#191 Maximum Product Subarray

题目描述：

Find the contiguous subarray within an array (containing at least one number) which has the largest product.

Have you met this question in a real interview? 

Yes

Example

For example, given the array [2,3,-2,4], the contiguous subarray[2,3] has the largest product = 6.

题目思路：

这题如果都是positive number，答案就是所有数都相乘。但是由于数组中有negative number和0，情况就复杂了。因为当年的小弟（negative min）有朝一日遇到nums[i] < 0，就有可能变成老大(positive max)。所以，在遍历数组的同时，需要记下local max和local min两种。对于每个i来说，local max/min都各有3个candidates：local max * nums[i] （之前的local max和nums[i]符号都为正的情况），local min * nums[i] （某些之前的local min和nums[i]符号都为负的情况），nums[i] （比如nums[i - 1]为0的情况）。我们遍历完数组，找出最大的local max就可以了。

Mycode（AC = 28ms）：

class Solution {public:    /**     * @param nums: a vector of integers     * @return: an integer     */    int maxProduct(vector<int>& nums) {        // write your code here        if (nums.size() == 0) return 0;                int local_max = nums[0], local_min = nums[0];        int global = nums[0];                for (int i = 1; i < nums.size(); i++) {            int tmp = local_max;                        // 3 candidates for local max/min:            // single current number, 2 local extremes * nums[i]            local_max = max(nums[i], max(local_max * nums[i], local_min * nums[i]));            local_min = min(nums[i], min(local_min * nums[i], tmp * nums[i]));                        global = max(global, local_max);        }                return global;    }};