Radix Sort

A non-comparison based sorting algorithm that sorts integers digit by digit from the least significant to the most significant.

How It Works

1. Start with the least significant digit.

2. Use a stable sorting algorithm (e.g., Counting Sort) to sort by that digit.

3. Repeat for all digits (moving left).

Example:

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

• Sort by units → [170, 90, 802, 2, 24, 45, 75, 66]
• Sort by tens → [802, 2, 24, 45, 66, 170, 75, 90]
• Sort by hundreds → [2, 24, 45, 66, 75, 90, 170, 802]

Properties

Property	Description
Stable	Yes - uses stable sort at each digit
In-place	No - needs extra space for buckets
Not Comparison-Based	Yes
Efficient for Integers	Yes, especially large numbers

Time and Space Complexity

Time complexity - O(nk) where k is number of digits
Space complexity - O(n + k)

When to Use

• Large number of integers
• When all values are non-negative integers
• When stability is important

When Not to Use

• Floating point or negative numbers
• When memory usage is a concern

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Pseudocode

def counting_sort_exp(arr, exp):
    n = len(arr)
    output = [0] * n
    count = [0] * 10
    for i in range(n):
        index = (arr[i] // exp) % 10
        count[index] += 1
    for i in range(1, 10):
        count[i] += count[i - 1]
    for i in range(n - 1, -1, -1):
        index = (arr[i] // exp) % 10
        output[count[index] - 1] = arr[i]
        count[index] -= 1
    for i in range(n):
        arr[i] = output[i]
 
def radix_sort(arr):
    max_val = max(arr)
    exp = 1
    while max_val // exp > 0:
        counting_sort_exp(arr, exp)
        exp *= 10
    ```