FIX MakeContributions#1276 Added to the Dynamic programming folder in…

… cpp

algorithms/CPlusPlus/Dynamic-Programming/Longest-Increasing-Subsequence.cpp

@@ -0,0 +1,35 @@
+//We are given an array arr[] , we have to find the longest increasing subsequecne ,
+//Subsequence is descirbed as all elements of the subsequence are in increaseing order
+// ex. arr[]=[4,6,2,8]  lis= 3 (4,6,8)
+//brute force: generate all the subsequence and return the longest such subsequence
+//time complexity . 2^n
+//optimal approach is Dynamic Programming  time complexity O(N*N) where N is the lenght of the array
+//space complexity is O(N*N)+O(N)
+// code..
+
+#include <bits/stdc++.h>
+using namespace std;
+
+int solve(int arr[], int n, int ind, int prev,vector<vector<int>>&dp){
+    if(ind==n){
+        return 0;
+    }
+    if(dp[ind][prev+1]!=-1)return dp[ind][prev+1];
+    int nottake=0+solve(arr,n,ind+1,prev,dp);
+    int take=0;
+    if(prev==-1||arr[ind]>arr[prev]){
+        take=1+solve(arr,n,ind+1,ind,dp);
+    }
+    return dp[ind][prev+1]=max(nottake,take);
+
+}
+int lis(int arr[],int n){
+    vector<vector<int>>dp(n,vector<int>(n+1,-1));
+    return solve(arr,n,0,-1,dp);
+}
+int main(){
+    int arr[]={11,24,9,4,0,22,29};
+    int n=sizeof(arr)/sizeof(arr[0]);
+    cout<<"the length of longest increase subsequence is "<<lis(arr,n);
+    return 0;
+}