LeetCode Maximum Product Subarray(最大子数组乘积)

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

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

题意：给出一个数组，求其最大子数组的乘积

思路：动态规划法，因为在数组中可能存在负数，因为既要计算最小值，又要计算最大值。

用minValue(n) 表示从0到n得到的最小子数组乘积，用maxValue(n)表示从0到n得到的最大子数组乘积

状态转移方程为dp(n) = max{minValue(n-1)*array[n], maxValue(n-1)*array[n], array[n]}

代码如下：

class Solution {public int maxProduct(int[] nums){int minValue = 1, maxValue = 1, productValue = Integer.MIN_VALUE;int len = nums.length;for (int i = 0; i < len; i++){int tmpMax = Math.max(minValue * nums[i], Math.max(maxValue * nums[i], nums[i]));int tmpMin  = Math.min(minValue * nums[i], Math.min(maxValue * nums[i], nums[i]));maxValue = tmpMax;minValue = tmpMin;productValue = Math.max(productValue, maxValue);}return productValue;}
}

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