Radix Sort Algorithm in DSA Javascript - Build from Scratch

Radix Sort Algorithm

📖 Scenario: You work in a warehouse where boxes are labeled with numbers. You want to organize these boxes in order from smallest to largest number quickly and efficiently.

🎯 Goal: Build a program that sorts a list of numbers using the Radix Sort algorithm, which sorts numbers digit by digit from the least significant digit to the most significant digit.

📋 What You'll Learn

Create an array called numbers with the exact values: [170, 45, 75, 90, 802, 24, 2, 66]

Create a variable called maxDigits to store the number of digits in the largest number

Write a function called radixSort that sorts the numbers array using Radix Sort

Print the sorted array after applying Radix Sort

💡 Why This Matters

🌍 Real World

Radix Sort is used in systems where sorting large sets of numbers quickly is important, like organizing warehouse inventory or processing large datasets.

💼 Career

Understanding Radix Sort helps in roles involving data processing, optimization, and algorithm design, which are common in software engineering and data science jobs.

1

Create the initial array of numbers

Create an array called numbers with these exact values: [170, 45, 75, 90, 802, 24, 2, 66]

DSA Javascript

// Create the array called numbers with the given values
// Your code here

Hint

Use const numbers = [...] to create the array with the exact numbers.

2

Find the maximum number of digits

Create a variable called maxDigits that stores the number of digits in the largest number in the numbers array

DSA Javascript

const numbers = [170, 45, 75, 90, 802, 24, 2, 66];
// Create maxDigits to hold the number of digits in the largest number
// Your code here

Hint

Use Math.max(...numbers) to find the largest number, then convert it to string and get its length.

3

Write the Radix Sort function

Write a function called radixSort that takes the numbers array and sorts it using Radix Sort algorithm by processing digits from least significant to most significant

DSA Javascript

const numbers = [170, 45, 75, 90, 802, 24, 2, 66];
const maxDigits = Math.max(...numbers).toString().length;
// Write the radixSort function below
// Your code here

Hint

Use a loop from 0 to maxDigits - 1. Create 10 buckets for digits 0-9. Place numbers in buckets based on current digit. Flatten buckets back to array. Return sorted array.

4

Print the sorted array

Call the radixSort function with the numbers array and print the sorted result using console.log

DSA Javascript

const numbers = [170, 45, 75, 90, 802, 24, 2, 66];
const maxDigits = Math.max(...numbers).toString().length;

function radixSort(arr) {
    for (let digit = 0; digit  []);
        for (const num of arr) {
            const digitValue = Math.floor(num / Math.pow(10, digit)) % 10;
            buckets[digitValue].push(num);
        }
        arr = [].concat(...buckets);
    }
    return arr;
}

// Call radixSort and print the sorted array
// Your code here

Hint

Call radixSort(numbers) and print the result with console.log.

Practice

1. What is the main idea behind the Radix Sort Algorithm?

easy

A. Sort numbers by swapping adjacent elements repeatedly

B. Sort numbers by comparing each pair directly

C. Sort numbers by dividing them into two halves recursively

D. Sort numbers digit by digit starting from the least significant digit

Solution

1. Step 1: Understand Radix Sort approach

   Radix Sort sorts numbers by processing each digit separately, starting from the least significant digit (rightmost).

2. Step 2: Compare with other sorting methods

   Unlike comparison-based sorts, Radix Sort groups numbers by digits without direct comparisons between whole numbers.

3. Final Answer:

   Sort numbers digit by digit starting from the least significant digit -> Option D

4. Quick Check:

   Radix Sort = Digit by digit sorting [OK]

Hint: Radix Sort processes digits from right to left [OK]

Common Mistakes:

• Thinking Radix Sort compares whole numbers directly
• Confusing Radix Sort with quicksort or mergesort
• Assuming it sorts from most significant digit first

2. Which of the following is the correct way to initialize a bucket array for Radix Sort in JavaScript?

easy

A. const buckets = [].map(() => []);

B. const buckets = new Array(10).fill([]);

C. const buckets = Array.from({ length: 10 }, () => []);

D. const buckets = Array(10).fill(null);

Solution

1. Step 1: Understand bucket initialization

   We need 10 separate arrays (buckets) for digits 0-9. Using Array.from with a function creates independent arrays.

2. Step 2: Why other options fail

   const buckets = new Array(10).fill([]); fills with the same array reference, causing all buckets to share one array. const buckets = [].map(() => []); fails because map on empty array does nothing. const buckets = Array(10).fill(null); fills with null, not arrays.

3. Final Answer:

   const buckets = Array.from({ length: 10 }, () => []); -> Option C

4. Quick Check:

   Use Array.from with function for separate buckets [OK]

Hint: Use Array.from with arrow function for unique buckets [OK]

Common Mistakes:

• Using fill([]) creates shared references
• Using map on uninitialized array returns empty
• Filling buckets with null instead of arrays

3. What will be the output of the following JavaScript code snippet using Radix Sort on the array [170, 45, 75, 90, 802, 24, 2, 66]?

function getDigit(num, place) {
  return Math.floor(Math.abs(num) / Math.pow(10, place)) % 10;
}

function radixSort(arr) {
  let maxDigit = Math.floor(Math.log10(Math.max(...arr))) + 1;
  for (let k = 0; k < maxDigit; k++) {
    let buckets = Array.from({ length: 10 }, () => []);
    for (let num of arr) {
      buckets[getDigit(num, k)].push(num);
    }
    arr = [].concat(...buckets);
  }
  return arr;
}

console.log(radixSort([170, 45, 75, 90, 802, 24, 2, 66]));

medium

A. [170, 45, 75, 90, 802, 24, 2, 66]

B. [2, 24, 45, 66, 75, 90, 170, 802]

C. [802, 170, 90, 75, 66, 45, 24, 2]

D. [2, 24, 45, 66, 75, 170, 90, 802]

Solution

1. Step 1: Understand digit extraction and sorting

   The code sorts numbers by each digit from least significant (units) to most significant. After each pass, numbers are grouped by that digit.

2. Step 2: Trace sorting passes

   After sorting by units digit, then tens, then hundreds, the array becomes fully sorted ascending: [2, 24, 45, 66, 75, 90, 170, 802].

3. Final Answer:

   [2, 24, 45, 66, 75, 90, 170, 802] -> Option B

4. Quick Check:

   Radix Sort output = Sorted ascending array [OK]

Hint: Radix Sort outputs sorted array ascending [OK]

Common Mistakes:

• Confusing original array with sorted output
• Misunderstanding digit extraction order
• Assuming sorting is descending

4. Identify the bug in this Radix Sort snippet and choose the correct fix:

function radixSort(arr) {
  let maxDigit = Math.floor(Math.log10(Math.max(...arr))) + 1;
  for (let k = 0; k <= maxDigit; k++) {
    let buckets = Array.from({ length: 10 }, () => []);
    for (let num of arr) {
      buckets[Math.floor(num / Math.pow(10, k)) % 10].push(num);
    }
    arr = [].concat(...buckets);
  }
  return arr;
}

medium

A. Change loop condition to k < maxDigit instead of <= maxDigit

B. Initialize buckets with new Array(10).fill([])

C. Use Math.ceil instead of Math.floor for maxDigit

D. Remove Math.abs from digit calculation

Solution

1. Step 1: Analyze loop range for digit passes

   The loop runs from 0 to maxDigit inclusive, causing one extra pass beyond needed digits.

2. Step 2: Fix loop condition

   Changing k <= maxDigit to k < maxDigit ensures exactly maxDigit passes, avoiding unnecessary iteration.

3. Final Answer:

   Change loop condition to k < maxDigit instead of <= maxDigit -> Option A

4. Quick Check:

   Loop runs maxDigit times, not maxDigit+1 [OK]

Hint: Loop digits from 0 to less than maxDigit [OK]

Common Mistakes:

• Using <= causes extra unnecessary pass
• Initializing buckets incorrectly with shared arrays
• Changing floor to ceil breaks digit count

5. You want to use Radix Sort to sort an array containing both positive and negative integers, like [170, -45, 75, -90, 802, 24, -2, 66]. Which approach correctly adapts Radix Sort for this case?

hard

A. Separate negative and positive numbers, sort positives with Radix Sort, sort negatives by absolute value then reverse, then combine

B. Apply Radix Sort directly on all numbers including negatives without changes

C. Convert all numbers to strings and sort lexicographically

D. Use Radix Sort only on positive numbers and ignore negatives

Solution

1. Step 1: Understand Radix Sort limitation

   Radix Sort works only on non-negative integers because it sorts digits from least significant to most significant.

2. Step 2: Adapt for negatives

   Separate negatives and positives. Sort positives normally. For negatives, sort their absolute values, then reverse the result to get correct order. Finally, combine negatives (in reversed order) before positives.

3. Final Answer:

   Separate negative and positive numbers, sort positives with Radix Sort, sort negatives by absolute value then reverse, then combine -> Option A

4. Quick Check:

   Separate negatives and positives, sort separately [OK]

Hint: Sort negatives by absolute then reverse, positives normally [OK]

Common Mistakes:

• Trying to sort negatives directly with Radix Sort
• Ignoring negative numbers in sorting
• Sorting numbers as strings causing wrong order