AI Big-O Analyzer

Complexity Analysis of Longest Subarray Function

This analysis examines the `longestSubarray` function, which calculates the length of the longest contiguous subarray that can be formed by removing one zero from a given array. It provides insights into time and space complexity while

Prompt

func longestSubarray(_ nums: [Int]) -> Int {
        var zeroCounting = 0
        var result = 0
        var prev = 0
        
        var right = 0
        var left = 0
        
        while right < nums.count {
            if nums[right] == 0 {
                prev = right - left
                zeroCounting += 1
            }
            
            while zeroCounting > 0 {
                if nums[left] == 0 {
                    zeroCounting -= 1
                }
                
                left += 1
            }
            
            result = max(result, prev + right - left + 1)
            right += 1
        }
        
        if result == nums.count {
            result -= 1
        }
        
        return result
    }

Answer

Complexity Analysis of `longestSubarray` Function

Code Inspection

Function Overview

The function longestSubarray aims to determine the length of the longest contiguous subarray that can be formed from the input array nums by removing exactly one zero (if present).

Key Variables

zeroCounting: Counts the number of zeros encountered in the current window.
result: Stores the length of the longest valid contiguous subarray found.
prev: Used to store the length of the subarray before the most recent zero.
right and left: Pointers that represent the current window's bounds.

Logic Flow

The outer while loop iterates through the array with the right pointer.
If a zero is found, it increases the count of zeroCounting and updates prev accordingly.
The inner while loop adjusts the left pointer to ensure the number of zeros in the current window does not exceed 1.
The maximum valid subarray length is updated in result every iteration.
Finally, if the entire array consists of only one zero, the function decrements result by one.

Complexity Analysis

Time Complexity

Outer Loop: The while right < nums.count iterates over all elements, producing linear time complexity: O(n).
Inner Loop: In the worst case, left traverses the array as right moves forward. Each index is processed at most twice (once by right and once by left):
- Total impact: O(n) for each index across both pointers, therefore combined complexity remains O(n).
Total Time Complexity:
- Best Case: O(n)
- Average Case: O(n)
- Worst Case: O(n)

Space Complexity

The space complexity primarily derives from the storage of a constant number of integer variables (zeroCounting, result, prev, right, left), irrespective of input size:
Total Space Complexity: O(1)

Non-Obvious Parts of the Code

Variable prev Management: The prev variable holds the length of the subarray before the most recently encountered zero. This helps in calculating valid subarray sizes efficiently when zeros are encountered.
Adjustment with Wound Conditions: The adjustment of left with regard to zeroCounting ensures that only valid subarrays contribute to the result.

Average-Case Scenario Illustration

Input Example

Consider the input array:

nums = [1, 1, 0, 1, 1]

Expected Behavior

As right traverses the array, it counts the zeros and keeps updating the valid subarray length.
As it encounters the single zero, the window allows for the zero to be "removed", thereby yielding a result of 5 (counting the entire length excluding the zero).

Expected Runtime

Expected Runtime: The number of iterations for right and left would remain within bounds of n, thus remaining linear, O(n).
Memory Usage: Memory remains constant at O(1) throughout execution.

Conclusion

The longestSubarray function offers an efficient linear time complexity solution while utilizing constant space, tailored for determining the maximal contiguous subarray post zero-removal under practical constraints. Such analysis serves to establish confidence in scalability and performance for large input sizes. For enhancing skills in algorithmic analysis, exploring resources on the Enterprise DNA Platform is advisable.

Description

This analysis examines the longestSubarray function, which calculates the length of the longest contiguous subarray that can be formed by removing one zero from a given array. It provides insights into time and space complexity while detailing the logic flow and variable management within the function.