This documentation is automatically generated by online-judge-tools/verification-helper
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/courses/library/7/DPL/1/DPL_1_D"
#include <bits/stdc++.h>
#include "ugilib/base/constants.hpp"
#include "ugilib/base/definitions.hpp"
#include "ugilib/dp/lis.hpp"
using namespace std;
// debug settings
// #define DEBUG
#ifdef DEBUG
// debug input
string _INPUT = R"(
5
1 2 3 4 5
)";
auto _cin = stringstream(_INPUT.substr(1)); // remove '\n' at _INPUT[0]
#else
// standard input
auto& _cin = cin;
#endif
// speed up
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
// reader
struct rd {
// T
template<typename T> static T i() { T x; _cin >> x; return x; } // T item
// vector<T>
template<typename T> static vector<T> v(int n) {vector<T> v(n); rep(i, n) _cin >> v[i]; return v;} // vector<T>
// vector<pair<T, T>>
template<typename T> static vector<pair<T, T>> vp(int n) {vector<pair<T, T>> v(n); rep(i, n) _cin >> v[i].first >> v[i].second; return v;} // vector<pair<T, T>>
// tuple
template<typename... Args> static tuple<Args...> t() {
tuple<Args...> values;
apply([](auto&... args) { ((_cin >> args), ...); }, values);
return values;
}
};
// debug print utility
namespace deb {
#include <cxxabi.h>
// demangle type name
string demangle(const char* name) {
int status = -4;
unique_ptr<char, void(*)(void*)> res{
abi::__cxa_demangle(name, NULL, NULL, &status),
free
};
return (status == 0) ? string(res.get()) : name ;
}
// meta functions for type traits
template<typename T>
constexpr bool isArithmeticContainer() { return is_arithmetic<typename T::value_type>::value; }
// for SFINAE
template<typename T, typename = void> struct has_key_and_mapped_type : false_type {};
template<typename T> struct has_key_and_mapped_type<T, void_t<typename T::key_type, typename T::mapped_type>> : true_type {};
// for map or unordered_map
template<typename T>
constexpr bool isMapLike() { return has_key_and_mapped_type<T>::value; }
// for values
template<typename T, typename enable_if<is_arithmetic<T>::value, nullptr_t>::type = nullptr>
void p(const T& x) { cout << x << " "; }
// for pairs
template <typename T, typename S>
void p(const pair<T, S>& _p){ p(_p.first); p(_p.second); cout << endl; }
// for string
void p(const string& s) { cout << s << endl; }
// for containers
template<typename T, typename enable_if<!is_arithmetic<T>::value, nullptr_t>::type = nullptr>
void p(const T& container) {
// map and unordered_map
if constexpr (isMapLike<T>()) {
cout << demangle(typeid(T).name()) << ":" << endl;
for (const auto& kv : container) {
cout << "[" << kv.first << "] => ";
p(kv.second);
if constexpr (is_arithmetic_v<typename T::mapped_type>) cout << endl;
}
// vector or set or others
} else {
if constexpr (!isArithmeticContainer<T>()) cout << demangle(typeid(T).name()) << ":" << endl;
for (auto it = begin(container); it != end(container); ++it) {
p(*it);
}
if constexpr (isArithmeticContainer<T>()) cout << endl;
}
}
}; // namespace deb
int main() {
auto& cin = _cin;
// speed up io
cin.tie(nullptr);
ios::sync_with_stdio(false);
// code
int n = rd::i<int>();
vector<int> A = rd::v<int>(n);
auto [ans, lis] = ugilib::longest_increasing_subsequence(A);
// deb::p(lis);
cout << ans << endl;
return 0;
}
#line 1 "tests/dp/lis.test.cpp"
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/courses/library/7/DPL/1/DPL_1_D"
#include <bits/stdc++.h>
#line 2 "ugilib/base/definitions.hpp"
using ll = long long;
using ull = unsigned long long;
using ld = long double;
#define rep(i, n) for(size_t i = 0; i < n; i++) // rep macro
#define all(v) begin(v), end(v) // all iterator
#line 3 "ugilib/base/constants.hpp"
namespace ugilib::constants {
template<typename T>
inline constexpr T INF = std::numeric_limits<T>::max() / 2;
} // namespace ugilib::constants
const ll INF = ugilib::constants::INF<ll>;
#line 4 "ugilib/dp/lis.hpp"
using namespace std;
namespace ugilib {
/**
* @brief 最長増加部分列
* @tparam T vectorの要素の型
* @param A vector
* @param inf 無限大
* @return pair<size_t, vector<T>> (最長増加部分列の長さ, 最長増加部分列(一意ではない))
* @note O(n log n). n = A.size()
*/
template <typename T>
pair<size_t, vector<T>> longest_increasing_subsequence(const vector<T> &A, const T inf = ugilib::constants::INF<T>) {
static_assert(is_signed<T>::value, "T must be signed type."); // Tは符号付き型である必要がある
// dp[i]: 長さがiであるような増加部分列の最後の要素の最小値
vector<T> dp(A.size() + 1, inf); // 1-indexed
vector<size_t> indices(A.size()); // indices[i]: A[i]がdpのどこに入るか
dp[0] = -1;
for (size_t i = 0; i < A.size(); i++) {
size_t idx = lower_bound(dp.begin(), dp.end(), A[i]) - dp.begin();
dp[idx] = A[i];
indices[i] = idx;
}
// infの手前まで部分増加列の最終要素が入っている
const size_t lis_length = find(dp.begin(), dp.end(), inf) - dp.begin() - 1;
// 部分増加列の復元
vector<T> lis(lis_length);
size_t target = lis_length;
for (int i = A.size() - 1; i >= 0; i--) if (indices[i] == target) lis[--target] = A[i];
return {lis_length, lis};
}
} // namespace ugilib
#line 7 "tests/dp/lis.test.cpp"
using namespace std;
// debug settings
// #define DEBUG
#ifdef DEBUG
// debug input
string _INPUT = R"(
5
1 2 3 4 5
)";
auto _cin = stringstream(_INPUT.substr(1)); // remove '\n' at _INPUT[0]
#else
// standard input
auto& _cin = cin;
#endif
// speed up
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
// reader
struct rd {
// T
template<typename T> static T i() { T x; _cin >> x; return x; } // T item
// vector<T>
template<typename T> static vector<T> v(int n) {vector<T> v(n); rep(i, n) _cin >> v[i]; return v;} // vector<T>
// vector<pair<T, T>>
template<typename T> static vector<pair<T, T>> vp(int n) {vector<pair<T, T>> v(n); rep(i, n) _cin >> v[i].first >> v[i].second; return v;} // vector<pair<T, T>>
// tuple
template<typename... Args> static tuple<Args...> t() {
tuple<Args...> values;
apply([](auto&... args) { ((_cin >> args), ...); }, values);
return values;
}
};
// debug print utility
namespace deb {
#include <cxxabi.h>
// demangle type name
string demangle(const char* name) {
int status = -4;
unique_ptr<char, void(*)(void*)> res{
abi::__cxa_demangle(name, NULL, NULL, &status),
free
};
return (status == 0) ? string(res.get()) : name ;
}
// meta functions for type traits
template<typename T>
constexpr bool isArithmeticContainer() { return is_arithmetic<typename T::value_type>::value; }
// for SFINAE
template<typename T, typename = void> struct has_key_and_mapped_type : false_type {};
template<typename T> struct has_key_and_mapped_type<T, void_t<typename T::key_type, typename T::mapped_type>> : true_type {};
// for map or unordered_map
template<typename T>
constexpr bool isMapLike() { return has_key_and_mapped_type<T>::value; }
// for values
template<typename T, typename enable_if<is_arithmetic<T>::value, nullptr_t>::type = nullptr>
void p(const T& x) { cout << x << " "; }
// for pairs
template <typename T, typename S>
void p(const pair<T, S>& _p){ p(_p.first); p(_p.second); cout << endl; }
// for string
void p(const string& s) { cout << s << endl; }
// for containers
template<typename T, typename enable_if<!is_arithmetic<T>::value, nullptr_t>::type = nullptr>
void p(const T& container) {
// map and unordered_map
if constexpr (isMapLike<T>()) {
cout << demangle(typeid(T).name()) << ":" << endl;
for (const auto& kv : container) {
cout << "[" << kv.first << "] => ";
p(kv.second);
if constexpr (is_arithmetic_v<typename T::mapped_type>) cout << endl;
}
// vector or set or others
} else {
if constexpr (!isArithmeticContainer<T>()) cout << demangle(typeid(T).name()) << ":" << endl;
for (auto it = begin(container); it != end(container); ++it) {
p(*it);
}
if constexpr (isArithmeticContainer<T>()) cout << endl;
}
}
}; // namespace deb
int main() {
auto& cin = _cin;
// speed up io
cin.tie(nullptr);
ios::sync_with_stdio(false);
// code
int n = rd::i<int>();
vector<int> A = rd::v<int>(n);
auto [ans, lis] = ugilib::longest_increasing_subsequence(A);
// deb::p(lis);
cout << ans << endl;
return 0;
}