Problem Description
Given an integer array nums, find a subarray that has the largest product, and return the product.
Key Insights
- The product of a subarray can be maximized by considering both positive and negative numbers.
- A negative number can turn a small product into a large product when multiplied with another negative number.
- We need to keep track of both the maximum and minimum product at each position to account for negative numbers.
Space and Time Complexity
Time Complexity: O(n)
Space Complexity: O(1)
Solution
To solve the problem, we use a single pass through the array while maintaining two variables: max_product and min_product. max_product keeps track of the maximum product up to the current index, while min_product keeps track of the minimum product (which could be negative). At each step, we update these variables based on the current number and the products derived from the previous maximum and minimum products. The overall maximum product found during this process will be our answer.