Maximum Sum of Distinct Subarrays With Length K - Problem
You're given an integer array nums and an integer k. Your task is to find the maximum sum among all subarrays that satisfy two important conditions:
- The subarray has exactly k elements
- All elements in the subarray are distinct (no duplicates)
If no such subarray exists, return 0.
Note: A subarray is a contiguous sequence of elements within an array.
Example: For nums = [1,5,4,2,9,9,9] and k = 3, the subarray [5,4,2] has sum 11 and all distinct elements, making it a valid candidate.
Input & Output
example_1.py โ Basic Case
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Input:
nums = [1,5,4,2,9,9,9], k = 3
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Output:
15
๐ก Note:
The subarray [4,2,9] has all distinct elements and sum 15, which is the maximum possible.
example_2.py โ All Same Elements
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Input:
nums = [4,4,4], k = 3
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Output:
0
๐ก Note:
No subarray of length 3 has all distinct elements, so return 0.
example_3.py โ Small Array
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Input:
nums = [1,2], k = 3
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Output:
0
๐ก Note:
Array length is less than k, so no valid subarray exists.
Constraints
- 1 โค k โค nums.length โค 105
- -104 โค nums[i] โค 104
- All subarrays must have exactly k elements
- All elements in valid subarrays must be distinct
Visualization
Tap to expand
Understanding the Visualization
1
Initialize Window
Start with the first k seats, count frequencies and calculate total revenue
2
Slide Right
Add new customer on right, remove customer on left
3
Update Tracking
Update frequency map and total sum efficiently
4
Check Validity
If all k customers have unique IDs, compare with maximum revenue
Key Takeaway
๐ฏ Key Insight: The sliding window with hash map approach achieves optimal O(n) time by maintaining both the sum and distinctness check efficiently as we move through the array, processing each element exactly once.
๐ก
Explanation
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