Average Salary Excluding the Minimum and Maximum Salary

Average Salary Excluding the Minimum and Maximum Salary

What is this problem about?

The Average Salary Excluding the Minimum and Maximum Salary interview question provides an array of unique integers representing salaries. You are required to calculate the average of all salaries, but only after removing the lowest and the highest values. This Average Salary Excluding the Minimum and Maximum Salary coding problem is a straightforward arithmetic task with a focus on range identification.

Why is this asked in interviews?

Bloomberg and others use this as an introductory "sanity check" question. It tests if you can perform a single pass over an array to find multiple values (sum, min, max) simultaneously, rather than sorting the array which would be less efficient (O(N log N) vs O(N)).

Algorithmic pattern used

The primary Array, Sorting interview pattern is relevant, but the optimal approach is a Single Pass Linear Scan. You initialize min and max to very high and very low values respectively, and sum to 0. As you iterate, you update these three values. Finally, subtract the min and max from the sum and divide by (length - 2).

Example explanation

Salaries: [4000, 3000, 1000, 2000]

1. Min: 1000, Max: 4000.
2. Total Sum: 4000+3000+1000+2000 = 10000.
3. Excluded Sum: 10000 - (1000 + 4000) = 5000.
4. Count: 4 - 2 = 2.
5. Average: 5000 / 2 = 2500.

Common mistakes candidates make

• Sorting: Sorting the array just to get the min and max. While it works, it's O(N log N), whereas a simple loop is O(N).
• Integer Overflow: Although rare for salary values, always be mindful of sum overflows in large datasets.
• Division by Zero: Not considering what happens if the array has only 2 elements (though most constraints will prevent this).

Interview preparation tip

Whenever you need the smallest, largest, or sum of an array, always aim for a single-pass O(N) solution. It shows you are thinking about time complexity even for simple tasks.