This documentation is automatically generated by online-judge-tools/verification-helper
View the Project on GitHub kmyk/competitive-programming-library
#define PROBLEM "https://yukicoder.me/problems/no/1031"
#include "../utils/macros.hpp"
#include "../data_structure/sparse_table.hpp"
#include "../data_structure/segment_tree.hpp"
#include "../monoids/max.hpp"
#include <climits>
#include <cmath>
#include <deque>
#include <functional>
#include <iostream>
#include <optional>
#include <tuple>
#include <utility>
#include <vector>
using namespace std;
#include "../old/rollback-square-decomposition.inc.cpp"
template <class T>
struct rollbackable_deque {
deque<T> data;
vector<pair<char, optional<T> > > history;
rollbackable_deque() = default;
bool empty() const { return data.empty(); }
size_t size() const { return data.size(); }
T operator [] (size_t i) const { return data[i]; }
const T & front() const { return data.front(); }
const T & back() const { return data.back(); }
void push_front(T value) {
history.emplace_back('f', optional<T>());
data.push_front(value);
}
void pop_front() {
history.emplace_back('F', data.front());
data.pop_front();
}
void push_back(T value) {
history.emplace_back('b', optional<T>());
data.push_back(value);
}
void pop_back() {
history.emplace_back('B', data.back());
data.pop_back();
}
void snapshot() {
history.emplace_back('$', optional<T>());
}
void rollback() {
while (history.back().first != '$') {
char op = history.back().first;
optional<T> value = history.back().second;
history.pop_back();
if (op == 'f') {
data.pop_front();
} else if (op == 'F') {
data.push_front(*value);
} else if (op == 'b') {
data.pop_back();
} else if (op == 'B') {
data.push_back(*value);
}
}
history.pop_back();
}
};
struct rollback_mo_inc {
const vector<int> & p;
int64_t & ans;
int l, r;
vector<pair<int, int> > history;
rollbackable_deque<int> deq;
rollback_mo_inc(const vector<int> & p_, int64_t & ans_) : p(p_), ans(ans_) {
reset(0);
}
void reset(int l_) {
l = l_;
r = l_;
history.clear();
deq = rollbackable_deque<int>();
}
void extend_left(int nl, int r) {
for (; nl < l; -- l) {
if (deq.empty() or p[l - 1] < deq.front()) {
deq.push_front(p[l - 1]);
}
}
}
void extend_right(int l, int nr) {
for (; r < nr; ++ r) {
while (not deq.empty() and p[r] < deq.back()) {
deq.pop_back();
}
deq.push_back(p[r]);
}
}
void snapshot() {
deq.snapshot();
history.emplace_back(l, r);
}
void rollback() {
deq.rollback();
tie(l, r) = history.back();
history.pop_back();
}
void query() {
ans += deq.size();
}
};
int64_t solve1(int n, const vector<int> & p) {
vector<pair<int, int> > query_inc;
vector<int> lookup(n);
REP (i, n) {
lookup[p[i]] = i;
}
sparse_table<max_monoid<int> > table(ALL(p));
function<void (int, int)> go = [&](int l, int r) {
if (r - l < 2) return;
int m = lookup[table.range_get(l, r)];
query_inc.emplace_back(l, m);
go(l, m);
go(m + 1, r);
};
go(0, n);
int64_t ans = 0;
rollback_mo_inc interface_inc(p, ans);
rollback_square_decomposition(n, query_inc, interface_inc, [&](int l, int r) {
int last = INT_MAX;
REP3R (i, l, r) {
if (p[i] < last) {
last = p[i];
++ ans;
}
}
});
return ans;
}
int64_t solve(int n, vector<int> p) {
int64_t ans = solve1(n, p);
reverse(ALL(p));
return ans + solve1(n, p);
}
// generated by online-judge-template-generator v4.1.0 (https://github.com/kmyk/online-judge-template-generator)
int main() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
constexpr char endl = '\n';
int N;
cin >> N;
vector<int> p(N);
REP (i, N) {
cin >> p[i];
-- p[i];
}
auto ans = solve(N, p);
cout << ans << endl;
return 0;
}
#line 1 "old/rollback-square-decomposition.yukicoder-1031.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1031"
#line 2 "utils/macros.hpp"
#define REP(i, n) for (int i = 0; (i) < (int)(n); ++ (i))
#define REP3(i, m, n) for (int i = (m); (i) < (int)(n); ++ (i))
#define REP_R(i, n) for (int i = (int)(n) - 1; (i) >= 0; -- (i))
#define REP3R(i, m, n) for (int i = (int)(n) - 1; (i) >= (int)(m); -- (i))
#define ALL(x) std::begin(x), std::end(x)
#line 2 "data_structure/sparse_table.hpp"
#include <cassert>
#include <vector>
#line 5 "data_structure/sparse_table.hpp"
/**
* @brief Sparse Table (idempotent monoid)
* @note the unit is required just for convenience
* @note $O(N \log N)$ space
*/
template <class IdempotentMonoid>
struct sparse_table {
typedef typename IdempotentMonoid::value_type value_type;
std::vector<std::vector<value_type> > table;
IdempotentMonoid mon;
sparse_table() = default;
/**
* @note $O(N \log N)$ time
*/
template <class InputIterator>
sparse_table(InputIterator first, InputIterator last, const IdempotentMonoid & mon_ = IdempotentMonoid())
: mon(mon_) {
table.emplace_back(first, last);
int n = table[0].size();
int log_n = 32 - __builtin_clz(n);
table.resize(log_n, std::vector<value_type>(n));
REP (k, log_n - 1) {
REP (i, n) {
table[k + 1][i] = i + (1ll << k) < n ?
mon.mult(table[k][i], table[k][i + (1ll << k)]) :
table[k][i];
}
}
}
/**
* @note $O(1)$
*/
value_type range_get(int l, int r) const {
if (l == r) return mon.unit(); // if there is no unit, remove this line
assert (0 <= l and l < r and r <= (int)table[0].size());
int k = 31 - __builtin_clz(r - l); // log2
return mon.mult(table[k][l], table[k][r - (1ll << k)]);
}
};
#line 2 "data_structure/segment_tree.hpp"
#include <algorithm>
#line 6 "data_structure/segment_tree.hpp"
/**
* @brief Segment Tree / セグメント木 (monoids, 完全二分木)
* @docs data_structure/segment_tree.md
* @tparam Monoid (commutativity is not required)
*/
template <class Monoid>
struct segment_tree {
typedef typename Monoid::value_type value_type;
Monoid mon;
int n;
std::vector<value_type> a;
segment_tree() = default;
segment_tree(int n_, const Monoid & mon_ = Monoid()) : mon(mon_) {
n = 1; while (n < n_) n *= 2;
a.resize(2 * n - 1, mon.unit());
}
void point_set(int i, value_type b) { // 0-based
assert (0 <= i and i < n);
a[i + n - 1] = b;
for (i = (i + n) / 2; i > 0; i /= 2) { // 1-based
a[i - 1] = mon.mult(a[2 * i - 1], a[2 * i]);
}
}
value_type range_get(int l, int r) { // 0-based, [l, r)
assert (0 <= l and l <= r and r <= n);
value_type lacc = mon.unit(), racc = mon.unit();
for (l += n, r += n; l < r; l /= 2, r /= 2) { // 1-based loop, 2x faster than recursion
if (l % 2 == 1) lacc = mon.mult(lacc, a[(l ++) - 1]);
if (r % 2 == 1) racc = mon.mult(a[(-- r) - 1], racc);
}
return mon.mult(lacc, racc);
}
value_type point_get(int i) { // 0-based
assert (0 <= i and i < n);
return a[i + n - 1];
}
/**
* @note O(min(n, (r - l) log n))
*/
void range_set(int l, int r, value_type b) {
assert (0 <= l and l <= r and r <= n);
range_set(0, 0, n, l, r, b);
}
void range_set(int i, int il, int ir, int l, int r, value_type b) {
if (l <= il and ir <= r and ir - il == 1) { // 0-based
a[i] = b;
} else if (ir <= l or r <= il) {
// nop
} else {
range_set(2 * i + 1, il, (il + ir) / 2, l, r, b);
range_set(2 * i + 2, (il + ir) / 2, ir, l, r, b);
a[i] = mon.mult(a[2 * i + 1], a[2 * i + 2]);
}
}
/**
* @brief a fast & semigroup-friendly version constructor
* @note $O(n)$
*/
template <class InputIterator>
segment_tree(InputIterator first, InputIterator last, const Monoid & mon_ = Monoid()) : mon(mon_) {
int size = std::distance(first, last);
n = 1; while (n < size) n *= 2;
a.resize(2 * n - 1, mon.unit());
std::copy(first, last, a.begin() + (n - 1));
unsafe_rebuild();
}
/**
* @brief update a leaf node without updating ancestors
* @note $O(1)$
*/
void unsafe_point_set(int i, value_type b) { // 0-based
assert (0 <= i and i < n);
a[i + n - 1] = b;
}
/**
* @brief re-build non-leaf nodes from leaf nodes
* @note $O(n)$
*/
void unsafe_rebuild() {
REP_R (i, n - 1) {
a[i] = mon.mult(a[2 * i + 1], a[2 * i + 2]);
}
}
};
#line 3 "monoids/max.hpp"
#include <limits>
template <class T>
struct max_monoid {
typedef T value_type;
value_type unit() const { return std::numeric_limits<T>::lowest(); }
value_type mult(value_type a, value_type b) const { return std::max(a, b); }
};
#line 6 "old/rollback-square-decomposition.yukicoder-1031.test.cpp"
#include <climits>
#include <cmath>
#include <deque>
#include <functional>
#include <iostream>
#include <optional>
#include <tuple>
#include <utility>
#line 15 "old/rollback-square-decomposition.yukicoder-1031.test.cpp"
using namespace std;
#line 1 "old/rollback-square-decomposition.inc.cpp"
/**
* @brief the extended Mo's algorithm
* @arg stupid is called O(Q) times, each length is O(\sqrt{N})
* @arg mo si the following:
* struct rollback_mo_interface {
* void reset(int l); // called O(N) times
* void extend_left( int l, int r); // called O(Q) times, the sum of length is O(N \sqrt {N})
* void extend_right(int l, int r); // called O(Q) times, the sum of length is O(Q \sqrt {N})
* void snapshot(); // called O(Q) times
* void rollback(); // called O(Q) times
* void query(); // called O(Q) times
* };
* @see http://snuke.hatenablog.com/entry/2016/07/01/000000
* @see http://codeforces.com/blog/entry/7383?#comment-161520
*/
template <class Func, class RollbackMoInterface>
void rollback_square_decomposition(int n, vector<pair<int, int> > const & range, RollbackMoInterface & mo, Func stupid) {
int bucket_size = sqrt(n);
int bucket_count = (n + bucket_size - 1) / bucket_size;
vector<vector<int> > bucket(bucket_count);
REP (i, int(range.size())) {
int l, r; tie(l, r) = range[i];
if (r - l <= bucket_size) {
stupid(l, r);
} else {
bucket[l / bucket_size].push_back(i);
}
}
REP (b, bucket_count) {
sort(ALL(bucket[b]), [&](int i, int j) { return range[i].second < range[j].second; });
int l = (b + 1) * bucket_size;
mo.reset(l);
int r = l;
for (int i : bucket[b]) {
int l_i, r_i; tie(l_i, r_i) = range[i];
mo.extend_right(r, r_i);
mo.snapshot();
mo.extend_left(l_i, l);
mo.query();
mo.rollback();
r = r_i;
}
}
}
#line 17 "old/rollback-square-decomposition.yukicoder-1031.test.cpp"
template <class T>
struct rollbackable_deque {
deque<T> data;
vector<pair<char, optional<T> > > history;
rollbackable_deque() = default;
bool empty() const { return data.empty(); }
size_t size() const { return data.size(); }
T operator [] (size_t i) const { return data[i]; }
const T & front() const { return data.front(); }
const T & back() const { return data.back(); }
void push_front(T value) {
history.emplace_back('f', optional<T>());
data.push_front(value);
}
void pop_front() {
history.emplace_back('F', data.front());
data.pop_front();
}
void push_back(T value) {
history.emplace_back('b', optional<T>());
data.push_back(value);
}
void pop_back() {
history.emplace_back('B', data.back());
data.pop_back();
}
void snapshot() {
history.emplace_back('$', optional<T>());
}
void rollback() {
while (history.back().first != '$') {
char op = history.back().first;
optional<T> value = history.back().second;
history.pop_back();
if (op == 'f') {
data.pop_front();
} else if (op == 'F') {
data.push_front(*value);
} else if (op == 'b') {
data.pop_back();
} else if (op == 'B') {
data.push_back(*value);
}
}
history.pop_back();
}
};
struct rollback_mo_inc {
const vector<int> & p;
int64_t & ans;
int l, r;
vector<pair<int, int> > history;
rollbackable_deque<int> deq;
rollback_mo_inc(const vector<int> & p_, int64_t & ans_) : p(p_), ans(ans_) {
reset(0);
}
void reset(int l_) {
l = l_;
r = l_;
history.clear();
deq = rollbackable_deque<int>();
}
void extend_left(int nl, int r) {
for (; nl < l; -- l) {
if (deq.empty() or p[l - 1] < deq.front()) {
deq.push_front(p[l - 1]);
}
}
}
void extend_right(int l, int nr) {
for (; r < nr; ++ r) {
while (not deq.empty() and p[r] < deq.back()) {
deq.pop_back();
}
deq.push_back(p[r]);
}
}
void snapshot() {
deq.snapshot();
history.emplace_back(l, r);
}
void rollback() {
deq.rollback();
tie(l, r) = history.back();
history.pop_back();
}
void query() {
ans += deq.size();
}
};
int64_t solve1(int n, const vector<int> & p) {
vector<pair<int, int> > query_inc;
vector<int> lookup(n);
REP (i, n) {
lookup[p[i]] = i;
}
sparse_table<max_monoid<int> > table(ALL(p));
function<void (int, int)> go = [&](int l, int r) {
if (r - l < 2) return;
int m = lookup[table.range_get(l, r)];
query_inc.emplace_back(l, m);
go(l, m);
go(m + 1, r);
};
go(0, n);
int64_t ans = 0;
rollback_mo_inc interface_inc(p, ans);
rollback_square_decomposition(n, query_inc, interface_inc, [&](int l, int r) {
int last = INT_MAX;
REP3R (i, l, r) {
if (p[i] < last) {
last = p[i];
++ ans;
}
}
});
return ans;
}
int64_t solve(int n, vector<int> p) {
int64_t ans = solve1(n, p);
reverse(ALL(p));
return ans + solve1(n, p);
}
// generated by online-judge-template-generator v4.1.0 (https://github.com/kmyk/online-judge-template-generator)
int main() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
constexpr char endl = '\n';
int N;
cin >> N;
vector<int> p(N);
REP (i, N) {
cin >> p[i];
-- p[i];
}
auto ans = solve(N, p);
cout << ans << endl;
return 0;
}