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

Recall & Review

beginner

What is the main idea behind Radix Sort Algorithm?

Radix Sort sorts numbers by processing individual digits. It starts from the least significant digit and moves to the most significant digit, grouping numbers by each digit to sort them step by step.

intermediate

How does Radix Sort differ from comparison-based sorting algorithms?

Radix Sort does not compare elements directly. Instead, it sorts numbers digit by digit using counting sort or bucket sort as a subroutine, making it faster for certain types of data like integers.

intermediate

What is the time complexity of Radix Sort for n numbers with d digits?

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

intermediate

Why is Counting Sort used as a subroutine in Radix Sort?

Counting Sort is stable and efficient for sorting digits because it sorts elements in linear time based on digit values, preserving the order of equal elements which is important for Radix Sort's correctness.

beginner

What kind of data is Radix Sort best suited for?

Radix Sort works best for sorting integers or fixed-length strings where the number of digits or characters is limited and known, making it very efficient compared to comparison-based sorts.

Which digit does Radix Sort process first when sorting numbers?

A Middle digit

B Most significant digit

C Least significant digit

D Random digit

Radix Sort starts sorting from the least significant digit to the most significant digit.

What sorting method is commonly used inside Radix Sort for sorting digits?

A Bubble Sort

B Counting Sort

C Merge Sort

D Quick Sort

Counting Sort is used because it is stable and efficient for sorting digits.

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

A It can sort in linear time for fixed digit lengths

B It uses less memory

C It works on any data type

D It is simpler to implement

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

Radix Sort is best used for which type of data?

A Integers or fixed-length strings

B Floating point numbers

C Unstructured text

D Linked lists

Radix Sort works best with integers or fixed-length strings where digit positions are well defined.

What property must the sorting subroutine have in Radix Sort?

A Recursive

B In-place sorting

C Divide and conquer

D Stability

The subroutine must be stable to maintain the order of digits sorted in previous steps.

Explain how Radix Sort processes numbers step by step.

Think about sorting digits one by one from right to left.

Describe why stability in the sorting subroutine is important for Radix Sort.

Consider what happens if order changes between digit sorts.

Practice

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

easy

A. Sort numbers by dividing the list into halves recursively

B. Sort numbers by processing individual digits from least to most significant

C. Sort numbers by comparing each pair directly

D. Sort numbers by swapping adjacent elements repeatedly

Solution

1. Step 1: Understand Radix Sort approach

   Radix Sort sorts numbers by grouping digits and sorting them digit by digit, starting from the least significant digit.

2. Step 2: Compare with other sorting methods

   Unlike comparison-based sorts (like bubble or merge sort), Radix Sort processes digits individually without direct element comparisons.

3. Final Answer:

   Sort numbers by processing individual digits from least to most significant -> Option B

4. Quick Check:

   Radix Sort = Digit-wise sorting [OK]

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

Common Mistakes:

• Thinking Radix Sort compares elements directly
• Confusing Radix Sort with divide and conquer methods
• Assuming it swaps adjacent elements like bubble sort

2. Which of the following is the correct way to initialize a slice of buckets for Radix Sort in Go?

easy

A. buckets := [][]int{}

B. buckets := make([]int, 10)

C. buckets := make([][]int, 10)

D. buckets := [10]int{}

Solution

1. Step 1: Identify bucket type needed

   Radix Sort uses buckets to hold multiple integers per digit, so each bucket must be a slice of ints.

2. Step 2: Choose correct slice initialization

   Using make([][]int, 10) creates a slice of 10 slices, perfect for buckets 0-9.

3. Final Answer:

   buckets := make([][]int, 10) -> Option C

4. Quick Check:

   Slice of slices for buckets = buckets := make([][]int, 10) [OK]

Hint: Buckets hold slices, so use [][]int with make [OK]

Common Mistakes:

• Using single int slice instead of slice of slices
• Using array instead of slice for dynamic buckets
• Initializing empty slice without length

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

package main
import "fmt"
func main() {
  arr := []int{170, 45, 75, 90, 802, 24, 2, 66}
  radixSort(arr)
  fmt.Println(arr)
}

func radixSort(arr []int) {
  max := getMax(arr)
  exp := 1
  for max/exp > 0 {
    countSort(arr, exp)
    exp *= 10
  }
}

func getMax(arr []int) int {
  max := arr[0]
  for _, v := range arr {
    if v > max {
      max = v
    }
  }
  return max
}

func countSort(arr []int, exp int) {
  n := len(arr)
  output := make([]int, n)
  count := make([]int, 10)

  for i := 0; i < n; i++ {
    index := (arr[i] / exp) % 10
    count[index]++
  }

  for i := 1; i < 10; i++ {
    count[i] += count[i-1]
  }

  for i := n - 1; i >= 0; i-- {
    index := (arr[i] / exp) % 10
    output[count[index]-1] = arr[i]
    count[index]--
  }

  for i := 0; i < n; i++ {
    arr[i] = output[i]
  }
}

medium

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

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

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

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

Solution

1. Step 1: Understand Radix Sort process on given array

   Radix Sort sorts by digits from least significant to most significant. After sorting by units, tens, and hundreds place, the array becomes sorted.

2. Step 2: Trace final sorted array

   The final sorted array is ascending: [2, 24, 45, 66, 75, 90, 170, 802].

3. Final Answer:

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

4. Quick Check:

   Radix Sort output = Sorted ascending array [OK]

Hint: Radix Sort outputs sorted array ascending [OK]

Common Mistakes:

• Confusing order of digits processed
• Misreading output as original array
• Mixing up output with descending order

4. Identify the bug in this Radix Sort countSort function snippet in Go:

func countSort(arr []int, exp int) {
  n := len(arr)
  output := make([]int, n)
  count := make([]int, 10)

  for i := 0; i < n; i++ {
    index := (arr[i] / exp) % 10
    count[index]++
  }

  for i := 1; i < 10; i++ {
    count[i] += count[i-1]
  }

  for i := 0; i < n; i++ {
    index := (arr[i] / exp) % 10
    output[count[index]-1] = arr[i]
    count[index]--
  }

  for i := 0; i < n; i++ {
    arr[i] = output[i]
  }
}

medium

A. The last for loop should iterate backwards from n-1 to 0

B. The count array size should be 100 instead of 10

C. The output slice should be initialized with zeros explicitly

D. The index calculation should use modulo 100 instead of 10

Solution

1. Step 1: Check order of placing elements in output

   To maintain stable sorting, elements must be placed from right to left (backwards) in output.

2. Step 2: Identify incorrect loop direction

   The code uses a forward loop (0 to n-1) which breaks stability; it should loop from n-1 down to 0.

3. Final Answer:

   The last for loop should iterate backwards from n-1 to 0 -> Option A

4. Quick Check:

   Stable sort needs backward loop [OK]

Hint: Place elements backward to keep stable order [OK]

Common Mistakes:

• Looping forward breaks stability
• Changing count array size unnecessarily
• Misunderstanding index calculation

5. You want to sort a list of strings representing numbers with varying lengths using Radix Sort in Go. Which approach correctly adapts Radix Sort for this case?

hard

A. Pad all strings with leading zeros to equal length, then sort digit by digit from right to left

B. Sort strings by length first, then apply Radix Sort on digits from left to right

C. Convert strings to integers and apply normal Radix Sort directly

D. Use Radix Sort only on the first character of each string

Solution

1. Step 1: Handle varying string lengths

   Pad strings with leading zeros so all have equal length, ensuring digit positions align.

2. Step 2: Apply Radix Sort digit by digit from right to left

   After padding, sort from least significant digit (rightmost) to most significant (leftmost) to maintain correct order.

3. Final Answer:

   Pad all strings with leading zeros to equal length, then sort digit by digit from right to left -> Option A

4. Quick Check:

   Padding equalizes length for Radix Sort [OK]

Hint: Pad strings to same length before sorting digits [OK]

Common Mistakes:

• Sorting by length first breaks digit alignment
• Converting strings to int may overflow or lose leading zeros
• Sorting only first character ignores full number