What is the time complexity of Maximize Y‑Sum by Picking a Triplet of Distinct X‑Values?

The optimal solution for Maximize Y‑Sum by Picking a Triplet of Distinct X‑Values runs in O(n log n) time and uses O(n) space. The time complexity is dominated by sorting the unique y-values, while space is used to store the maximum y-values for distinct x-values.

What is the brute force solution for Maximize Y‑Sum by Picking a Triplet of Distinct X‑Values?

The brute force approach for Maximize Y‑Sum by Picking a Triplet of Distinct X‑Values is Brute Force, with O(n²) time complexity and O(1) space complexity. We can check every combination of three indices to find the maximum sum of y-values. This method is straightforward but inefficient for large arrays. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Maximize Y‑Sum by Picking a Triplet of Distinct X‑Values?

Maximize Y‑Sum by Picking a Triplet of Distinct X‑Values uses the following concepts: Array, Hash Table, Greedy, Sorting, Heap (Priority Queue). The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Maximize Y‑Sum by Picking a Triplet of Distinct X‑Values?

Explain your thought process clearly. Discuss edge cases upfront. Optimize before coding.

What are common mistakes when solving Maximize Y‑Sum by Picking a Triplet of Distinct X‑Values?

Not checking for distinct x-values. Forgetting to handle cases with fewer than three distinct x-values.

#3572

Maximize Y‑Sum by Picking a Triplet of Distinct X‑Values

Medium

ArrayHash TableGreedySortingHeap (Priority Queue)Hash MapArray

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)

By storing the maximum y-value for each unique x-value, we can efficiently find the top three distinct x-values and their corresponding y-values to maximize the sum.

⚙️

Algorithm

3 steps

1Step 1: Create a dictionary to store the maximum y-value for each unique x-value.
2Step 2: Iterate through the arrays and populate the dictionary.
3Step 3: Extract the top three maximum y-values from the dictionary and return their sum.

solution.py8 lines

1def max_y_sum_optimal(x, y):
2    from collections import defaultdict
3    max_y = defaultdict(int)
4    for xi, yi in zip(x, y):
5        max_y[xi] = max(max_y[xi], yi)
6    if len(max_y) < 3:
7        return -1
8    return sum(sorted(max_y.values(), reverse=True)[:3])

ℹ

Complexity note: The time complexity is dominated by sorting the unique y-values, while space is used to store the maximum y-values for distinct x-values.

1Use a dictionary to track maximum values for unique keys.
2Sorting helps in quickly finding the top values.

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