## Algorithm

Problem Name: 553. Optimal Division

You are given an integer array `nums`. The adjacent integers in `nums` will perform the float division.

• For example, for `nums = [2,3,4]`, we will evaluate the expression `"2/3/4"`.

However, you can add any number of parenthesis at any position to change the priority of operations. You want to add these parentheses such the value of the expression after the evaluation is maximum.

Return the corresponding expression that has the maximum value in string format.

Note: your expression should not contain redundant parenthesis.

Example 1:

```Input: nums = [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 do not 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
```

Example 2:

```Input: nums = [2,3,4]
Output: "2/(3/4)"
Explanation: (2/(3/4)) = 8/3 = 2.667
It can be shown that after trying all possibilities, we cannot get an expression with evaluation greater than 2.667
```

Constraints:

• `1 <= nums.length <= 10`
• `2 <= nums[i] <= 1000`
• There is only one optimal division for the given input.

## Code Examples

### #1 Code Example with Java Programming

```Code - Java Programming```

``````
class Solution {
public String optimalDivision(int[] nums) {
StringBuilder sb = new StringBuilder("");

sb.append(nums[0]);

for(int i=1;i < nums.length;i++) {
if (i == 1 && nums.length > 2) {
sb.append("/(").append(nums[i]);
}
else {
sb.append("/").append(nums[i]);
}
}

return nums.length > 2 ? sb.append(")").toString() : sb.toString();
}
}
``````
Copy The Code &

Input

cmd
nums = [1000,100,10,2]

Output

cmd
"1000/(100/10/2)"

### #2 Code Example with Javascript Programming

```Code - Javascript Programming```

``````
onst optimalDivision = function(nums) {
const len = nums.length
if(len <= 2) return len === 2 ? `\${nums[0]}/\${nums[1]}` : nums.join('')
let res = `\${nums[0]}/(\${nums[1]}`
for(let i = 2; i  <  len; i++) {
res += `/\${nums[i]}`
}
return res + '>'
};
``````
Copy The Code &

Input

cmd
nums = [1000,100,10,2]

Output

cmd
"1000/(100/10/2)"

### #3 Code Example with Python Programming

```Code - Python Programming```

``````
class Solution:
def optimalDivision(self, nums):
"""
:type nums: List[int]
:rtype: str
"""
if len(nums) == 1: return str(nums[0])
elif len(nums) == 2: return str(nums[0])+"/"+str(nums[1])
else: return str(nums[0])+"/("+"/".join(str(i) for i in nums[1:])+")"
``````
Copy The Code &

Input

cmd
nums = [2,3,4]

Output

cmd
"2/(3/4)"