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Sliding Window

Maximum Sum of Subarrays of Size K

easy

DESCRIPTION

Given an array of integers nums and an integer k, find the maximum sum of any contiguous subarray of size k.

Example 1: Input:


nums = [2, 1, 5, 1, 3, 2]
k = 3

Output:

Explanation: The subarray with the maximum sum is [5, 1, 3] with a sum of 9.

Explanation

This problem uses a fixed-size sliding window to efficiently find the maximum sum among all subarrays of length k. Instead of recalculating the sum for each subarray from scratch, we slide the window across the array and update the sum incrementally.

This approach is efficient because we calculate each window's sum in constant time by:

Adding the new element entering the window (nums[end])
Subtracting the old element leaving the window (nums[start])

Instead of summing k elements for each window (which would be O(n*k)), we do constant work per window, giving us O(n) time complexity.

Solution


def max_subarray_sum(nums, k):
  max_sum = 0
  state = 0
  start = 0

  for end in range(len(nums)):
    state += nums[end]

    if end - start + 1 == k:
      max_sum = max(max_sum, state)
      state -= nums[start]
      start += 1

  return max_sum

start

max subarray sum of size k

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Maximum Sum of Subarrays of Size K

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