How do you solve Maximum Median Sum of Subsequences of Size 3 on LeetCode?

Maximum Median Sum of Subsequences of Size 3 (LeetCode #3627) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(1) space complexity. Key insight: Sorting helps in easily accessing medians.

What is the time complexity of Maximum Median Sum of Subsequences of Size 3?

The optimal solution for Maximum Median Sum of Subsequences of Size 3 runs in O(n log n) time and uses O(1) space. Sorting the array takes O(n log n), and iterating through the array takes O(n), leading to an overall efficient solution.

What is the brute force solution for Maximum Median Sum of Subsequences of Size 3?

The brute force approach for Maximum Median Sum of Subsequences of Size 3 is Brute Force, with O(n²) time complexity and O(1) space complexity. Select all possible combinations of three elements, compute their medians, and track the maximum sum. This approach is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Maximum Median Sum of Subsequences of Size 3?

Maximum Median Sum of Subsequences of Size 3 uses the following concepts: Array, Math, Greedy, Sorting, Game Theory. The recommended patterns to study are: Greedy, Sorting.

What are the interview tips for Maximum Median Sum of Subsequences of Size 3?

Explain your thought process clearly. Use examples to illustrate your approach. Practice similar problems for confidence.

What are common mistakes when solving Maximum Median Sum of Subsequences of Size 3?

Not sorting the array before selection. Confusing median selection in triplets.

#3627

Maximum Median Sum of Subsequences of Size 3

Medium

ArrayMathGreedySortingGame TheoryGreedySorting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n log n)Space O(1)

Sort the array and strategically select elements to maximize the median sum. The optimal choice is to take the largest two and the smallest one in each step.

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Algorithm

3 steps

1Step 1: Sort the array in non-decreasing order.
2Step 2: Select elements starting from the end of the array, taking the last two and the first one in each group of three.
3Step 3: Sum the medians (the second largest of each selected triplet) to get the maximum median sum.

solution.py4 lines

1def maxMedianSum(nums):
2    nums.sort()
3    n = len(nums)
4    return sum(nums[n//3 + i] for i in range(n // 3))

ℹ

Complexity note: Sorting the array takes O(n log n), and iterating through the array takes O(n), leading to an overall efficient solution.

1Sorting helps in easily accessing medians.
2Selecting strategically maximizes the sum.

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