题目

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:

1. The length of the input array is [1, 10].
2. Elements in the given array will be in range [2, 1000].
3. There is only one optimal division for each test case.

难度

Medium

方法

这题难度标为Medium，但是很简单。n1/n2/n3/n5/n5通过加括号改变运算优先级，它的最大值为n1*n3*n4*n5/n2，即n1/(n2/n3/n4/n5)。添加括号的位置是固定的，格式化输出即可

python代码

class Solution(object):
    def optimalDivision(self, nums):
        """
        :type nums: List[int]
        :rtype: str
        """
        nums = map(str, nums)
        if len(nums) <= 2:
            return '/'.join(nums)
        
        return "%s/(%s)" % (str(nums[0]), '/'.join(nums[1:]))

assert Solution().optimalDivision([1000,100,10,2]) == '1000/(100/10/2)'
assert Solution().optimalDivision([2]) == '2'