Subset Sum Equal To K

Moderate

0/80

Average time to solve is 30m

492 upvotes

Asked in companies

Problem statement

You are given an array/list ‘ARR’ of ‘N’ positive integers and an integer ‘K’. Your task is to check if there exists a subset in ‘ARR’ with a sum equal to ‘K’.

Note: Return true if there exists a subset with sum equal to ‘K’. Otherwise, return false.

For Example :

If ‘ARR’ is {1,2,3,4} and ‘K’ = 4, then there exists 2 subsets with sum = 4. These are {1,3} and {4}. Hence, return true.

Detailed explanation ( Input/output format, Notes, Images )

Input Format :

The first line contains a single integer T representing the number of test cases.

The first line of each test case contains two space-separated integers ‘N’ and ‘K’ representing the size of the input ‘ARR’ and the required sum as discussed above.

The next line of each test case contains ‘N’ single space-separated integers that represent the elements of the ‘ARR’.

Output Format :

For each test case, return true or false as discussed above.
Output for each test case will be printed in a separate line.

Note:

You don’t need to print anything, it has already been taken care of. Just implement the given function.

Constraints:

1 <= T <= 5
1 <= N <= 10^3
0 <= ARR[i] <= 10^9
0 <= K <= 10^3

Time Limit: 1 sec

Sample Input 1:

Sample Output 1:

true
false

Explanation For Sample Input 1:

In example 1, ‘ARR’ is {4,3,2,1} and ‘K’ = 5. There exist 2 subsets with sum = 5. These are {4,1} and {3,2}. Hence, return true.
In example 2, ‘ARR’ is {2,5,1,6,7} and ‘K’ = 4. There are no subsets with sum = 4. Hence, return false.

Sample Input 2:

Sample Output 2:

true
false

Explanation For Sample Input 2:

In example 1, ‘ARR’ is {6,1,2,1} and ‘K’ = 4. There exist 1 subset with sum = 4. That is {1,2,1}. Hence, return true.
In example 2, ‘ARR’ is {1,7,2,9,10} and ‘K’ = 6. There are no subsets with sum = 6. Hence, return false.

Hints:

1. Can you find every possible subset of ‘ARR’ and check if its sum is equal to ‘K’?
2. Can you use dynamic programming and use the previously calculated result to calculate the new result?
3. Try to use a recursive approach followed by memoization by including both index and sum we can form.

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