How do you solve Maximum Elegance of a K-Length Subsequence on LeetCode?

Maximum Elegance of a K-Length Subsequence (LeetCode #2813) 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 items by profit helps prioritize high-value selections.

What is the time complexity of Maximum Elegance of a K-Length Subsequence?

The optimal solution for Maximum Elegance of a K-Length Subsequence runs in O(n log n) time and uses O(n) space. The time complexity is O(n log n) due to sorting the items. The space complexity is O(n) for storing the items and the distinct categories.

What is the brute force solution for Maximum Elegance of a K-Length Subsequence?

The brute force approach for Maximum Elegance of a K-Length Subsequence is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves generating all possible subsequences of size k and calculating their elegance. This method is straightforward but inefficient due to the exponential number of combinations. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Maximum Elegance of a K-Length Subsequence?

Maximum Elegance of a K-Length Subsequence uses the following concepts: Array, Hash Table, Stack, Greedy, Sorting, Heap (Priority Queue). The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Maximum Elegance of a K-Length Subsequence?

Clearly explain your thought process while solving. Discuss the trade-offs of different approaches. Practice coding the solution to ensure fluency.

What are common mistakes when solving Maximum Elegance of a K-Length Subsequence?

Not considering distinct categories when calculating elegance. Overlooking the importance of sorting before selection.

#2813

Maximum Elegance of a K-Length Subsequence

Hard

ArrayHash TableStackGreedySortingHeap (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)

💡

Intuition

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

The optimal approach involves sorting the items by profit and using a greedy strategy to select the top profits while maximizing distinct categories. This reduces the number of combinations we need to consider.

⚙️

Algorithm

4 steps

1Step 1: Sort the items in descending order based on profit.
2Step 2: Use a min-heap to track the selected items and ensure we only keep k items.
3Step 3: Calculate the total profit and distinct categories from the selected items.
4Step 4: If the number of selected items is less than k, add items from the heap to maximize categories.

solution.py20 lines

1# Full working Python code
2import heapq
3
4def maxElegance(items, k):
5    items.sort(key=lambda x: -x[0])  # Sort by profit descending
6    total_profit = 0
7    distinct_categories = set()
8    min_heap = []
9
10    for profit, category in items:
11        heapq.heappush(min_heap, (profit, category))
12        total_profit += profit
13        distinct_categories.add(category)
14        if len(min_heap) > k:
15            removed = heapq.heappop(min_heap)
16            total_profit -= removed[0]
17            distinct_categories.remove(removed[1])
18
19    elegance = total_profit + len(distinct_categories) ** 2
20    return elegance

ℹ

Complexity note: The time complexity is O(n log n) due to sorting the items. The space complexity is O(n) for storing the items and the distinct categories.

1Sorting items by profit helps prioritize high-value selections.
2Using a min-heap allows efficient management of the top k items.

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