[LeetCode 152] Maximum Product SubArray (medium) DP

Given an integer array nums, find the contiguous subarray within an array (containing at least one number) which has the largest product.

Example 1:

Input: [2,3,-2,4]
Output: 6
Explanation: [2,3] has the largest product 6.

Example 2:

Input: [-2,0,-1]
Output: 0
Explanation: The result cannot be 2, because [-2,-1] is not a subarray.

Solution & Code

class Solution {
    // 用max sum subarray的思路， DP
    // 但是不能只求maxSubarray Array,因为乘法有正负，负负为正，所以不能只简单取 
    // preProductArray [i] = Math.max (preProductArray [i - 1] * nums[i], nums[i]);
    // max = Math.max (preProductArray [i], max); 
    // eg. [-2, 3, -4]。如果只上述算，那么结果就是3，因为到了3的时候，-6就被舍弃了。
    
    // 所以Idea是，keep max and min for current index, and keep it for the next iteration
    public int maxProduct(int[] nums) {
        if (nums == null || nums.length == 0)
            return 0;
        
        int maxProduct = nums[0];
        int minProduct = nums[0];
        int maxResult = nums[0];
        
        for (int i = 1; i < nums.length; i++) {
            int maxTemp = maxProduct;
            maxProduct = Math.max (Math.max (maxProduct * nums[i], nums[i]), minProduct * nums[i]);
            minProduct = Math.min (Math.min (minProduct * nums[i], nums[i]), maxTemp * nums[i]);
            
            maxResult = Math.max (maxResult, maxProduct);
        }
        
        return maxResult;
    }
}