Maximum Product Subarray — LeetCode 152 Python Solution

The problem

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

Input

nums = [2,3,-2,4]

Output

6

Explanation

[2,3] has the largest product 6.

Python solution

class Solution:
    def maxProduct(self, nums: List[int]) -> int:
        ans = f = g = nums[0]
        for x in nums[1:]:
            ff, gg = f, g
            f = max(x, ff * x, gg * x)
            g = min(x, ff * x, gg * x)
            ans = max(ans, f)
        return ans

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 152. Maximum Product Subarray is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

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