Create 152_Maximum_Product_Subarray.md

Author: koji

152_Maximum_Product_Subarray.md

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+## 152. Maximum Product Subarray
+
+
+```
+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.
+ 
+
+Constraints:
+
+1 <= nums.length <= 2 * 104
+-10 <= nums[i] <= 10
+The product of any prefix or suffix of nums is guaranteed to fit in a 32-bit integer.
+
+```
+
+
+```python
+class Solution:
+ def maxProduct(self, nums: List[int]) -> int:
+ # Kadane's Algorithm
+ max_cur = nums[0]
+ max_global = nums[0]
+ min_cur = nums[0]
+ 
+ for i in range(1, len(nums)):
+ prev_max_cur = max_cur
+ max_cur = max(nums[i], max(max_cur * nums[i], min_cur * nums[i]))
+ min_cur = min(nums[i], min(prev_max_cur * nums[i], min_cur*nums[i]))
+ max_global = max(max_global, max_cur)
+ 
+ 
+ return max_global
+```
+
+
+```
+Runtime: 44 ms, faster than 98.65% of Python3 online submissions for Maximum Product Subarray.
+Memory Usage: 14.3 MB, less than 83.87% of Python3 online submissions for Maximum Product Subarray.
+```