From a1d248ef0e4005bba92d800622df0b445b25e691 Mon Sep 17 00:00:00 2001
From: Neeraj Pathak <73093507+Nucleoo@users.noreply.github.com>
Date: Mon, 19 Oct 2020 12:19:24 +0530
Subject: [PATCH] LIS(nlogn).cpp

Algorithm for finding the length of the Longest Increasing Subsequence in O(NlogN)
---
 dynamic_programming/LIS(nlogn).cpp | 55 ++++++++++++++++++++++++++++++
 1 file changed, 55 insertions(+)
 create mode 100644 dynamic_programming/LIS(nlogn).cpp

diff --git a/dynamic_programming/LIS(nlogn).cpp b/dynamic_programming/LIS(nlogn).cpp
new file mode 100644
index 00000000..2a139b74
--- /dev/null
+++ b/dynamic_programming/LIS(nlogn).cpp
@@ -0,0 +1,55 @@
+#include <bits/stdc++.h>
+using namespace std;
+const int N=2e5+5;
+//const int mod = 998244353;
+const int mod = 1e9+7;
+#define pb push_back
+#define mp make_pair
+#define sz size
+#define fi first
+#define se second
+#define nl "\n"
+#define ps(x) fixed<<setprecision(x)
+#define all(x) (x).begin(), (x).end()
+int gcd(int a, int b) { return b?gcd(b,a%b):a; }
+//*****************************************************************************************//
+int LIS(vector<int>& arr, int n) {
+    if(n<=1) return n;
+    vector<int>dp; 
+    dp.push_back(arr[0]);
+    for(int i=1; i<n; i++){
+        if(dp.back()<arr[i])
+            dp.push_back(arr[i]);
+        else{
+            int j=lower_bound(dp.begin(), dp.end(), arr[i])-dp.begin();
+            dp[j]=arr[i];
+         }
+    }
+    return dp.size();
+}
+void code(){	
+	int n; cin>>n;
+	vector<int>arr(n);
+	for(int i=0; i<n; i++){
+		cin>>arr[i];
+	}
+	int res=LIS(arr, n);
+	cout<<res<<nl;
+}
+
+int main(){
+	ios_base::sync_with_stdio(false);
+	cin.tie(NULL); cout.tie(NULL);
+	#ifndef ONLINE_JUDGE
+	  freopen("input.txt", "r", stdin);
+	  	freopen("output.txt", "w", stdout);
+	#endif
+
+	int T=1; //cin>>T;
+	for(int i=1; i<=T; i++) code();
+	
+	#ifndef ONLINE_JUDGE
+    	cerr<<"Actual : "<<1.0*clock()/CLOCKS_PER_SEC<<" sec\n";
+	#endif
+	return 0;
+}