Update longest_increasing_subsequence.cpp

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;
 }