How Radix sort works

Radix sort is simple and unique sorting method.
It sorts number with LSD and MSD ( Lease Significant Digit to Most Significant Digit)

Radix Sort puts the elements in order by comparing the digits of the numbers. I will explain with an example.


Consider the following 9 numbers:

493   812   715   710   195   437   582   340   385

Step 1) We should start sorting by comparing and ordering the one's digits:

Digit	Sublist
0	340 710
1
2	812 582
3	493
4
5	715 195 385
6
7	437
8
9

Notice that the numbers were added onto the list in the order that they were found, which is why the numbers appear to be unsorted in each of the sublists above. Now, we gather the sublists (in order from the 0 sublist to the 9 sublist) into the main list again:

340   710   812   582   493   715   195   385   437

Step 2) Now, the sublists are created again, this time based on the ten's digit:

Digit	Sublist
0
1	710 812 715
2
3	437
4	340
5
6
7
8	582 385
9	493 195

Now the sublists are gathered in order from 0 to 9:

710   812   715   437   340   582   385   493   195

Step 3) the sublists are created according to the hundred's digit:

Digit	Sublist
0
1	195
2
3	340 385
4	437 493
5	582
6
7	710 715
8	812
9

At last, the list is gathered up again:

195   340   385   437   493   582   710   715   812

Code :

#include<iostream>
using namespace std;

// A utility function to get maximum value in arr[]
int getMax(int arr[], int n)
{
    int mx = arr[0];
    for (int i = 1; i < n; i++)
        if (arr[i] > mx)
            mx = arr[i];
    return mx;
}

// A function to do counting sort of arr[] according to
// the digit represented by exp.
void countSort(int arr[], int n, int exp)
{
    int output[n]; // output array
    int i, count[10] = {0};

    // Store count of occurrences in count[]
    for (i = 0; i < n; i++)
        count[ (arr[i]/exp)%10 ]++;

    // Change count[i] so that count[i] now contains actual position of
    // this digit in output[]
    for (i = 1; i < 10; i++)
        count[i] += count[i - 1];

    // Build the output array
    for (i = n - 1; i >= 0; i--)
    {
        output[count[ (arr[i]/exp)%10 ] - 1] = arr[i];
        count[ (arr[i]/exp)%10 ]--;
    }

    // Copy the output array to arr[], so that arr[] now
    // contains sorted numbers according to curent digit
    for (i = 0; i < n; i++)
        arr[i] = output[i];
}

// The main function to that sorts arr[] of size n using Radix Sort
void radixsort(int arr[], int n)
{
    // Find the maximum number to know number of digits
    int m = getMax(arr, n);

    // Do counting sort for every digit. Note that instead of passing digit
    // number, exp is passed. exp is 10^i where i is current digit number
    for (int exp = 1; m/exp > 0; exp *= 10)
        countSort(arr, n, exp);
}

// A utility function to print an array
void print(int arr[], int n)
{
    for (int i = 0; i < n; i++)
        cout << arr[i] << " ";
}

// Driver program to test above functions
int main()
{
    int arr[] = {170, 45, 75, 90, 802, 24, 2, 66};
    int n = sizeof(arr)/sizeof(arr[0]);
    radixsort(arr, n);
    print(arr, n);
    return 0;
}

Output:

2  24  45  66  75  90  170  802




References:

http://en.wikipedia.org/wiki/Radix_sort

Code : http://www.geeksforgeeks.org/radix-sort/