What is the time complexity of Average Salary Excluding the Minimum and Maximum Salary?

The optimal solution has a time complexity of O(n).

What data structures are used to solve Average Salary Excluding the Minimum and Maximum Salary?

This problem uses Array, Sorting. Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Average Salary Excluding the Minimum and Maximum Salary?

Insight 1: We need to find the minimum and maximum salaries efficiently to exclude them from the average calculation. Insight 2: A single pass through the array is sufficient to find the minimum, maximum, and sum of salaries simultaneously, optimizing for time complexity.

Which companies ask LeetCode 1491. Average Salary Excluding the Minimum and Maximum Salary in interviews?

This problem is frequently asked at Netsuite.

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Average Salary Excluding the Minimum and Maximum Salary - LeetCode 1491 Solution

Average Salary Excluding the Minimum and Maximum Salary - Complete Solution Guide

Average Salary Excluding the Minimum and Maximum Salary is LeetCode problem 1491, a Easy level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

You are given an array of unique integers salary where salary[i] is the salary of the i th employee. Return the average salary of employees excluding the minimum and maximum salary . Answers within 10 -5 of the actual answer will be accepted. Example 1: Input: salary = [4000,3000,1000,2000] Output: 2500.00000 Explanation: Minimum salary and maximum salary are 1000 and 4000 respectively. Average salary excluding minimum and maximum salary is (2000+3000) / 2 = 2500 Example 2: Input: salary = [1000

Detailed Explanation

The problem asks you to calculate the average salary of employees, excluding the highest and lowest salaries. The input is an array of integers representing individual employee salaries. All salaries are unique, and the array will always contain at least three salaries. The output is a floating-point number representing the average salary after excluding the minimum and maximum values. The output should be accurate within 10<sup>-5</sup>.

Solution Approach

The provided solutions use a linear scan approach. They iterate through the salary array once to find the minimum and maximum salaries while simultaneously calculating the sum of all salaries. Afterward, the minimum and maximum salaries are subtracted from the total sum, and the result is divided by the number of employees minus two (to exclude the minimum and maximum). This ensures the average is calculated correctly excluding the extreme values.

Step-by-Step Algorithm

Step 1: Initialize variables: `minSalary`, `maxSalary`, and `sum`. Initialize `minSalary` and `maxSalary` to the first element of the `salary` array. Initialize `sum` to 0.
Step 2: Iterate through the `salary` array. For each salary:
Step 2a: Update `minSalary` if the current salary is less than the current `minSalary`.
Step 2b: Update `maxSalary` if the current salary is greater than the current `maxSalary`.
Step 2c: Add the current salary to `sum`.
Step 3: Subtract `minSalary` and `maxSalary` from `sum`.
Step 4: Divide `sum` by `salary.length - 2` to get the average salary and return the result.

Key Insights

Insight 1: We need to find the minimum and maximum salaries efficiently to exclude them from the average calculation.
Insight 2: A single pass through the array is sufficient to find the minimum, maximum, and sum of salaries simultaneously, optimizing for time complexity.
Insight 3: Handling the case where there are only three salaries needs to be considered implicitly; the algorithm should gracefully handle this without needing special conditional logic.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(1)

Topics

This problem involves: Array, Sorting.

Companies

Asked at: Netsuite.

Average Salary Excluding the Minimum and Maximum Salary | LeetCode 1491

Easy

Array Sorting

Time: O(n)Space: O(1)

Solution Code

Available in:

class Solution {
    public double average(int[] salary) {
        int minSalary = salary[0];
        int maxSalary = salary[0];
        double sum = 0;

        for (int s : salary) {
            minSalary = Math.min(minSalary, s);
            maxSalary = Math.max(maxSalary, s);
            sum += s;
        }

        sum -= minSalary + maxSalary;
        return sum / (salary.length - 2);
    }
}

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Problem Info

Description

Problem 1491: Average Salary Excluding the Minimum and Maximum Salary - Detailed explanation and solution approaches.

Topics

Array Sorting

Companies

Netsuite

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:1491

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

7 steps

1
Step 1: Initialize variables: `minSalary`, `maxSalary`, and `sum`. Initialize `minSalary` and `maxSalary` to the first element of the `salary` array. Initialize `sum` to 0.
2
Step 2: Iterate through the `salary` array. For each salary:
3
Step 2a: Update `minSalary` if the current salary is less than the current `minSalary`.
4
Step 2b: Update `maxSalary` if the current salary is greater than the current `maxSalary`.
5
Step 2c: Add the current salary to `sum`.
6
Step 3: Subtract `minSalary` and `maxSalary` from `sum`.
7
Step 4: Divide `sum` by `salary.length - 2` to get the average salary and return the result.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(n)

👍 Linear - Good! Visits each element once.

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The algorithm iterates through the salary array once, making the time complexity linear with respect to the number of salaries. The space complexity is constant because only a few extra variables are used regardless of the input size.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Sorting

Sort the array first, then calculate the sum of elements excluding the first and last elements, and divide by (n-2).

Time: O(n log n) due to sortingSpace: O(1) or O(n) depending on the sorting algorithm (in-place vs. not)

Trade-offs: This approach is less efficient than the linear scan approach if you don't need a sorted array for other purposes. The linear scan is generally preferred for its better time complexity in this specific problem.

✨

Key Insights

1Insight 1: We need to find the minimum and maximum salaries efficiently to exclude them from the average calculation.
2Insight 2: A single pass through the array is sufficient to find the minimum, maximum, and sum of salaries simultaneously, optimizing for time complexity.
3Insight 3: Handling the case where there are only three salaries needs to be considered implicitly; the algorithm should gracefully handle this without needing special conditional logic.

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Sorting

Arranging elements in a specific order (ascending/descending).

Edge Cases

Edge case 1: The array contains only three salaries. The algorithm correctly handles this by subtracting two from the array length in the division step, avoiding division by zero.
Edge case 2: The minimum and maximum salaries are at the beginning or end of the array. The algorithm correctly identifies these regardless of their position due to the comparison within the loop.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to handle the case where the minimum or maximum salary appears multiple times. The problem statement guarantees unique salaries, eliminating this concern.

✗Common mistake 2: Incorrectly calculating the average by dividing by the original array length instead of (length - 2), leading to an inaccurate result.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Calculating the average performance metric of employees excluding outliers (top and bottom performers) for performance reviews or bonus calculations.

🏦Real-world scenario 2: In data analysis, removing outliers before calculating statistics to get a more representative average value. For example, calculating the average house price in a neighborhood, excluding extremely expensive or cheap houses.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

Even for easy problems, discuss time and space complexity. Interviewers want to see you think analytically.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: July 22, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJul 13

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 6

Try solving this without using extra space first. It's a great exercise for understanding the underlying pattern.

@CodeNinjaJun 29

❓

Frequently Asked Questions

When should I use in-place modification vs creating a new array?

Use in-place modification when space complexity matters (O(1) space requirement) and the original array can be modified. Create a new array when you need to preserve the original data or when the problem involves significant restructuring that would complicate in-place logic.

What should I learn from easy problems?

Easy problems introduce core patterns that appear in harder problems. Master basic operations (iteration, conditionals, simple data structures), recognize common patterns (counting, searching, basic transformations), and practice explaining your thought process clearly.

What is the importance of time and space complexity analysis?

Complexity analysis is crucial because: 1) Interviewers always ask about it, 2) It helps you choose between approaches, 3) It demonstrates CS fundamentals. Always state both time and space complexity, and be prepared to explain how you derived them.

What is the optimal approach for "Average Salary Excluding the Minimum and Maximum Salary"?

For this easy-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether sorting techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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