competitive-programming-library
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Segment Tree Beats
(data-structure/SegTreeBeats.hpp)
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- Last update: 2023-06-25 16:21:20+09:00
- Include:
#include "data-structure/SegTreeBeats.hpp"
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#pragma once
#include "../basic/template.hpp"
class SegTreeBeats {
unsigned int n;
std::vector<lint> width, min[2], minc, max[2], maxc, sum, lazy;
void eval(int k) {
if (n - 1 <= k) return;
if (lazy[k]) {
update_node_add(2 * k + 1, lazy[k]);
update_node_add(2 * k + 2, lazy[k]);
lazy[k] = 0;
}
if (max[0][k] < max[0][2 * k + 1]) {
update_node_max(2 * k + 1, max[0][k]);
}
if (min[0][k] > min[0][2 * k + 1]) {
update_node_min(2 * k + 1, min[0][k]);
}
if (max[0][k] < max[0][2 * k + 2]) {
update_node_max(2 * k + 2, max[0][k]);
}
if (min[0][k] > min[0][2 * k + 2]) {
update_node_min(2 * k + 2, min[0][k]);
}
}
void combine(int k) {
sum[k] = sum[2 * k + 1] + sum[2 * k + 2];
if (min[0][2 * k + 1] < min[0][2 * k + 2]) {
min[0][k] = min[0][2 * k + 1];
minc[k] = minc[2 * k + 1];
min[1][k] = std::min(min[1][2 * k + 1], min[0][2 * k + 2]);
} else if (min[0][2 * k + 1] > min[0][2 * k + 2]) {
min[0][k] = min[0][2 * k + 2];
minc[k] = minc[2 * k + 2];
min[1][k] = std::min(min[0][2 * k + 1], min[1][2 * k + 2]);
} else {
min[0][k] = min[0][2 * k + 1];
minc[k] = minc[2 * k + 1] + minc[2 * k + 2];
min[1][k] = std::min(min[1][2 * k + 1], min[1][2 * k + 2]);
}
if (max[0][2 * k + 1] > max[0][2 * k + 2]) {
max[0][k] = max[0][2 * k + 1];
maxc[k] = maxc[2 * k + 1];
max[1][k] = std::max(max[1][2 * k + 1], max[0][2 * k + 2]);
} else if (max[0][2 * k + 1] < max[0][2 * k + 2]) {
max[0][k] = max[0][2 * k + 2];
maxc[k] = maxc[2 * k + 2];
max[1][k] = std::max(max[0][2 * k + 1], max[1][2 * k + 2]);
} else {
max[0][k] = max[0][2 * k + 1];
maxc[k] = maxc[2 * k + 1] + maxc[2 * k + 2];
max[1][k] = std::max(max[1][2 * k + 1], max[1][2 * k + 2]);
}
}
void update_node_max(int k, lint x) {
sum[k] += (x - max[0][k]) * maxc[k];
if (max[0][k] == min[0][k])
min[0][k] = x;
else if (max[0][k] == min[1][k])
min[1][k] = x;
max[0][k] = x;
}
void update_node_min(int k, lint x) {
sum[k] += (x - min[0][k]) * minc[k];
if (min[0][k] == max[0][k])
max[0][k] = x;
else if (min[0][k] == max[1][k])
max[1][k] = x;
min[0][k] = x;
}
void update_node_add(int k, lint x) {
min[0][k] += x;
if (min[1][k] != LINF) min[1][k] += x;
max[0][k] += x;
if (max[1][k] != -LINF) max[1][k] += x;
sum[k] += x * width[k];
lazy[k] += x;
}
public:
SegTreeBeats(unsigned int size, lint def = 0) {
*this = SegTreeBeats(std::vector<lint>(size, def));
}
SegTreeBeats(std::vector<lint> initvec) {
n = 1;
while (n < initvec.size()) n *= 2;
width.resize(2 * n - 1);
min[0].resize(2 * n - 1);
min[1].resize(2 * n - 1, LINF);
minc.resize(2 * n - 1);
max[0].resize(2 * n - 1);
max[1].resize(2 * n - 1, -LINF);
maxc.resize(2 * n - 1);
sum.resize(2 * n - 1);
lazy.resize(2 * n - 1);
for (int i = n - 1; i < n - 1 + initvec.size(); i++) {
min[0][i] = max[0][i] = sum[i] = initvec[i - n + 1];
minc[i] = maxc[i] = 1;
}
for (int i = n - 2; i >= 0; i--) {
combine(i);
}
width[0] = n;
REP(i, 2 * n - 2) width[i] = width[(i - 1) / 2] / 2;
}
void update_chmin(int a, int b, lint x, int k = 0, int l = 0, int r = -1) {
if (r == -1) r = n;
if (b <= l || r <= a || max[0][k] <= x) return;
if (a <= l && r <= b && max[1][k] < x) {
update_node_max(k, x);
return;
}
eval(k);
update_chmin(a, b, x, 2 * k + 1, l, (l + r) / 2);
update_chmin(a, b, x, 2 * k + 2, (l + r) / 2, r);
combine(k);
}
void update_chmax(int a, int b, lint x, int k = 0, int l = 0, int r = -1) {
if (r == -1) r = n;
if (b <= l || r <= a || x <= min[0][k]) return;
if (a <= l && r <= b && x < min[1][k]) {
update_node_min(k, x);
return;
}
eval(k);
update_chmax(a, b, x, 2 * k + 1, l, (l + r) / 2);
update_chmax(a, b, x, 2 * k + 2, (l + r) / 2, r);
combine(k);
}
void update_add(int a, int b, lint x, int k = 0, int l = 0, int r = -1) {
if (r == -1) r = n;
if (b <= l || r <= a) return;
if (a <= l && r <= b) {
update_node_add(k, x);
return;
}
eval(k);
update_add(a, b, x, 2 * k + 1, l, (l + r) / 2);
update_add(a, b, x, 2 * k + 2, (l + r) / 2, r);
combine(k);
}
void update(int a, int b, lint x) {
update_chmin(a, b, x);
update_chmax(a, b, x);
}
lint query_sum(int a, int b, int k = 0, int l = 0, int r = -1) {
if (r == -1) r = n;
if (b <= l || r <= a) return 0;
if (a <= l && r <= b) return sum[k];
eval(k);
lint vl = query_sum(a, b, 2 * k + 1, l, (l + r) / 2);
lint vr = query_sum(a, b, 2 * k + 2, (l + r) / 2, r);
return vl + vr;
}
lint query_min(int a, int b, int k = 0, int l = 0, int r = -1) {
if (r == -1) r = n;
if (b <= l || r <= a) return LINF;
if (a <= l && r <= b) return min[0][k];
eval(k);
lint vl = query_min(a, b, 2 * k + 1, l, (l + r) / 2);
lint vr = query_min(a, b, 2 * k + 2, (l + r) / 2, r);
return std::min(vl, vr);
}
lint query_max(int a, int b, int k = 0, int l = 0, int r = -1) {
if (r == -1) r = n;
if (b <= l || r <= a) return -LINF;
if (a <= l && r <= b) return max[0][k];
eval(k);
lint vl = query_max(a, b, 2 * k + 1, l, (l + r) / 2);
lint vr = query_max(a, b, 2 * k + 2, (l + r) / 2, r);
return std::max(vl, vr);
}
};
/**
* @title Segment Tree Beats
*/#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/SegTreeBeats.hpp"
class SegTreeBeats {
unsigned int n;
std::vector<lint> width, min[2], minc, max[2], maxc, sum, lazy;
void eval(int k) {
if (n - 1 <= k) return;
if (lazy[k]) {
update_node_add(2 * k + 1, lazy[k]);
update_node_add(2 * k + 2, lazy[k]);
lazy[k] = 0;
}
if (max[0][k] < max[0][2 * k + 1]) {
update_node_max(2 * k + 1, max[0][k]);
}
if (min[0][k] > min[0][2 * k + 1]) {
update_node_min(2 * k + 1, min[0][k]);
}
if (max[0][k] < max[0][2 * k + 2]) {
update_node_max(2 * k + 2, max[0][k]);
}
if (min[0][k] > min[0][2 * k + 2]) {
update_node_min(2 * k + 2, min[0][k]);
}
}
void combine(int k) {
sum[k] = sum[2 * k + 1] + sum[2 * k + 2];
if (min[0][2 * k + 1] < min[0][2 * k + 2]) {
min[0][k] = min[0][2 * k + 1];
minc[k] = minc[2 * k + 1];
min[1][k] = std::min(min[1][2 * k + 1], min[0][2 * k + 2]);
} else if (min[0][2 * k + 1] > min[0][2 * k + 2]) {
min[0][k] = min[0][2 * k + 2];
minc[k] = minc[2 * k + 2];
min[1][k] = std::min(min[0][2 * k + 1], min[1][2 * k + 2]);
} else {
min[0][k] = min[0][2 * k + 1];
minc[k] = minc[2 * k + 1] + minc[2 * k + 2];
min[1][k] = std::min(min[1][2 * k + 1], min[1][2 * k + 2]);
}
if (max[0][2 * k + 1] > max[0][2 * k + 2]) {
max[0][k] = max[0][2 * k + 1];
maxc[k] = maxc[2 * k + 1];
max[1][k] = std::max(max[1][2 * k + 1], max[0][2 * k + 2]);
} else if (max[0][2 * k + 1] < max[0][2 * k + 2]) {
max[0][k] = max[0][2 * k + 2];
maxc[k] = maxc[2 * k + 2];
max[1][k] = std::max(max[0][2 * k + 1], max[1][2 * k + 2]);
} else {
max[0][k] = max[0][2 * k + 1];
maxc[k] = maxc[2 * k + 1] + maxc[2 * k + 2];
max[1][k] = std::max(max[1][2 * k + 1], max[1][2 * k + 2]);
}
}
void update_node_max(int k, lint x) {
sum[k] += (x - max[0][k]) * maxc[k];
if (max[0][k] == min[0][k])
min[0][k] = x;
else if (max[0][k] == min[1][k])
min[1][k] = x;
max[0][k] = x;
}
void update_node_min(int k, lint x) {
sum[k] += (x - min[0][k]) * minc[k];
if (min[0][k] == max[0][k])
max[0][k] = x;
else if (min[0][k] == max[1][k])
max[1][k] = x;
min[0][k] = x;
}
void update_node_add(int k, lint x) {
min[0][k] += x;
if (min[1][k] != LINF) min[1][k] += x;
max[0][k] += x;
if (max[1][k] != -LINF) max[1][k] += x;
sum[k] += x * width[k];
lazy[k] += x;
}
public:
SegTreeBeats(unsigned int size, lint def = 0) {
*this = SegTreeBeats(std::vector<lint>(size, def));
}
SegTreeBeats(std::vector<lint> initvec) {
n = 1;
while (n < initvec.size()) n *= 2;
width.resize(2 * n - 1);
min[0].resize(2 * n - 1);
min[1].resize(2 * n - 1, LINF);
minc.resize(2 * n - 1);
max[0].resize(2 * n - 1);
max[1].resize(2 * n - 1, -LINF);
maxc.resize(2 * n - 1);
sum.resize(2 * n - 1);
lazy.resize(2 * n - 1);
for (int i = n - 1; i < n - 1 + initvec.size(); i++) {
min[0][i] = max[0][i] = sum[i] = initvec[i - n + 1];
minc[i] = maxc[i] = 1;
}
for (int i = n - 2; i >= 0; i--) {
combine(i);
}
width[0] = n;
REP(i, 2 * n - 2) width[i] = width[(i - 1) / 2] / 2;
}
void update_chmin(int a, int b, lint x, int k = 0, int l = 0, int r = -1) {
if (r == -1) r = n;
if (b <= l || r <= a || max[0][k] <= x) return;
if (a <= l && r <= b && max[1][k] < x) {
update_node_max(k, x);
return;
}
eval(k);
update_chmin(a, b, x, 2 * k + 1, l, (l + r) / 2);
update_chmin(a, b, x, 2 * k + 2, (l + r) / 2, r);
combine(k);
}
void update_chmax(int a, int b, lint x, int k = 0, int l = 0, int r = -1) {
if (r == -1) r = n;
if (b <= l || r <= a || x <= min[0][k]) return;
if (a <= l && r <= b && x < min[1][k]) {
update_node_min(k, x);
return;
}
eval(k);
update_chmax(a, b, x, 2 * k + 1, l, (l + r) / 2);
update_chmax(a, b, x, 2 * k + 2, (l + r) / 2, r);
combine(k);
}
void update_add(int a, int b, lint x, int k = 0, int l = 0, int r = -1) {
if (r == -1) r = n;
if (b <= l || r <= a) return;
if (a <= l && r <= b) {
update_node_add(k, x);
return;
}
eval(k);
update_add(a, b, x, 2 * k + 1, l, (l + r) / 2);
update_add(a, b, x, 2 * k + 2, (l + r) / 2, r);
combine(k);
}
void update(int a, int b, lint x) {
update_chmin(a, b, x);
update_chmax(a, b, x);
}
lint query_sum(int a, int b, int k = 0, int l = 0, int r = -1) {
if (r == -1) r = n;
if (b <= l || r <= a) return 0;
if (a <= l && r <= b) return sum[k];
eval(k);
lint vl = query_sum(a, b, 2 * k + 1, l, (l + r) / 2);
lint vr = query_sum(a, b, 2 * k + 2, (l + r) / 2, r);
return vl + vr;
}
lint query_min(int a, int b, int k = 0, int l = 0, int r = -1) {
if (r == -1) r = n;
if (b <= l || r <= a) return LINF;
if (a <= l && r <= b) return min[0][k];
eval(k);
lint vl = query_min(a, b, 2 * k + 1, l, (l + r) / 2);
lint vr = query_min(a, b, 2 * k + 2, (l + r) / 2, r);
return std::min(vl, vr);
}
lint query_max(int a, int b, int k = 0, int l = 0, int r = -1) {
if (r == -1) r = n;
if (b <= l || r <= a) return -LINF;
if (a <= l && r <= b) return max[0][k];
eval(k);
lint vl = query_max(a, b, 2 * k + 1, l, (l + r) / 2);
lint vr = query_max(a, b, 2 * k + 2, (l + r) / 2, r);
return std::max(vl, vr);
}
};
/**
* @title Segment Tree Beats
*/