<p>Given an integer array <code>nums</code>, find a <span data-keyword="subarray-nonempty">subarray</span> that has the largest product, and return <em>the product</em>.</p>

<p>The test cases are generated so that the answer will fit in a <strong>32-bit</strong> integer.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [2,3,-2,4]
<strong>Output:</strong> 6
<strong>Explanation:</strong> [2,3] has the largest product 6.
</pre>

<p><strong class="example">Example 2:</strong></p>

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

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 2 * 10<sup>4</sup></code></li>
	<li><code>-10 &lt;= nums[i] &lt;= 10</code></li>
	<li>The product of any subarray of <code>nums</code> is <strong>guaranteed</strong> to fit in a <strong>32-bit</strong> integer.</li>
</ul>

class Solution:
    def maxProduct(self, nums: List[int]) -> int:
        n = len(nums)
        dp_pos = [0] * (n + 1)
        dp_pos[0] = 1
        dp_neg = [0] * (n + 1)
        dp_neg[0] = 1
        prod_max = -inf
        for i, v in enumerate(nums):
            dp_pos[i + 1] = max(dp_pos[i] * v, v)
            dp_pos[i + 1] = max(dp_neg[i] * v, dp_pos[i + 1])
            dp_neg[i + 1] = min(dp_neg[i] * v, v)
            dp_neg[i + 1] = min(dp_pos[i] * v, dp_neg[i + 1])
            prod_max = max(dp_pos[i + 1], prod_max)
            # prod_max = max(dp_neg[i] * v, prod_max)
        return prod_max 

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