longest_increasing_sequence
(src/dp/longest_increasing_sequence.hpp)

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• Last update: 2025-02-27 04:36:58+09:00
• Include: #include "src/dp/longest_increasing_sequence.hpp"

longest_increasing_sequence

vector<int> longest_increasing_sequence(vector<T> a)

長さ $n$ の配列 a の最長増加部分列 lcp を計算します．
lcp[i] は，最長増加部分列の $i$ 番目の要素の添え字を表します．

計算量

• $O(n \log n)$

Depends on

• template (src/template/template.hpp)

Verified with

• verify/library_checker/other/longest_increasing_sequence.test.cpp

Code

#pragma once
#include "../template/template.hpp"
template <typename T>
vector<int> longest_increasing_sequence(const vector<T>& a) {
    const int n = a.size();
    vector<pair<T, int>> dp;
    vector<int> p(n, -1);
    for(int i = 0; i < n; ++i) {
        auto it = lower_bound(begin(dp), end(dp), make_pair(a[i], -i));
        if(it != begin(dp)) p[i] = -prev(it)->second;
        if(it == end(dp)) {
            dp.emplace_back(a[i], -i);
        } else {
            *it = make_pair(a[i], -i);
        }
    }
    vector<int> res;
    for(int i = -dp.back().second; i != -1; i = p[i]) res.push_back(i);
    reverse(begin(res), end(res));
    return res;
}

#line 2 "src/template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using P = pair<long long, long long>;
#define rep(i, a, b) for(long long i = (a); i < (b); ++i)
#define rrep(i, a, b) for(long long i = (a); i >= (b); --i)
constexpr long long inf = 4e18;
struct SetupIO {
    SetupIO() {
        ios::sync_with_stdio(0);
        cin.tie(0);
        cout << fixed << setprecision(30);
    }
} setup_io;
#line 3 "src/dp/longest_increasing_sequence.hpp"
template <typename T>
vector<int> longest_increasing_sequence(const vector<T>& a) {
    const int n = a.size();
    vector<pair<T, int>> dp;
    vector<int> p(n, -1);
    for(int i = 0; i < n; ++i) {
        auto it = lower_bound(begin(dp), end(dp), make_pair(a[i], -i));
        if(it != begin(dp)) p[i] = -prev(it)->second;
        if(it == end(dp)) {
            dp.emplace_back(a[i], -i);
        } else {
            *it = make_pair(a[i], -i);
        }
    }
    vector<int> res;
    for(int i = -dp.back().second; i != -1; i = p[i]) res.push_back(i);
    reverse(begin(res), end(res));
    return res;
}

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