Dynamic Programming is the correct answer to find the solution of the problem in minimum time.



Dynamic Programming is a programming paradigm that involves solving complex problems by breaking them down into simpler subproblems and storing the intermediate results for future use. It is particularly useful when the problem has overlapping subproblems, as it avoids redundant computation by using memoization or tabulation.



1. Define the subproblem: In this problem, the subproblem can be defined as finding a subset of the given set with a sum equal to a specific value K.

2. Identify the base case: The base case in this problem is when the sum of the subset is equal to K. If the sum is equal to K, we can return true as we have found a subset that satisfies the given condition.

3. Define the recurrence relation: The recurrence relation in this problem can be defined as follows:
- If the last element of the set is greater than K, we ignore it and recur for the remaining elements.
- Otherwise, we have two choices:
- Include the last element in the subset and recur for the remaining elements with the reduced sum (K - last element).
- Exclude the last element from the subset and recur for the remaining elements with the same sum (K).

4. Build the DP table: We can create a 2D DP table to store the intermediate results. The rows of the table represent the elements of the set, and the columns represent the possible sums from 0 to K. Each cell (i, j) of the table represents whether there exists a subset of the first i elements with a sum equal to j.

5. Fill in the DP table: We can fill in the DP table using the recurrence relation. Starting from the first row and column, we can iterate over the elements of the set and the possible sums. If the last element is greater than the current sum, we can simply copy the value from the previous row. Otherwise, we can use the recurrence relation to calculate the value for the current cell.

6. Return the result: Finally, we can return the value in the last cell of the DP table, which represents whether there exists a subset with a sum equal to K.



- Efficiently solves problems with overlapping subproblems.
- Avoids redundant computation by storing intermediate results.
- Can have better time complexity compared to other paradigms like Divide and Conquer in certain cases.



Dynamic Programming is a powerful paradigm for solving problems with overlapping subproblems. In this specific problem, it can be used to efficiently find a subset of a given set with a sum equal to a specific value K. By breaking down the problem into smaller subproblems and using memoization or tabulation to store intermediate results, Dynamic Programming can provide a solution in minimum time.