Question

Given a list of positive integers, the adjacent integers will perform the float division. For example, [2,3,4] -> 2 / 3 / 4.

However, you can add any number of parenthesis at any position to change the priority of operations. You should find out how to add parenthesis to get the maximum result, and return the corresponding expression in string format. Your expression should NOT contain redundant parenthesis.
Example:
Input: [1000,100,10,2]
Output: ""1000/(100/10/2)""
Explanation:
1000/(100/10/2) = 1000/((100/10)/2) = 200
However, the bold parenthesis in ""1000/((100/10)/2)"" are redundant,
since they don't influence the operation priority. So you should return "1000/(100/10/2)".
Other cases:
1000/(100/10)/2 = 50
1000/(100/(10/2)) = 50
1000/100/10/2 = 0.5
1000/100/(10/2) = 2
Note:
The length of the input array is [1, 10].
Elements in the given array will be in range [2, 1000].
There is only one optimal division for each test case.

Answer 1

The question pertains to optimizing an arithmetic expression consisting of positive integers and division operations by using parentheses, with the objective of achieving the maximum possible result. One must understand precedence rules and strategically place parentheses in the given array of numbers.

Step-by-step explanation:

The student is asking about a mathematics concept involving the optimization of an expression through the strategic placement of parentheses during division. Specifically, the goal is to arrange a given array of positive integers so that the expression yields the maximum result when the adjacent integers are divided as floating-point numbers. In the example provided, the maximum result is obtained by placing parentheses as follows: 1000/(100/10/2). This maximizes the result because dividing 100 by 10 and then by 2 before dividing 1000 by the outcome produces the largest number. It's important to remember that the rules of operation within mathematics dictate that division and multiplication have the same precedence and are performed from left to right; however, this can be altered by the strategic use of parentheses. Therefore, by understanding these rules and considering the range of numbers in the array, one can determine the optimal arrangement to achieve the highest possible division result.