## 题目描述：

LeetCode 553. Optimal Division

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.

## 题目大意：

1. 输入整数长度范围[1, 10]
2. 元素范围[2, 1000]
3. 输入确保有唯一解

## 解题思路：

`a / b / c / d / ... = a / (b * c * d * ...)`

`a / (b / c / d / ...) = a * c * d * ... / b`

## Python代码：

``````class Solution(object):
def optimalDivision(self, nums):
"""
:type nums: List[int]
:rtype: str
"""
nums = map(str, nums)
return len(nums) < 3 and '/'.join(nums) or nums[0] + '/(' + '/'.join(nums[1:]) + ')'
``````

## Python代码：

``````class Solution(object):
def optimalDivision(self, nums):
"""
:type nums: List[int]
:rtype: str
"""
def solve(snums):
if len(snums) == 1: yield snums[0]
for x in range(1, len(snums)):
left, right = snums[:x], snums[x:]
l = '/'.join(left)
if len(right) == 1:
yield l + '/' + right[0]
else:
for r in solve(right):
yield l + '/(' + r + ')'
ans, best = '', 0
for expr in solve(map(str, nums)):
val = eval(expr.replace('/', '.0/'))
if val > best: ans, best = expr, val
return ans
``````

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