19. Find the Difference Between Maximum and Minimum

Difficulty:EasyPattern:Linear ScanTime:O(n)Space:O(1)

Given an array of numbers, find the difference between the largest and smallest values.

How It Works & Algorithmic Design

Instead of sorting the array:

Track the maximum value.
Track the minimum value.
Traverse the array once and update both when necessary.
Return max - min.
Handle an empty array appropriately.

Why This Approach Works Best

Sorting is unnecessary. Both extremes can be found in one pass, resulting in $O(n)$ time and $O(1)$ auxiliary space.

Example Walkthrough

Input: [4, 10, 2, 8, 15]

Maximum is 15 and minimum is 2.

Calculation: 15 - 2 = 13

Subtract the smallest value from the largest value.

Output: 13

The range between the minimum and maximum is 13.

Answer: Find max-min difference

function maxMinDifference(arr) {
  if (!arr.length) return null;

  let min = arr[0];
  let max = arr[0];

  for (let i = 1; i < arr.length; i++) {
    if (arr[i] < min) min = arr[i];
    if (arr[i] > max) max = arr[i];
  }

  return max - min;
}

💡 Track both extremes during one traversal and subtract them at the end.

Key Takeaways

Maximum and minimum can be found simultaneously.
Sorting is unnecessary for calculating the range.
The algorithm requires O(n) time and O(1) auxiliary space.