Maximum Product Subarray

Problem

https://leetcode.com/problems/maximum-product-subarray/

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.

Note that the product of an array with a single element is the value of that element.

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 * 10:sup:`4`

• -10 <= nums[i] <= 10

• The product of any subarray of nums is guaranteed to fit in a 32-bit integer.

Pattern

Array, Dynamic Programming

Approaches

Dynamic Programming

Code

def maxProduct(nums: list[int]) -> int:
    max_product = nums[0]
    min_product = nums[0]
    result = nums[0]

    for num in nums[1:]:
        candidates = [num, max_product * num, min_product * num]
        max_product = max(candidates)
        min_product = min(candidates)
        result = max(result, max_product)

    return result

Test

>>> from maximum_product_subarray__dynamic_programming import maxProduct
>>> maxProduct([2, 3, -2, 4])
6
>>> maxProduct([-2, 0, -1])
0

maximum_product_subarray__dynamic_programming.maxProduct(nums: list[int]) → int