Optimal Division

Problem Description

You are given an integer array nums. The adjacent integers in nums will perform the float division. You can add any number of parenthesis at any position to change the priority of operations. You want to add these parentheses such that the value of the expression after the evaluation is maximum. Return the corresponding expression that has the maximum value in string format.

Key Insights

• The optimal way to maximize the division expression is to divide the first number by the result of the division of all subsequent numbers.
• This means that all numbers after the first should be grouped together in parentheses.
• For a single element, the expression is simply that element itself.
• The problem can be solved in O(n) time, where n is the length of the input array.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(n)

Solution

To achieve the maximum value from the division of the numbers, we will use a greedy approach. The first number in the array will be the numerator, and all subsequent numbers will be divided together as a single entity. We can achieve this by creating a string that represents this division.

1. If the length of the array is 1, just return the string representation of that number.
2. If the length is greater than 1, format the expression as nums[0]/(nums[1]/nums[2]/.../nums[n-1]).
3. This ensures that the first number is divided by the total result of the divisions that follow.

Code Solutions