152. Maximum Product Subarray

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.

 

Approach #1: Math. [C++]

class Solution {
public:
    int maxProduct(vector<int>& nums) {
        int size = nums.size();
        if (size == 0) return size;
        
        int ans = nums[0];
        int curmax = nums[0];
        int curmin = nums[0];
        for (int i = 1; i < size; ++i) {
            int nextmax = curmax * nums[i];
            int nextmin = curmin * nums[i];
            curmax = max(nums[i], max(nextmax, nextmin));
            curmin = min(nums[i], min(nextmax, nextmin));
            ans = max(ans, max(curmax, curmin));
        }
        
        return ans;
    }
};

　　

Analysis:

Because nums is an integer array, so nums[i] > 1.  In this travel's every step(++i) we find the curmin and curmax and ans from 0 to current index(i), curmin can become curmax and curmax can become curmin, if both curmin and curmax are less than 0, nums[i] > 0 so nums[i] is the curmax.