Added LIS O(nlogn)

Dynamic Programming/Longest Increasing Subsequence (nlogn).cpp

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+//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;
+}