Radix Sort Algorithm in DSA Go - Build from Scratch

Radix Sort Algorithm

📖 Scenario: You work in a warehouse where packages are labeled with numbers. You want to sort these package numbers quickly to organize shipments.

🎯 Goal: Build a program that sorts a list of package numbers using the Radix Sort algorithm.

📋 What You'll Learn

Create a list of integers representing package numbers

Create a variable to track the maximum number of digits

Implement the Radix Sort logic using counting sort by digit

Print the sorted list of package numbers

💡 Why This Matters

🌍 Real World

Sorting package numbers quickly helps warehouses organize shipments efficiently.

💼 Career

Understanding Radix Sort is useful for software engineers working on performance-critical sorting tasks.

1

Create the list of package numbers

Create a list called packages with these exact integers: 170, 45, 75, 90, 802, 24, 2, 66

DSA Go

# Create the list called packages with the given numbers
# Your code here

Hint

Use packages := []int{170, 45, 75, 90, 802, 24, 2, 66} to create the list.

2

Find the maximum number in the list

Create a variable called maxNum and set it to the maximum value in the packages list using a simple loop

DSA Go

packages := []int{170, 45, 75, 90, 802, 24, 2, 66}
// Find the maximum number in packages and assign it to maxNum
// Your code here

Hint

Start with maxNum := packages[0] and update it inside a for loop.

3

Implement Radix Sort logic

Write a loop that sorts packages by each digit place using counting sort logic. Use a variable exp starting at 1 and multiply by 10 each iteration until exp is greater than maxNum. Inside the loop, create a count array of size 10, count digits, and reorder packages accordingly.

DSA Go

packages := []int{170, 45, 75, 90, 802, 24, 2, 66}
maxNum := packages[0]
for _, num := range packages {
    if num > maxNum {
        maxNum = num
    }
}
// Implement radix sort using exp starting at 1
// Your code here

Hint

Use a loop with exp starting at 1 and multiply by 10 each time. Use counting sort steps inside.

4

Print the sorted list

Write a print statement to display the sorted packages list

DSA Go

packages := []int{170, 45, 75, 90, 802, 24, 2, 66}
maxNum := packages[0]
for _, num := range packages {
    if num > maxNum {
        maxNum = num
    }
}

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

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

    exp *= 10
}
// Print the sorted packages list
// Your code here

Hint

Use fmt.Println(packages) to print the sorted list.

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