0152. Maximum Product Subarray (M)

Maximum Product Subarray (M)

题目

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.

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题意

在给定数组中找到一个子数组，使其积最大。

思路

动态规划。sm[i]表示以nums[i]为结尾的子数组能得到的最小乘积，lg[i]表示以nums[i]为结尾的子数组能得到的最大乘积。可以得到递推式：

\[sm[i]=min(nums[i],\ nums[i]*sm[i-1],\ nums[i]*lg[i-1])\\ lg[i]=max(nums[i],\ nums[i]*sm[i-1],\ nums[i]*lg[i-1]) \]

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代码实现

Java

class Solution {
    public int maxProduct(int[] nums) {
        int ans = nums[0];
        int[] sm = new int[nums.length];
        int[] lg = new int[nums.length];
        sm[0] = nums[0];
        lg[0] = nums[0];
        for (int i = 1; i < nums.length; i++) {
            sm[i] = Math.min(nums[i], Math.min(nums[i] * sm[i - 1], nums[i] * lg[i - 1]));
            lg[i] = Math.max(nums[i], Math.max(nums[i] * sm[i - 1], nums[i] * lg[i - 1]));
            ans = Math.max(ans, lg[i]);
        }
        return ans;
    }
}