From cf9fed5b11a9c33c838d3114de8a123701b7e27d Mon Sep 17 00:00:00 2001
From: Akshat Sharma <83509798+akshatsh0610@users.noreply.github.com>
Date: Fri, 6 Dec 2024 23:14:03 +0530
Subject: [PATCH] Update longest_increasing_subsequence.cpp

Added Memoization method to longest_increasing_subsequence.cpp
---
 .../longest_increasing_subsequence.cpp        | 26 +++++++++++++++++--
 1 file changed, 24 insertions(+), 2 deletions(-)

diff --git a/algorithms/dynamic-programming/longest_increasing_subsequence.cpp b/algorithms/dynamic-programming/longest_increasing_subsequence.cpp
index 55073440..db002ccb 100644
--- a/algorithms/dynamic-programming/longest_increasing_subsequence.cpp
+++ b/algorithms/dynamic-programming/longest_increasing_subsequence.cpp
@@ -1,6 +1,7 @@
 #include <iostream>
+#include <vector>
 using namespace std;
-int longestIncreasingSubsequence(int A[],int size){
+int longestIncreasingSubsequenceThroughTabulation(int A[],int size){
     int dp[size];
     for(int i=0;i<size;i++) dp[i] = 1;
     for(int i=1;i<size;i++){
@@ -17,9 +18,30 @@ int longestIncreasingSubsequence(int A[],int size){
     
     return lis;
 }
+int longestIncreasingSubsequenceThroughMemoization(int A[],int idx,int prev,int size,vector<vector<int>>&dp){
+	if(idx>=size)
+		return 0;
+	if(dp[idx][prev+1]!=-1){
+		return dp[idx][prev+1];
+	}
+	int choise1=0;
+	int choise2=0;
+	if(prev==-1){
+		choise1=1+longestIncreasingSubsequenceThroughMemoization(A,idx+1,idx,size);
+	}
+	if(A[prev]<A[idx]){
+		choise1=1+longestIncreasingSubsequenceThroughMemoization(A,idx+1,idx,size);
+	}
+	choise2=longestIncreasingSubsequenceThroughMemoization(A,idx+1,prev,size);
+	return dp[idx][prev+1]=max(choise1,choise2);	
+}
 int main() {
 	
 	int A[] = {1,3,5,9,8};
-	cout<<longestIncreasingSubsequence(A,5);
+	cout<<"Tabulation -> "<<endl;
+	cout<<longestIncreasingSubsequenceThroughTabulation(A,5)<<endl;
+	vector<vector<int>>dp(size,vector<int>(size,-1));
+	cout<<"Memoization -> "<<endl;
+	cout<<longestIncreasingSubsequenceThroughMemoization(A,0,-1,5,dp)<<endl;
 	return 0;
 }