Radix Sort

Implement Radix Sort. Sort integers by processing individual digits from least significant to most significant, using a stable sort (counting sort) as a subroutine.

Example 1

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

Example 2

Input: [329, 457, 657, 839, 436, 720, 355] → Output: [329, 355, 436, 457, 657, 720, 839]

Solution Approach

Sort numbers digit by digit starting from the least significant digit (ones place). For each digit position, apply a stable counting sort using that digit as the key.

Find the maximum number to determine the number of digits.
For each digit position (1, 10, 100, ...): do a stable counting sort by that digit.
Use modulo and division to extract each digit.
After processing all digit positions, array is sorted.

Java

import java.util.Arrays;

class RadixSort {
    public void sort(int[] arr) {
        int max = Arrays.stream(arr).max().getAsInt();
        for (int exp = 1; max / exp > 0; exp *= 10)
            countingSortByDigit(arr, exp);
    }

    private void countingSortByDigit(int[] arr, int exp) {
        int n = arr.length;
        int[] output = new int[n];
        int[] count = new int[10];
        for (int v : arr) count[(v / exp) % 10]++;
        for (int i = 1; i < 10; i++) count[i] += count[i - 1];
        for (int i = n - 1; i >= 0; i--)
            output[--count[(arr[i] / exp) % 10]] = arr[i];
        System.arraycopy(output, 0, arr, 0, n);
    }
}

Time Complexity: O(D * (N + K)) where D=digits, K=10
Space Complexity: O(N + K)