Optimal Division
You are given an integer array nums. The adjacent integers in nums will perform float division.
- For example, for
nums = [2,3,4], we will evaluate the expression"2/3/4".
However, you can add any number of parentheses at any position to change the priority of operations. You want to add these parentheses such that the value of the expression after evaluation is maximum.
Return the corresponding expression that has the maximum value in string format.
Note: your expression should not contain redundant parentheses.
Example 1
Input
nums = [1000,100,10,2]Output
"1000/(100/10/2)"The maximum value is achieved by
1000/(100/10/2) = 200, and adding parentheses around 100/10 would be redundant because they do not change operation priority.Example 2
Input
nums = [2,3,4]Output
"2/(3/4)"2/(3/4) = 8/3 = 2.667, and no other parenthesization gives a greater value.Constraints
- 1 <= nums.length <= 10
- 2 <= nums[i] <= 1000
- There is only one optimal division for the given input.