DSCPPAS277 - Editorial

editorial
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Problem Statement:

Given a binary array arr (containing only 0s and 1s), you need to find the length of the longest subarray that contains only 1s after flipping exactly one contiguous subarray of 0s to 1s.

Approach:

To solve this problem efficiently, we can break it down into a series of steps. The key idea is to first identify and group contiguous segments of 0s and 1s. By analyzing these segments, we can determine the best place to flip a segment of 0s to maximize the length of 1s.

Step-by-Step Explanation:

  1. Identify Contiguous Segments:

    • Traverse the array and group contiguous segments of 0s and 1s.
    • Store the lengths of these segments in a list called freq.

  2. Calculate Maximum Possible Length After Flip:

    • Iterate through the freq list and evaluate the maximum possible length of 1s that can be obtained by flipping one segment of 0s.
    • Specifically, focus on segments of 0s surrounded by 1s (e.g., [1s] 0 [1s]):
      • The effective length of 1s after flipping a segment of 0s is the sum of the lengths of the surrounding 1s plus the length of the 0 segment.
    • Also, consider edge cases where the array contains only one segment of 1s or where the flip results in a continuous segment of 1s.

  3. Edge Case Handling:

    • If the array has only two segments and the first is all 0s, flipping all the 0s results in a segment of length n-1 (if n is the length of the array), as flipping an empty array would trivially not yield any 1s.

Example:

For an array like [1, 0, 0, 1, 1, 0, 1]:

  • Segments are: [1], [2], [2], [1].
  • Possible flips:
    • Flip the first segment of 0s: results in [3].
    • Flip the second segment of 0s: results in [4].
  • The maximum possible length of 1s is 4.

Complexity:

  • Time Complexity: The solution runs in O(N) time, where N is the length of the array. This is because we make a single pass through the array to build the freq list and then another pass to calculate the maximum possible length of 1s.

  • Space Complexity: The space complexity is O(N) due to the storage used by the freq list.