LIS.cpp

/*--------------------------"SABUJ-JANA"------"JADAVPUR UNIVERSITY"--------*/
/*-------------------------------@greenindia-----------------------------------*/
//
//		  _____       _           _        _
//		 / ____|     | |         (_)      | |
//		| (___   __ _| |__  _   _ _       | | __ _ _ __   __ _
//		 \___ \ / _` | '_ \| | | | |  _   | |/ _` | '_ \ / _` |
//		 ____) | (_| | |_) | |_| | | | |__| | (_| | | | | (_| |
//		|_____/ \__,_|_.__/ \__,_| |  \____/ \__,_|_| |_|\__,_|
//		                        _/ |
//		                       |__/
/*---------------------- Magic. Do not touch.-----------------------------*/
/*------------------------------God is Great/\---------------------------------*/
#include <bits/stdc++.h>
using namespace std;
#define crap ios::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL)
//cout<<fixed<<showpoint<<setprecision(12)<<ans<<endl;
#define int long long int
#define double long double
#define PI acos(-1)

void print1d(const vector<int>& vec) {for (auto val : vec) {cout << val << " ";} cout << endl;}

void print2d(const vector<vector<int>>& vec) {for (auto row : vec) {for (auto val : row) {cout << val << " ";} cout << endl;}}

int lenLIS(const vector<int>& arr) {
	int n = arr.size();
	if (n == 0)
		return 0;
	vector<int> seq;
	seq.push_back(arr[0]);

	for (int i = 0; i < n; ++i) {
		if (seq.back() < arr[i])
			seq.push_back(arr[i]);
		else {
			int ind = lower_bound(seq.begin(), seq.end(), arr[i]) - seq.begin();
			seq[ind] = arr[i];
		}
	}

	return seq.size();
}

signed main() {
#ifndef ONLINE_JUDGE
	freopen("input.txt", "r", stdin);
	freopen("error.txt", "w", stderr);
#endif
	crap;

	vector<int> arr = {2, 3, 4, 1, 7 , 8, 10, 5, 6};
	cout << lenLIS(arr) << endl;

	return 0;
}