Max Sum Subarray of Size K

The sliding window technique is an optimization used to find subarrays or substrings that satisfy certain conditions, often related to sums, averages, or specific element counts. It significantly improves performance by avoiding redundant computations that would occur if each subarray were processed independently.

How the Sliding Window Works

Instead of re-calculating the sum (or other property) for every possible window from scratch, the sliding window approach maintains a fixed-size window and updates its aggregate value incrementally as it moves across the data structure. This involves subtracting the element that is leaving the window and adding the element that is entering it.

Consider finding the maximum sum of any contiguous subarray of a given size `k` within an array `nums`.

Initial Window Calculation

First, the sum of the initial window (the first `k` elements) is calculated. This sum also serves as the initial `max_sum`.

Sliding the Window

For each subsequent step, the window slides one position to the right. To update the current sum efficiently, the element at the leftmost position of the previous window is subtracted, and the new element at the rightmost position of the current window is added. This incremental update maintains the sum of the `k` elements within the current window without iterating through all `k` elements again.

Updating the Maximum

After each slide, the newly calculated current window sum is compared with the `max_sum` found so far. If the current sum is greater, `max_sum` is updated accordingly.

def max_sub_array(nums, k):
    curr_sum = sum(nums[:k])
    max_sum = curr_sum
    for i in range(len(nums) - k):
        curr_sum += nums[i + k] - nums[i]
        max_sum = max(max_sum, curr_sum)
    return max_sum

Key takeaways

• The sliding window technique optimizes array/string problems by reducing redundant computations.
• It maintains a fixed-size window and updates its aggregate value incrementally.
• Updates involve subtracting the outgoing element and adding the incoming element.
• This approach is efficient for problems requiring analysis of contiguous subarrays or substrings.