Use Counting Sort on the last digit of each number.
Example array transformed: [3, 9, 0, 6, 3, 3].
Stable Sorting: Critical as it maintains the order of elements with the same key (e.g., 53, 633, and 233 remain in order).
Step 2: Sort by Second to Last Digit
Repeat Counting Sort using the second last digit as the key.
Step 3: Sort by First Digit
Repeat the process using the first digit.
Use 0 for numbers lacking a certain place digit.
Importance of Stability
Stable Sort Requirement: Ensures elements with the same digit key appear in the same order as the original array.
Time Complexity Analysis
Definitions
n: Number of elements in the array (e.g., n=6).
D: Number of digits needed to represent each number (e.g., D=3).
B: Base of the number system used (e.g., B=10).
Time Complexity Calculation
Counting Sort Complexity: O(n + B).
K is the range of keys, which is B (e.g., 0 to 9).
Radix Sort Complexity: O(D * (n + B)).
Efficiency: Faster when the input range is small compared to the number of elements, potentially outperforming comparison-based sorts like quicksort or mergesort with complexity O(n log n).*
Considerations for Base (B)
Base Choices: Can be any positive integer, such as 2, 4, 8, or 100.
Trade-off: Larger B requires more space for Counting Sort but reduces D (number of digits), which can balance time and space efficiency.