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Medium

Maximum Sum of Distinct Subarrays With Length K

Find the maximum sum of a fixed-size subarray where all elements are distinct.
20 min
Solve on LeetCode

Problem Understanding

You are given an integer array nums and an integer k. Find the maximum subarray sum of all the subarrays of nums that meet the following conditions:

  1. The length of the subarray is k.
  2. All elements of the subarray are distinct.

Return 0 if no subarray meets the conditions.

Algorithm Strategy

A brute force check for distinctness takes O(k). Doing this for every window results in O(Nk) or O(Nk^2). We need O(N).

Strategy: Fixed Sliding Window + Frequency Map

  1. Window: Maintain a window of size k.
  2. Tracking: Use a Hash Map (or frequency array) to count occurrences of each number in the current window.
  3. Validity: Maintain a counter of 'duplicates' (or check if map size == k).
    • If count[num] > 1, we have a duplicate.
  4. Updates:
    • Add incoming element: Update map. If count becomes 2, duplicate found.
    • Remove outgoing element: Update map. If count drops to 1, duplicate resolved.
    • If valid (0 duplicates), update max_sum.

Visual Walkthrough

Step 1 / 1

Initializing...

1x

Observe how the window slides. The window turns Green when valid (distinct) and Red when it contains duplicates.

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