Problem Description
Given an array of integers nums, find the maximum length of a subarray where the product of all its elements is positive. A subarray of an array is a consecutive sequence of zero or more values taken out of that array. Return the maximum length of a subarray with positive product.
Key Insights
- A product is positive if it contains an even number of negative numbers.
- Any zero in the array will reset the product, requiring a restart of the subarray count.
- Maintain two lengths: one for the longest subarray with a positive product and one for the longest subarray with a negative product.
- Iterate through the array while updating the lengths based on the current number.
Space and Time Complexity
Time Complexity: O(n)
Space Complexity: O(1)
Solution
We will use a single pass approach through the array to keep track of two variables: max_len for the maximum length of the subarray with a positive product, and neg_len for the length of the current subarray with a negative product. We will reset our counters whenever we encounter a zero. If we encounter a positive number, we will increment our positive subarray length, and if we encounter a negative number, we will swap our lengths accordingly. This approach ensures that we efficiently calculate the maximum length of the desired subarray.