Longest Subarray of 1's After Deleting One Element

Problem Description

Given a binary array nums, you should delete one element from it. Return the size of the longest non-empty subarray containing only 1s in the resulting array. Return 0 if there is no such subarray.

Key Insights

• The goal is to find the longest contiguous subarray of 1s after removing exactly one element, which can be a 0 or a 1.
• A sliding window approach can efficiently track the count of 1s and handle the removal of elements.
• The window needs to expand until the count of 0s exceeds one, at which point it should shrink from the left to maintain at most one 0 in the window.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

The problem can be solved using the sliding window technique. We maintain a window that counts the number of 1s and allows at most one 0 to be present. The steps are as follows:

1. Initialize two pointers for the sliding window: left and right.
2. Expand the right pointer to include elements in the window.
3. Count the number of 0s in the window.
4. If the count of 0s exceeds one, increment the left pointer to shrink the window until we have at most one 0 left.
5. Calculate the length of the valid window as right - left + 1, and keep track of the maximum length found.
6. Finally, subtract one from the maximum length to account for the deleted element.

Code Solutions