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 <= 102 <= 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();
}
}
Input
Output
#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 + '>'
};
Input
Output
#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:])+")"
Input
Output