553. Optimal Division LeetCode Solution

Last updated: February 18, 2025

In this guide, you will get 553. Optimal Division LeetCode Solution with the best time and space complexity. The solution to Optimal Division problem is provided in various programming languages like C++, Java, and Python. This will be helpful for you if you are preparing for placements, hackathons, interviews, or practice purposes. The solutions provided here are very easy to follow and include detailed explanations.

Problem Statement
Complexity Analysis
Optimal Division solution in C++
Optimal Division solution in Java
Optimal Division solution in Python
Additional Resources

553. Optimal Division LeetCode Solution image

Problem Statement of 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.

Complexity Analysis

Time Complexity: O(n)
Space Complexity: O(n)

553. Optimal Division LeetCode Solution in C++

class Solution {
 public:
  string optimalDivision(vector<int>& nums) {
    string ans = to_string(nums[0]);

    if (nums.size() == 1)
      return ans;
    if (nums.size() == 2)
      return ans + "/" + to_string(nums[1]);

    ans += "/(" + to_string(nums[1]);
    for (int i = 2; i < nums.size(); ++i)
      ans += "/" + to_string(nums[i]);
    ans += ")";
    return ans;
  }
};
/* code provided by PROGIEZ */

553. Optimal Division LeetCode Solution in Java

class Solution {
  public String optimalDivision(int[] nums) {
    StringBuilder sb = new StringBuilder(String.valueOf(nums[0]));

    if (nums.length == 1)
      return sb.toString();
    if (nums.length == 2)
      return sb.append('/').append(nums[1]).toString();

    sb.append("/(").append(nums[1]);
    for (int i = 2; i < nums.length; ++i)
      sb.append('/').append(nums[i]);
    sb.append(')');
    return sb.toString();
  }
}
// code provided by PROGIEZ

553. Optimal Division LeetCode Solution in Python

class Solution:
  def optimalDivision(self, nums: list[int]) -> str:
    ans = str(nums[0])

    if len(nums) == 1:
      return ans
    if len(nums) == 2:
      return ans + '/' + str(nums[1])

    ans += '/(' + str(nums[1])
    for i in range(2, len(nums)):
      ans += '/' + str(nums[i])
    ans += ')'
    return ans
 # code by PROGIEZ

Additional Resources

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