Radix Sort Algorithm in DSA Javascript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is Radix Sort?

Radix Sort is a sorting method that sorts numbers digit by digit, starting from the least significant digit to the most significant digit.

beginner

How does Radix Sort handle sorting of numbers?

It groups numbers by each digit using buckets, sorts them by that digit, and repeats for each digit until all digits are processed.

intermediate

Why is Radix Sort efficient for sorting integers?

Because it sorts numbers by digits without comparing whole numbers, making it faster than comparison-based sorts for large lists of integers.

intermediate

What is the time complexity of Radix Sort?

The time complexity is O(d * (n + k)) where d is the number of digits, n is the number of elements, and k is the range of digits (usually 10).

advanced

Can Radix Sort be used for sorting strings?

Yes, Radix Sort can sort strings by processing characters from right to left, similar to digits in numbers.

Radix Sort processes digits starting from which position?

A Least significant digit

B Most significant digit

C Middle digit

D Random digit

Radix Sort starts sorting from the least significant digit to ensure correct order after all digits are processed.

What data structure is commonly used in Radix Sort to group numbers by digit?

A Stack

B Queue

C Linked list

D Buckets or arrays

Buckets or arrays are used to group numbers by their current digit during each pass.

Which of these is NOT true about Radix Sort?

A It compares whole numbers directly.

B It sorts digit by digit.

C It can be faster than comparison sorts for integers.

D It uses stable sorting at each digit.

Radix Sort does not compare whole numbers directly; it sorts based on individual digits.

What is the main advantage of Radix Sort over comparison-based sorts?

A It uses less memory.

B It can sort in linear time for fixed digit size.

C It sorts in place.

D It works only on strings.

Radix Sort can achieve linear time complexity when the number of digits is fixed.

Radix Sort is best suited for which type of data?

A Random strings of varying length

B Floating point numbers with many decimals

C Large integers with fixed digit length

D Unsorted linked lists

Radix Sort works best on large integers with fixed digit length because it processes digits uniformly.

Explain how Radix Sort sorts a list of numbers step-by-step.

Think about sorting by each digit one at a time.

Describe the advantages and limitations of Radix Sort compared to other sorting algorithms.

Consider speed and data types it works best with.

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