• Difficulty: Medium

• Related Topics: Array, Dynamic Programming

• Link: https://leetcode.com/problems/maximum-product-subarray/

Description

Given an integer array nums, find the contiguous subarray within an array (containing at least one number) which has the largest product.
給定一個整數陣列 nums，找到積最大的子陣列（至少包含一個整數）。

Examples

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.

Solution

這題看上去和最大子陣列類似，只是把和最大變成了積最大。但是做法就發生了變化，由於無論怎麼乘，結果的絕對值都是遞增的（當然，0 的情況需要單獨討論）。所以，只要算一遍字首和，一遍字尾和，就能得到結果。程式碼如下：

class Solution {
    fun maxProduct(nums: IntArray): Int {
        var result = nums[0]
        var left = 0
        var right = 0

        for (i in nums.indices) {
            left = (if (left == 0) 1 else left) * nums[i]
            right = (if (right == 0) 1 else right) * nums[nums.lastIndex - i]

            result = maxOf(result, left, right)
        }

        return result
    }
}