How to move the window in the sliding window algorithm?

In the sliding window algorithm, the window moves to efficiently process subsets of data without re-traversing the entire array.

Main ways to shift the window:

1. Fixed-size window:

   • The window shifts by one element to the right, removing the leftmost element and adding the next element on the right.

2. Variable-size window:

   • The left and right pointers (window boundaries) move independently, expanding or shrinking the window depending on the problem conditions.

Example in Go for calculating the sum of a fixed-size subarray:

func slidingWindowSum(arr []int, k int) []int {
    if len(arr) < k {
        return nil
    }
    sums := make([]int, 0, len(arr)-k+1)
    windowSum := 0
    for i := 0; i < k; i++ {
        windowSum += arr[i]
    }
    sums = append(sums, windowSum)
    for i := k; i < len(arr); i++ {
        windowSum += arr[i] - arr[i-k]
        sums = append(sums, windowSum)
    }
    return sums
}

Here, the window moves by one element, updating the sum in O(1) instead of recalculating the entire sum.