Radix Sort - Python

Given an array of integers, the task is to sort the elements in ascending order using Radix Sort. Radix Sort processes each digit of the numbers starting from the least significant digit to the most significant digit. It groups numbers into buckets based on their digit values and rearranges them after every pass until all digits are processed.

For Example:

Input: [170, 45, 75, 90, 802, 24, 2, 66]
Output: [2, 24, 45, 66, 75, 90, 170, 802]
Explanation: The elements are sorted digit by digit first by units, then tens, then hundreds place, resulting in the final ascending order.

Working of Radix Sort Algorithm

To sort the array [170, 45, 75, 90, 802, 24, 2, 66], Radix Sort processes digits one place at a time, starting from the least significant digit (LSD) to the most significant digit (MSD).

Step 1: Find the largest number 802, which has 3 digits, so the algorithm performs 3 iterations (units, tens, hundreds).

Step 2: Sort by units place

Using a stable counting sort, the array becomes -> [170, 90, 802, 2, 24, 45, 75, 66].

Step 3: Sort by tens place

Sorting again by the tens digit gives -> [802, 2, 24, 45, 66, 170, 75, 90].

Step 4: Sort by hundreds place

Sorting by the hundreds digit results in -> [2, 24, 45, 66, 75, 90, 170, 802].

Step 5: After all digits are processed, the array is fully sorted

Final Output: [2, 24, 45, 66, 75, 90, 170, 802]

Using Counting Sort (Digit-by-Digit Approach)

This method performs sorting for each digit using a stable version of Counting Sort, ensuring numbers with the same digit maintain their order. It’s memory-efficient and works well for integer data.

def radix_sort(arr):
    max_num = max(arr)
    exp = 1  # Represents current digit place (1, 10, 100, ...)

    while max_num // exp > 0:
        n = len(arr)
        output = [0] * n
        count = [0] * 10  # For digits 0–9

        # Count occurrences of each digit
        for num in arr:
            index = (num // exp) % 10
            count[index] += 1

        # Convert count[] to actual positions
        for i in range(1, 10):
            count[i] += count[i - 1]

        # Build output array (in reverse for stability)
        for i in range(n - 1, -1, -1):
            index = (arr[i] // exp) % 10
            output[count[index] - 1] = arr[i]
            count[index] -= 1

        # Copy output to arr[]
        for i in range(n):
            arr[i] = output[i]

        exp *= 10

arr = [170, 45, 75, 90, 802, 24, 2, 66]
radix_sort(arr)
print(arr)

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

Explanation:

• (num // exp) % 10 extracts the current digit of each number.
• count[] stores the frequency of each digit (0–9).
• The array is rebuilt in reverse to maintain the stable order.
• After each pass, digits of the next higher place are processed until fully sorted.

Using Bucket Sort Logic

This version uses digit buckets (lists) instead of counting arrays. Each digit’s bucket stores numbers belonging to it, and the list is flattened after each pass.

def radix_sort_bucket(arr):
    max_num = max(arr)
    exp = 1

    while max_num // exp > 0:
        buckets = [[] for _ in range(10)]

        # Distribute numbers into buckets based on current digit
        for num in arr:
            index = (num // exp) % 10
            buckets[index].append(num)

        # Recombine buckets into the main list
        arr = [num for bucket in buckets for num in bucket]

        exp *= 10

    return arr

arr = [170, 45, 75, 90, 802, 24, 2, 66]
print(radix_sort_bucket(arr))

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

Explanation:

• Creates 10 buckets (0–9) for current digit values.
• Places each number into its respective bucket based on the digit.
• Merges all buckets to form a partially sorted list.
• Repeats the process for higher digit places until the array is sorted.

Please refer complete article on Radix Sort for more details!