How do you solve Find Subsequence of Length K With the Largest Sum on LeetCode?

Find Subsequence of Length K With the Largest Sum (LeetCode #2099) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(n) space complexity. Key insight: Sorting the array helps in efficiently finding the largest elements.

What is the time complexity of Find Subsequence of Length K With the Largest Sum?

The optimal solution for Find Subsequence of Length K With the Largest Sum runs in O(n log n) time and uses O(n) space. The sorting step dominates the time complexity, making it O(n log n). The space complexity is O(n) due to storing the indexed elements.

What is the brute force solution for Find Subsequence of Length K With the Largest Sum?

The brute force approach for Find Subsequence of Length K With the Largest Sum is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves generating all possible subsequences of length k and calculating their sums. This method is straightforward but inefficient for larger arrays. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Find Subsequence of Length K With the Largest Sum?

Find Subsequence of Length K With the Largest Sum uses the following concepts: Array, Hash Table, Sorting, Heap (Priority Queue). The recommended patterns to study are: Sorting, Greedy Algorithms.

What are the interview tips for Find Subsequence of Length K With the Largest Sum?

Always clarify if the order of elements matters in the subsequence. Discuss your thought process and approach before jumping into coding. Consider edge cases, such as all negative numbers or duplicates.

What are common mistakes when solving Find Subsequence of Length K With the Largest Sum?

Not considering the order of elements in the subsequence. Forgetting to handle negative numbers correctly.

#2099

Find Subsequence of Length K With the Largest Sum

Easy

ArrayHash TableSortingHeap (Priority Queue)SortingGreedy Algorithms

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(1)	O(n)

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Intuition

Time O(n log n)Space O(n)

To find the largest sum subsequence of length k, we can sort the array and select the largest k elements. This is efficient because we are directly targeting the elements that contribute to the maximum sum.

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Algorithm

3 steps

1Step 1: Sort the array while keeping track of the original indices.
2Step 2: Select the largest k elements from the sorted array.
3Step 3: Sort the selected elements based on their original indices to maintain the subsequence order.

solution.py6 lines

1def max_sum_subsequence(nums, k):
2    indexed_nums = list(enumerate(nums))
3    indexed_nums.sort(key=lambda x: x[1], reverse=True)
4    top_k = indexed_nums[:k]
5    top_k.sort(key=lambda x: x[0])
6    return [num for index, num in top_k]

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Complexity note: The sorting step dominates the time complexity, making it O(n log n). The space complexity is O(n) due to storing the indexed elements.

1Sorting the array helps in efficiently finding the largest elements.
2Maintaining the original indices is crucial to ensure the subsequence order.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.