Maximum Product Subarray
<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>
Array; Dynamic Programming
class Solution {
public:
    int maxProduct(vector<int>& nums) {
        int f = nums[0], g = nums[0], ans = nums[0];
        for (int i = 1; i < nums.size(); ++i) {
            int ff = f, gg = g;
            f = max({nums[i], ff * nums[i], gg * nums[i]});
            g = min({nums[i], ff * nums[i], gg * nums[i]});
            ans = max(ans, f);
        }
        return ans;
    }
};