TheAlgorithms-C-Plus-Plus/Dynamic Programming/Longest Increasing Subsequence (nlogn).cpp

//Program to calculate length of longest increasing subsequence in an array
// in O(n log n)
// tested on : https://cses.fi/problemset/task/1145/

#include <bits/stdc++.h>
using namespace std;
int LIS(int arr[], int n)
{
	set<int> active;  // The current built LIS.
	active.insert(arr[0]);
	// Loop through every element.
	for(int i=1; i<n; ++i){
		auto get = active.lower_bound(arr[i]);
		if( get == active.end() ){ active.insert(arr[i]); } // current element is the greatest so LIS increases by 1.
		else{
			int val = *get;   // we find the position where arr[i] will be in the LIS. If it is in the LIS already we do nothing
			if( val > arr[i] ){
				// else we remove the bigger element and add a smaller element (which is arr[i]) and continue;
				active.erase(get);
				active.insert(arr[i]);
			}
		}
	}
	return active.size(); // size of the LIS.
}
int main(int argc, char const *argv[])
{
	int n;
	cout << "Enter size of array: ";
	cin >> n;
	int a[n];
	cout << "Enter array elements: ";
	for (int i = 0; i < n; ++i)
	{
		cin >> a[i];
	}
	cout << LIS(a, n) << endl;
	return 0;
}