Radix Sort

Radix sort is an efficient algorithm that has been used to sort data since the 1950s. It is a non-comparative sorting technique which is based on the distribution of the elements in an array. It is one of the oldest sorting algorithms still in use today and is primarily used in computer science and data analysis.

In this article, we’ll cover the basics of radix sort and how it works in detail, its time complexity and space complexity, and a few examples of Python code to help you understand the algorithm better. We’ll also include some coding exercises with solutions that test your understanding of what was covered in the article.

What is Radix Sort?

Radix sort is a non-comparative sorting algorithm that works by sorting data in a particular order based on the digits of the elements in the array. It is used to sort the elements of an array in linear time, which is much faster than other sorting algorithms like insertion or selection sort.

The algorithm works by first dividing the elements of the array into groups based on their individual digits and then sorting the groups in order from least to greatest. This process is repeated until all the elements have been sorted.

How Does Radix Sort Work?

Radix sort works by dividing the elements of the array into groups based on their individual digits and then sorting the groups in order from least to greatest. This process is repeated until all the elements have been sorted.

Let’s look at an example to understand the algorithm better. Suppose we have an array of numbers:

[314, 299, 4, 8, 99]

If we want to sort this array using radix sort, we can divide the elements into groups based on their individual digits:

Group 1: [4, 8]

Group 2: [99, 299]

Group 3: [314]

Now, we can sort the groups in order from least to greatest:

Group 1: [4, 8]

Group 2: [99, 299]

Group 3: [314]

Once the groups have been sorted, we can combine them together to get the sorted array:

[4, 8, 99, 299, 314]

Time Complexity of Radix Sort

Radix sort has a time complexity of O(nk), where n is the number of elements in the array and k is the number of digits in the largest element. This means that the time it takes to sort an array using radix sort is dependent on the size of the array and the number of digits in the elements.

It is important to note that radix sort is a very fast algorithm and has a better time complexity than other sorting algorithms such as insertion and selection sort.

Space Complexity of Radix Sort

The space complexity of radix sort is O(n+k), where n is the number of elements in the array and k is the number of digits in the largest element. This means that the amount of space required to sort an array using radix sort is dependent on the size of the array and the number of digits in the elements.

It is important to note that radix sort does not require any additional memory, as it works in place. This makes radix sort a very efficient algorithm for sorting large arrays.

Python Code for Radix Sort

Now that we understand how radix sort works and its time and space complexity, let’s look at a few examples of Python code to help us understand the algorithm better.

First, we’ll define a function that takes an array and returns the sorted array using radix sort:

def radix_sort(arr):
  # Find the maximum number to know number of digits
  max_num = max(arr) 
 
  # Loop over each digit
  exp = 1
  while max_num/exp > 0: 
    # Create buckets
    buckets = [[] for _ in range(10)] 
 
    # Put elements in respective buckets
    for element in arr: 
      buckets[(element//exp) % 10].append(element) 
 
    # Flatten all the buckets
    arr = [x for bucket in buckets for x in bucket] 
 
    # Move to next digit
    exp *= 10
 
  return arr

Now, let’s look at a few examples of using the radix_sort() function:

# Example 1
arr = [314, 299, 4, 8, 99]
sorted_arr = radix_sort(arr)
print(sorted_arr)

# Output: [4, 8, 99, 299, 314]

# Example 2
arr = [3, 27, 4, 9, 1]
sorted_arr = radix_sort(arr)
print(sorted_arr)

# Output: [1, 3, 4, 9, 27]

Conclusion

In this article, we covered the basics of radix sort and how it works in detail, its time complexity and space complexity, and a few examples of Python code to help you understand the algorithm better. We also included some coding exercises with solutions to test your understanding of what was covered in the article.

Radix sort is an efficient algorithm that has been used to sort data since the 1950s. It is a non-comparative sorting technique which is based on the distribution of the elements in an array. It is one of the oldest sorting algorithms still in use today and is primarily used in computer science and data analysis.

Radix sort has a time complexity of O(nk), where n is the number of elements in the array and k is the number of digits in the largest element. The space complexity of radix sort is O(n+k), where n is the number of elements in the array and k is the number of digits in the largest element. This makes radix sort a very efficient algorithm for sorting large arrays.

Now that you know the basics of radix sort and how it works in Python, you can use it to sort large arrays quickly and efficiently.

Exercises

Now that you know the basics of radix sort and how it works in Python, let’s test your understanding with a few coding exercises.

def radix_sort(arr):
  # Find the maximum number to know number of digits
  max_num = max(arr) 
 
  # Loop over each digit
  exp = 1
  while max_num/exp > 0: 
    # Create buckets
    buckets = [[] for _ in range(10)] 
 
    # Put elements in respective buckets
    for element in arr: 
      buckets[(element//exp) % 10].append(element) 
 
    # Flatten all the buckets
    arr = [x for bucket in buckets for x in bucket] 
 
    # Move to next digit
    exp *= 10
 
  return arr

def radix_sort_str(arr):
  # Find the maximum length string to know number of digits
  max_len = max([len(s) for s in arr]) 
 
  # Loop over each character
  for i in range(max_len): 
    # Create buckets
    buckets = [[] for _ in range(26)] 
 
    # Put elements in respective buckets
    for element in arr: 
      if i < len(element): 
        buckets[ord(element[i]) - ord('a')].append(element) 
      else: 
        buckets[0].append(element) 
 
    # Flatten all the buckets
    arr = [x for bucket in buckets for x in bucket] 
 
  return arr

def radix_sort_float(arr):
  # Find the maximum number to know number of digits
  max_num = max(arr) 
 
  # Loop over each digit
  exp = 1
  while max_num/exp > 0: 
    # Create buckets
    buckets = [[] for _ in range(10)] 
 
    # Put elements in respective buckets
    for element in arr: 
      buckets[int(element//exp % 10)].append(element) 
 
    # Flatten all the buckets
    arr = [x for bucket in buckets for x in bucket] 
 
    # Move to next digit
    exp *= 10
 
  return arr

def radix_sort_char(arr):
  # Find the maximum length string to know number of digits
  max_len = max([len(s) for s in arr]) 
 
  # Loop over each character
  for i in range(max_len): 
    # Create buckets
    buckets = [[] for _ in range(26)] 
 
    # Put elements in respective buckets
    for element in arr: 
      if i < len(element): 
        buckets[ord(element[i]) - ord('a')].append(element) 
      else: 
        buckets[0].append(element) 
 
    # Flatten all the buckets
    arr = [x for bucket in buckets for x in bucket] 
 
  return arr

def radix_sort_tuple(arr):
  # Find the maximum number to know number of digits
  max_num = max([t[0] for t in arr]) 
 
  # Loop over each digit
  exp = 1
  while max_num/exp > 0: 
    # Create buckets
    buckets = [[] for _ in range(10)] 
 
    # Put elements in respective buckets
    for element in arr: 
      buckets[int(element[0]//exp % 10)].append(element) 
 
    # Flatten all the buckets
    arr = [x for bucket in buckets for x in bucket] 
 
    # Move to next digit
    exp *= 10
 
  return arr