Check if there exists a subsequence with sum K

Slug: check-if-there-exists-a-subsequence-with-sum-k

Difficulty: Medium

Id: 712211

Topic Tags: None

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Summary

Given an array of integers, we need to find out whether there exists a subsequence in the given array with sum equal to K. A subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.

Detailed Explanation

The problem involves finding a subsequence in the given array whose sum equals K. We will use a dynamic programming approach for this solution. Let's initialize an array dp of size K + 1, where dp[i] represents whether there exists a subsequence with sum equal to i.

Here are the steps:

• Initialize dp[0] = true, since an empty subsequence has a sum of 0.
• Iterate over the given array. For each element, update the dp array as follows:
  • If the current element is greater than K, then we don't need to consider it in our subsequence, so dp[i + arr[i]] = dp[i] for all i <= K - arr[i].
  • Otherwise, update dp[i + arr[i]] = true, since we have found a new way to reach sum i + arr[i].

At the end of this process, check if dp[K] is true. If it is, then there exists a subsequence with sum K. Otherwise, return false.

Time complexity: O(n), where n is the size of the given array. Space complexity: O(K), since we are using an array of size K + 1 to store our dynamic programming table.

Optimized Solutions

Java