LeetCode 152: Maximum Product Subarray

Problem Description

LeetCode Problem 152

Given an integer array nums, find a subarray that has the largest product, and return the product.

The test cases are generated so that the answer will fit in a 32-bit integer.

Example 1:

Input: nums = [2,3,-2,4]
Output: 6
Explanation: [2,3] has the largest product 6.

Example 2:

Input: nums = [-2,0,-1]
Output: 0
Explanation: The result cannot be 2, because [-2,-1] is not a subarray.

Constraints:

• 1 <= nums.length <= 2 * 104
• -10 <= nums[i] <= 10
• The product of any subarray of nums is guaranteed to fit in a 32-bit integer.

Difficulty: Medium

Tags: array, dynamic programming

Rating: 96.16%

Solution

Here’s my Python solution to this problem:

class Solution:
    def maxProduct(self, nums: List[int]) -> int:
        if not nums: return 0

        curr_max = curr_min = result = nums[0]
    
        for num in nums[1:]:
            temp_max = curr_max
            
            # For each number, we need to compare:
            # 1. The number itself
            # 2. Number * current maximum (could be good if both are positive or both negative)
            # 3. Number * current minimum (could be good if both are negative)
            curr_max = max(num, temp_max * num, curr_min * num)
            curr_min = min(num, temp_max * num, curr_min * num)
            
            result = max(result, curr_max)
        
        return result

Complexity Analysis

The solution has the following complexity characteristics:

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

Note: This is an automated analysis and may not capture all edge cases or specific algorithmic optimizations.