Maximum Product Subarray问题及解法

问题描述：

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

示例

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

问题分析：

我们设maxi[i]表示以i为结尾的值最大子数组的积，mini[i]表示以i为结尾的值最小子数组的积，则根据定义maxi[i + 1] = max(nums[i + 1], max(maxi[i] * nums[i + 1], mini[i] * nums[i + 1]))，mini[i + 1] = min(nums[i + 1], min(maxi[i] * nums[i + 1], mini[i] * nums[i + 1]))。

过程详见代码：

class Solution {public:    int maxProduct(vector<int>& nums) {        int n = nums.size();if (!n) return 0;vector<int> maxi(n, 0);vector<int> mini(n, 0);int res = nums[0];maxi[0] = nums[0];mini[0] = nums[0];for (int i = 1; i < n; i++){maxi[i] = max(nums[i], max(maxi[i - 1] * nums[i], mini[i - 1] * nums[i]));mini[i] = min(nums[i], min(maxi[i - 1] * nums[i], mini[i - 1] * nums[i]));res = max(res, maxi[i]);}return res;    }};