Mastering Algorithms with C

Description of Radix Sort

Radix sort is another efficient, linear-time sorting algorithm. It works by sorting data in pieces called digits, one digit at a time, from the digit in the least significant position to the most significant. Using radix sort to sort the set of radix-10 numbers {15, 12, 49, 16, 36, 40}, for example, produces {40, 12, 15, 16, 36, 49} after sorting on the least significant digit, and {12, 15, 16, 36, 40, 49} after sorting on the most significant digit.

It is very important that radix sort use a stable sort for sorting on the digit values in each position. This is because once an element has been assigned a place according to the digit value in a less significant position, its place must not change unless sorting on one of the more significant digits requires it. For example, in the set given earlier, when 12 and 15 were sorted on the digits in the most significant position, since both integers contained a “1,” a nonstable sort may not have left them in the order they were placed when sorted by their least significant digit. A stable sort ensures that these two are not reordered. Radix sort uses counting sort because, aside from being stable, it runs in linear time, and for any radix, we know the largest integer any digit may be.

Radix sort is not limited to sorting data keyed by integers, as long as we can divide the elements into integer pieces. For example, we might sort a set of strings as radix-2⁸ values. Or we might sort a set of 64-bit integers as ...