Sliding Window — Explained with Examples

In this tutorial, you'll learn about Sliding Window. We cover key concepts, practical examples, and best practices to help you understand and apply this topic effectively.

Sliding Window maintains a subarray subset of data using Two Pointers, optimizing problems involving contiguous sequences from O(n²) to O(n).

Sliding Window defines a window (range) that slides across the data. Fixed window maintains a constant size (e.g., max sum of k consecutive elements). Variable window expands and contracts based on conditions (e.g., smallest subarray with sum ≥ target). The window is tracked by left and right pointers, and the window state is updated incrementally as pointers move.

Think of Sliding Window like looking through a moving car window at a landscape. You see a fixed-width section of scenery that changes as the car moves. To calculate the total number of trees visible, you add new trees entering the view and subtract trees leaving — no need to recount everything from scratch.

The technique transforms many O(n²) subarray problems into O(n) solutions by avoiding recomputation.

# Fixed window: max sum of k consecutive elements
def max_sum_fixed(arr, k):
    if len(arr) < k:
        return -1
    window_sum = sum(arr[:k])
    max_sum = window_sum
    for i in range(k, len(arr)):
        window_sum += arr[i] - arr[i - k]
        max_sum = max(max_sum, window_sum)
    return max_sum

# Variable window: smallest subarray with sum ≥ target
def min_subarray_length(nums, target):
    left = 0
    current_sum = 0
    min_length = float('inf')
    for right in range(len(nums)):
        current_sum += nums[right]
        while current_sum >= target:
            min_length = min(min_length, right - left + 1)
            current_sum -= nums[left]
            left += 1
    return min_length if min_length != float('inf') else 0

print(max_sum_fixed([2, 1, 5, 1, 3, 2], 3))  # 9 (5+1+3)
print(min_subarray_length([2, 3, 1, 2, 4, 3], 7))  # 2 ([4, 3])

Sliding Window applies to subarray/substring problems: longest substring without repeating characters, maximum average subarray, and string permutations.

Two Pointers, Array, Hash Table, Queue

Two Pointers