Sliding Window

The sliding window technique is a highly effective method for solving problems that require finding a contiguous subarray (or substring) that satisfies a certain condition. The naive approach to such problems often involves two nested loops, leading to an O(n^2) complexity. The sliding window approach optimizes this to O(n) by avoiding redundant calculations. The technique involves maintaining a 'window' (a subarray defined by a start and end pointer) over the main array. The window `[start, end]` is first expanded by moving the `end` pointer to the right. As the window expands, we update our state (e.g., the sum of elements in the window, a frequency map of characters, etc.). Once the condition of the problem is met or violated, we try to shrink the window from the left by moving the `start` pointer to the right, again updating our state. This process of expanding and shrinking the window continues until the `end` pointer reaches the end of the array. This pattern is particularly useful for problems like 'find the longest subarray with a sum less than k', 'find the minimum size subarray with a sum greater than or equal to k', or 'find the longest substring with no repeating characters'. Recognizing when a problem can be solved with a sliding window is a key skill.