To implement the radix sort algorithm, follow these steps:

  1. Determine the maximum number of digits in the given array. This can be done by finding the maximum number in the array and counting the number of digits it has.

  2. Initialize 10 buckets, numbered 0 to 9, corresponding to the digits from 0 to 9.

  3. Iterate through each digit position (from the least significant digit to the most significant digit) in the given array.

  4. For each digit position, distribute the numbers into the buckets based on the value of the current digit. For example, if the current digit is 3, distribute the numbers into bucket 3.

  5. Gather the numbers back from the buckets into the original array.

  6. Repeat steps 4 and 5 for the next digit position.

  7. Once all the digits have been processed, the array will be sorted.

  Here is a step-by-step example to demonstrate the radix sort algorithm:

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

  Step 1: The maximum number of digits is 3.

  Step 2: Initialize empty buckets 0 to 9.

  Step 3: Start with the least significant digit (rightmost) and move towards the most significant digit (leftmost).

  Step 4: Distribute the numbers into the buckets based on the current digit:

  Digit 0: [170, 90, 802, 2]

  Digit 1: []

  Digit 2: [2]

  Digit 3: []

  Digit 4: [24]

  Digit 5: [75, 45]

  Digit 6: [66]

  Digit 7: []

  Digit 8: []

  Digit 9: []

  Step 5: Gather the numbers back into the original array in the order of the buckets:

  [170, 90, 802, 2, 24, 75, 45, 66]

  Step 6: Repeat steps 4 and 5 for the next digit:

  Digit 0: [802, 2]

  Digit 1: [170, 90]

  Digit 2: [24]

  Digit 3: []

  Digit 4: [45]

  Digit 5: [75]

  Digit 6: [66]

  Digit 7: []

  Digit 8: []

  Digit 9: []

  Gather the numbers back into the original array:

  [802, 2, 170, 90, 24, 45, 75, 66]

  Step 7: Repeat steps 4 and 5 for the final digit:

  Digit 0: [2, 24, 45, 66, 75, 90]

  Digit 1: [170]

  Digit 2: []

  Digit 3: []

  Digit 4: []

  Digit 5: []

  Digit 6: []

  Digit 7: []

  Digit 8: []

  Digit 9: [802]

  Gather the numbers back into the original array:

  [2, 24, 45, 66, 75, 90, 170, 802]

  The array is now sorted in ascending order using the radix sort algorithm.

  It is worth noting that the radix sort algorithm is a non-comparative sorting algorithm, meaning it does not compare elements directly like other sorting algorithms such as bubble sort or quicksort. Radix sort works based on the premise of sorting elements by their digits, making it an efficient sorting algorithm for integers.