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152.MaximumProductSubarray.md

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152. Maximum Product Subarray

Medium

Given an integer array nums, find a contiguous non-empty subarray within the array that has the largest product, and return the product.

It is guaranteed that the answer will fit in a 32-bit integer.

A subarray is a contiguous subsequence of the array.

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.

Approach: Dynamic Programming

class Solution {
public:
    int maxProduct(vector<int>& nums) {
        int dp_max[nums.size()+1];
        int dp_min[nums.size()+1];
        dp_max[0] = nums[0];
        dp_min[0] = nums[0];
        for(int i = 1; i < nums.size(); i++){
            dp_max[i] = max(dp_min[i-1]*nums[i], max(dp_max[i-1]*nums[i], nums[i]));
            dp_min[i] = min(dp_min[i-1]*nums[i], min(dp_max[i-1]*nums[i], nums[i]));
        }
        int max_product = max(dp_max[0], dp_min[0]);
        for(int i = 1; i < nums.size(); i++)
            max_product = max(max_product, max(dp_max[i], dp_min[i]));
        
        return max_product;
    }
};