Perfect Sum Problem DP solution Recursion Memoization & Top Down Approach Hello World

In this video on Recursion and DP, part of the DATA STRUCTURE & ALGORITHM series, we will solve a Problem stated as the "Perfect Sum Problem" by using Recursion and Memoization in DP
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🟠 Perfect Sum Problem
Given an array arr[] of non-negative integers and an integer sum, the task is to count all subsets of the given array with a sum equal to a given sum. Note: The answer can be very large, so, output answer modulo 109+7
Input: N = 6, arr[] = {2, 3, 5, 6, 8, 10} sum = 10
Output: 3
Explanation: {2, 3, 5}, {2, 8}, {10}
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Comment "#Princebhai" if you read this 😉😉

[@sreyashisaha6852]

Thanks a lot for the clearing of initialization concept. You gave the only video which clarified it. All other videos are using top-down approach which I am not comfortable in. Super grateful!

[@shuvbhowmickbestin]

Instead of so many base cases we can simply initialise the 2D array like this and then replace the base cases with the fist line that you've written:
double [,] dp = new double [n+1, sum+1];
dp[0,0] = 1;
for (int j=1; j

[@ritikshandilya7075]

great explanation , thanks

[@advitkothari7302]

much helpful vid sir!

[@shantanu2322]

thank you brother

[@shadabkalim9102]

bhaIyya i want to meet u, im studying in bits pilani and i came to ranchi during summer vacations, i heard u also live in ranchi, big fan, please reply to this comment!

[@gauravmishra8782]

thank you sir...

[@HelloWorldbyprince]

Most welcome

[@deepak-ly3ob]

Thanks sir

[@HelloWorldbyprince]

Welcome

[@ahadkhan8872]

Top Down Approach :
vector dp(n+1,vector(sum+1,-1));
int zero=0;
for(int i=0;i

[@esmamanyt7048]

recursive solutin bana but optimization nahi howa

[@AhmadKaif-rv2df]

int helper(int i,int arr[], int n, int sum,vector &dp){
//base case
if(i>=n){
if(sum == 0){
return 1;
}else return 0;
}
if(dp[i][sum] != -1){
return dp[i][sum];
}
int take=0;
if(arr[i]

[@sakshamshrivastava3482]

bhai samajh nhi aaya