What is the optimal strategy for placing parentheses in the "Optimal Division" problem?

The optimal strategy involves using dynamic programming to track the maximum and minimum results of subarrays, then strategically placing parentheses to maximize the result.

How does dynamic programming apply to the "Optimal Division" problem?

Dynamic programming helps by storing the maximum and minimum results for subarrays, allowing you to combine smaller subproblems and find the best placement of parentheses.

What is the time complexity of the "Optimal Division" problem solution?

The time complexity is O(n^3) in the worst case due to the need to evaluate all possible subarrays and placements of parentheses.

What are some common pitfalls in solving "Optimal Division"?

Common pitfalls include not properly handling division precedence, failing to track both maximum and minimum results, and overcomplicating the solution by ignoring dynamic programming.

How does GhostInterview help with the "Optimal Division" problem?

GhostInterview provides detailed guidance on applying dynamic programming, optimizing parentheses placement, and understanding the time and space complexity involved in solving the problem.

#553

Medium

auto_awesome状态·转移·动态规划

LeetCode 题解工作台

最优除法

给定一正整数数组 nums ， nums 中的相邻整数将进行浮点除法。例如， nums = [2,3,4] ，我们将求表达式的值 "2/3/4" 。但是，你可以在任意位置添加任意数目的括号，来改变算数的优先级。你需要找出怎么添加括号，以便计算后的表达式的值为最大值。以字符串格式返回具有最大值的…

数组数学动态规划

题目描述

给定一正整数数组 nums，nums 中的相邻整数将进行浮点除法。

例如，nums = [2,3,4]，我们将求表达式的值 "2/3/4"。

但是，你可以在任意位置添加任意数目的括号，来改变算数的优先级。你需要找出怎么添加括号，以便计算后的表达式的值为最大值。

以字符串格式返回具有最大值的对应表达式。

注意：你的表达式不应该包含多余的括号。

示例 1：

输入: [1000,100,10,2]
输出: "1000/(100/10/2)"
解释: 1000/(100/10/2) = 1000/((100/10)/2) = 200
但是，以下加粗的括号 "1000/((100/10)/2)" 是冗余的，
因为他们并不影响操作的优先级，所以你需要返回 "1000/(100/10/2)"。

其他用例:
1000/(100/10)/2 = 50
1000/(100/(10/2)) = 50
1000/100/10/2 = 0.5
1000/100/(10/2) = 2

示例 2:

输入: nums = [2,3,4]
输出: "2/(3/4)"
解释: (2/(3/4)) = 8/3 = 2.667
可以看出，在尝试了所有的可能性之后，我们无法得到一个结果大于 2.667 的表达式。

说明:

1 <= nums.length <= 10
2 <= nums[i] <= 1000
对于给定的输入只有一种最优除法。

lightbulb

解题思路

方法一

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class Solution:
    def optimalDivision(self, nums: List[int]) -> str:
        n = len(nums)
        if n == 1:
            return str(nums[0])
        if n == 2:
            return f'{nums[0]}/{nums[1]}'
        return f'{nums[0]}/({"/".join(map(str, nums[1:]))})'

speed

复杂度分析

指标	值
时间	Depends on the final approach
空间	O(n^2)

psychology

面试官常问的追问

外企场景

question_mark
Can the candidate explain how to apply dynamic programming to a problem with state transitions?
question_mark
Does the candidate understand how to optimize the placement of parentheses for maximum value?
question_mark
Is the candidate able to describe the time and space complexity of the solution?

warning

常见陷阱

外企场景

error
Misunderstanding the division operation and how parentheses affect the evaluation order.
error
Failing to recognize the need to track both the maximum and minimum values for subarrays.
error
Overcomplicating the solution by not using dynamic programming to efficiently explore subarray possibilities.

swap_horiz

进阶变体

外企场景

arrow_right_alt
What if the array has only two elements?
arrow_right_alt
How does the problem change if other operations, like addition or multiplication, are involved?
arrow_right_alt
What if the array contains decimal values instead of integers?

help

常见问题

外企场景

继续练习

#486 预测赢家 #396 旋转函数 #368 最大整除子集