:orphan:

Maximum Product Subarray
========================

.. highlight:: none

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.

.. highlight:: python

Pattern
-------
Array, Dynamic Programming

Approaches
----------

.. tab-set::

    .. tab-item:: Dynamic Programming

        **Code**

        .. literalinclude:: ../problems/medium/maximum-product-subarray/maximum_product_subarray__dynamic_programming.py
            :language: python
            :lines: 10-

        **Test**

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

        .. autofunction:: maximum_product_subarray__dynamic_programming.maxProduct