctBitVector.hpp"
template <typename T>
constexpr static int8_t bit_count() {
int8_t res = 0;
std::make_unsigned_t<T> x = ~0;
while (x) {
res++;
x >>= 1;
}
return res;
}
template <typename T, int8_t word_size = bit_count<T>()>
class WaveletMatrix {
using i8 = int8_t;
int N;
std::array<SuccinctBitVector, word_size> bit;
std::array<int, word_size> zero_cnt;
std::vector<int> head;
public:
WaveletMatrix(std::vector<T> vec) : N(vec.size()), head(vec.size()) {
zero_cnt.fill(0);
std::vector<T> nvec(N);
std::vector<bool> bvec;
bvec.reserve(N);
for (i8 i = word_size - 1; i >= 0; i--) {
int cnt[] = {0, 0};
bvec.resize(0);
for (T j : vec) {
bvec.emplace_back(j & (1LL << i));
if (!(j & (1LL << i))) {
cnt[1]++;
zero_cnt[i]++;
}
}
nvec.resize(N);
for (T j : vec) {
if (j & (1LL << i))
nvec[cnt[1]++] = j;
else
nvec[cnt[0]++] = j;
}
vec = std::move(nvec);
bit[i].init(bvec);
}
REP(i, N - 1) {
if (vec[i - 1] == vec[i])
head[i] = head[i - 1];
else
head[i] = i;
}
}
int rank(int r, lint c) const {
for (i8 i = word_size - 1; i >= 0; i--) {
r--;
if (c & ((lint)1 << i))
r = bit[i].rank(false, bit[i].size() - 1) +
bit[i].rank(true, r);
else
r = bit[i].rank(false, r);
}
return r - head[r];
}
T quantile(int l, int r, int k) const {
T res = 0;
for (i8 i = word_size - 1; i >= 0; i--) {
const int z_r = bit[i].rank(false, r - 1), o_r = r - z_r;
const int z_l = !l ? 0 : bit[i].rank(false, l - 1), o_l = l - z_l;
if (k <= z_r - z_l) {
l = z_l;
r = z_r;
} else {
l = r = zero_cnt[i];
l += o_l;
r += o_r;
k -= z_r - z_l;
res |= (1 << i);
}
}
return res;
}
};
/**
* @title Wavelet Matrix
*/#line 2 "basic/template.hpp"
#define _CRT_SECURE_NO_WARNINGS
#ifndef __clang__
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#endif
#include <string.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cfloat>
#include <chrono>
#include <climits>
#include <cmath>
#include <complex>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <memory>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
#define rep(i, n) for (int i = 0; i < int(n); i++)
#define REP(i, n) for (int i = 1; i <= int(n); i++)
#define all(V) V.begin(), V.end()
using i128 = __int128_t;
using u128 = __uint128_t;
using uint = unsigned int;
using lint = long long;
using ulint = unsigned long long;
using IP = std::pair<int, int>;
using LP = std::pair<lint, lint>;
constexpr int INF = INT_MAX / 2;
constexpr lint LINF = LLONG_MAX / 2;
constexpr double eps = DBL_EPSILON * 10;
constexpr double PI = 3.141592653589793238462643383279;
template <class T>
class prique : public std::priority_queue<T, std::vector<T>, std::greater<T>> {};
int popcount(uint x) {
#if __cplusplus >= 202002L
return std::popcount(x);
#else
#ifndef __clang__
return __builtin_popcount(x);
#endif
#endif
x = (x & 0x55555555) + (x >> 1 & 0x55555555);
x = (x & 0x33333333) + (x >> 2 & 0x33333333);
x = (x & 0x0f0f0f0f) + (x >> 4 & 0x0f0f0f0f);
x = (x & 0x00ff00ff) + (x >> 8 & 0x00ff00ff);
return (x & 0x0000ffff) + (x >> 16 & 0x0000ffff);
}
template <class F>
inline constexpr decltype(auto) lambda_fix(F&& f) {
return [f = std::forward<F>(f)](auto&&... args) {
return f(f, std::forward<decltype(args)>(args)...);
};
}
template <class T>
constexpr std::vector<T> make_vec(size_t n) {
return std::vector<T>(n);
}
template <class T, class... Args>
constexpr auto make_vec(size_t n, Args&&... args) {
return std::vector<decltype(make_vec<T>(args...))>(n, make_vec<T>(std::forward<Args>(args)...));
}
template <class T, class U, class Stream>
Stream& operator>>(Stream& ist, std::pair<T, U>& x) {
return ist >> x.first >> x.second;
}
template <class T, class U, class Stream>
Stream& operator<<(Stream& ost, const std::pair<T, U>& x) {
return ost << x.first << " " << x.second;
}
template <class Container,
std::enable_if_t<!std::is_same<Container, std::string>::value, std::nullptr_t> = nullptr>
auto operator>>(std::istream& ist, Container& cont)
-> decltype(typename Container::iterator(), std::cin)& {
Container tmp;
while (true) {
typename Container::value_type t;
ist >> t;
tmp.emplace_back(t);
if (getchar() == '\n') break;
}
cont = Container(std::move(tmp));
return ist;
}
template <class Container, class Stream,
std::enable_if_t<!std::is_same<Container, std::string>::value, std::nullptr_t> = nullptr>
auto operator<<(Stream& ost, const Container& cont)
-> decltype(typename Container::iterator(), ost)& {
for (auto it = cont.begin(); it != cont.end(); it++) {
if (it != cont.begin()) ost << ' ';
ost << *it;
}
return ost;
}
template <class Container>
auto sum(const Container& cont) -> decltype(typename Container::iterator(), 0LL) {
lint res = 0;
for (auto it = cont.begin(); it != cont.end(); it++) res += *it;
return res;
}
template <class T, class U>
constexpr inline bool chmax(T& lhs, const U& rhs) noexcept {
if (lhs < rhs) {
lhs = rhs;
return true;
}
return false;
}
template <class T, class U>
constexpr inline bool chmin(T& lhs, const U& rhs) noexcept {
if (lhs > rhs) {
lhs = rhs;
return true;
}
return false;
}
constexpr inline lint gcd(lint a, lint b) noexcept {
while (b) {
lint c = a;
a = b;
b = c % b;
}
return a;
}
inline lint lcm(lint a, lint b) noexcept { return a / gcd(a, b) * b; }
constexpr bool isprime(lint n) noexcept {
if (n == 1) return false;
for (int i = 2; i * i <= n; i++) {
if (n % i == 0) return false;
}
return true;
}
template <class T>
constexpr T mypow(T a, lint b) noexcept {
T res(1);
while (true) {
if (b & 1) res *= a;
b >>= 1;
if (!b) break;
a *= a;
}
return res;
}
constexpr lint modpow(lint a, lint b, lint m) noexcept {
a %= m;
lint res(1);
while (b) {
if (b & 1) res *= a, res %= m;
a *= a, a %= m, b >>= 1;
}
return res;
}
LP extGcd(lint a, lint b) noexcept {
if (b == 0) return {1, 0};
LP s = extGcd(b, a % b);
std::swap(s.first, s.second);
s.second -= a / b * s.first;
return s;
}
LP ChineseRem(const lint& b1, const lint& m1, const lint& b2, const lint& m2) noexcept {
auto p = extGcd(m1, m2);
lint g = gcd(m1, m2), l = m1 / g * m2;
lint tmp = (b2 - b1) / g * p.first % (m2 / g);
lint r = (b1 + m1 * tmp + l) % l;
return {r, l};
}
int LCS(const std::string& a, const std::string& b) {
auto dp = make_vec<int>(a.size() + 1, b.size() + 1);
rep(i, a.size()) {
rep(j, b.size()) {
chmax(dp[i + 1][j], dp[i][j]);
chmax(dp[i][j + 1], dp[i][j]);
if (a[i] == b[j]) chmax(dp[i + 1][j + 1], dp[i][j] + 1);
}
chmax(dp[i + 1][b.size()], dp[i][b.size()]);
}
rep(j, b.size()) chmax(dp[a.size()][j + 1], dp[a.size()][j]);
return dp[a.size()][b.size()];
}
template <class T, std::enable_if_t<std::is_convertible<int, T>::value, std::nullptr_t> = nullptr>
void compress(std::vector<T>& vec) {
auto tmp = vec;
std::sort(all(tmp));
tmp.erase(std::unique(all(tmp)), tmp.end());
for (T& i : vec) i = std::lower_bound(all(tmp), i) - tmp.begin();
}
template <class T>
void compress(T* l, T* r) {
std::vector<T> tmp(l, r);
std::sort(all(tmp));
tmp.erase(std::unique(all(tmp)), tmp.end());
for (auto i = l; i < r; i++) {
*i = std::lower_bound(all(tmp), *i) - tmp.begin();
}
}
template <class InputIter>
void compress(InputIter l, InputIter r) {
std::vector<typename InputIter::value_type> tmp(l, r);
std::sort(all(tmp));
tmp.erase(std::unique(all(tmp)), tmp.end());
for (auto i = l; i < r; i++) {
*i = std::lower_bound(all(tmp), *i) - tmp.begin();
}
}
template <class InputIter,
std::enable_if_t<std::is_same<typename InputIter::value_type, std::pair<IP, int>>::value,
std::nullptr_t> = nullptr>
void mo_sort(InputIter l, InputIter r, int N) {
const int M = std::max(1.0, std::sqrt(lint(N) * N / std::distance(l, r)));
std::sort(l, r, [M](const auto& lhs, const auto& rhs) {
if (lhs.first.first / M < rhs.first.first / M) return true;
if (lhs.first.first / M == rhs.first.first / M) return lhs.first.second < rhs.first.second;
return false;
});
int before = -1, cnt = 0;
bool f = false;
for (InputIter i = l; i != r; i++) {
if (before != i->first.first / M) {
if (f) std::reverse(i - cnt, i);
f ^= true, before = i->first.first / M, cnt = 1;
} else
cnt++;
}
if (f) std::reverse(r - cnt, r);
}
template <class T>
std::vector<T> xor_bases(const std::vector<T>& vec) {
std::vector<T> res;
for (T i : vec) {
for (T j : res) {
chmin(i, i ^ j);
}
if (i) res.emplace_back(i);
}
return res;
}
#line 3 "data-structure/SuccinctBitVector.hpp"
class SuccinctBitVector {
std::vector<bool> v;
using u8 = uint_least8_t;
using u16 = uint_least16_t;
using u32 = uint_least32_t;
constexpr static u8 chunk_bit = 10;
constexpr static u8 blocks_bit = 4;
constexpr static u16 chunk_size = 1 << chunk_bit; // log ^ 2 N bit
constexpr static u8 block_size = 1 << blocks_bit; // log N / 2 bit
constexpr static u8 blocks_in_chunk = 1 << (chunk_bit - blocks_bit);
size_t N; // MAX 2 ^ 32
std::vector<u32> chunks; // log N: 32
std::vector<u16> blocks, block_num; // 2 log log N: 10
public:
SuccinctBitVector() = default;
SuccinctBitVector(const std::vector<bool>& vec) { init(vec); }
void init(const std::vector<bool>& vec) {
N = vec.size();
chunks.resize((N + chunk_size - 1) >> chunk_bit, 0);
blocks.resize((N + block_size - 1) >> blocks_bit, 0);
block_num.resize((N + block_size - 1) >> blocks_bit, 0);
rep(i, N) {
if (vec[i]) {
chunks[i >> chunk_bit]++;
blocks[i >> blocks_bit]++;
block_num[i >> blocks_bit] |= 1 << (i & (block_size - 1));
}
}
rep(i, chunks.size() - 1) chunks[i + 1] += chunks[i];
rep(i, blocks.size() - 1) {
if ((i & (blocks_in_chunk - 1)) != blocks_in_chunk - 1)
blocks[i + 1] += blocks[i];
}
v = vec;
}
int rank(bool b, int x) const {
int res = 0;
res += x >= chunk_size ? chunks[(x >> chunk_bit) - 1] : 0;
res += (x & (chunk_size - 1)) >= block_size
? blocks[(x >> blocks_bit) - 1]
: 0;
res += __builtin_popcount(block_num[x >> blocks_bit] &
((1 << ((x & (block_size - 1)) + 1)) - 1));
return b ? res : x + 1 - res;
}
size_t size() const { return N; }
};
/**
* @title Succinct Bit Vector
*/
#line 4 "data-structure/WaveletMatrix.hpp"
template <typename T>
constexpr static int8_t bit_count() {
int8_t res = 0;
std::make_unsigned_t<T> x = ~0;
while (x) {
res++;
x >>= 1;
}
return res;
}
template <typename T, int8_t word_size = bit_count<T>()>
class WaveletMatrix {
using i8 = int8_t;
int N;
std::array<SuccinctBitVector, word_size> bit;
std::array<int, word_size> zero_cnt;
std::vector<int> head;
public:
WaveletMatrix(std::vector<T> vec) : N(vec.size()), head(vec.size()) {
zero_cnt.fill(0);
std::vector<T> nvec(N);
std::vector<bool> bvec;
bvec.reserve(N);
for (i8 i = word_size - 1; i >= 0; i--) {
int cnt[] = {0, 0};
bvec.resize(0);
for (T j : vec) {
bvec.emplace_back(j & (1LL << i));
if (!(j & (1LL << i))) {
cnt[1]++;
zero_cnt[i]++;
}
}
nvec.resize(N);
for (T j : vec) {
if (j & (1LL << i))
nvec[cnt[1]++] = j;
else
nvec[cnt[0]++] = j;
}
vec = std::move(nvec);
bit[i].init(bvec);
}
REP(i, N - 1) {
if (vec[i - 1] == vec[i])
head[i] = head[i - 1];
else
head[i] = i;
}
}
int rank(int r, lint c) const {
for (i8 i = word_size - 1; i >= 0; i--) {
r--;
if (c & ((lint)1 << i))
r = bit[i].rank(false, bit[i].size() - 1) +
bit[i].rank(true, r);
else
r = bit[i].rank(false, r);
}
return r - head[r];
}
T quantile(int l, int r, int k) const {
T res = 0;
for (i8 i = word_size - 1; i >= 0; i--) {
const int z_r = bit[i].rank(false, r - 1), o_r = r - z_r;
const int z_l = !l ? 0 : bit[i].rank(false, l - 1), o_l = l - z_l;
if (k <= z_r - z_l) {
l = z_l;
r = z_r;
} else {
l = r = zero_cnt[i];
l += o_l;
r += o_r;
k -= z_r - z_l;
res |= (1 << i);
}
}
return res;
}
};
/**
* @title Wavelet Matrix
*/