Radix Sort

A radix sort is an algorithm, a procedure, which can rearrange integer representations based on the processing of individual digits in such a way that the integer representations are eventually in either ascending or descending order. Integer representations can be used to represent things such as strings of characters (names of people, places, things, the words and characters that you are reading now, dates, etc.) and specially formatted floating point numbers as well as integers. So, anything which can be represented as an ordered sequence of integer representations can be rearranged to be in order by a radix sort. Most digital computers internally represent all of their data as electronic representations of binary numbers, so processing the digits of integer representations by groups of binary digit representations is most convenient. Two classifications of radix sorts are least significant digit (LSD) radix sorts and most significant digit (MSD) radix sorts. LSD radix sorts process the integer representations starting from the least significant digit and move the processing towards the most significant digit. MSD radix sorts process the integer representations starting from the most significant digit and move the processing towards the least significant digit. The integer representations that are processed by sorting algorithms are often called, "keys," which can exist all by themselves or be associated with other data. LSD radix sorts typically use the following sorting order: short keys come before longer keys, and keys of the same length are sorted lexicographically. This coincides with the normal order of integer representations, such as the sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. MSD radix sorts use lexicographic order, which is suitable for sorting strings, such as words, or fixed-length integer representations. A sequence such as b, c, d, e, f, g, h, i, j, ba would be lexicographically sorted as b, ba, c, d, e, f, g, h, i, j. If lexicographic ordering is used to sort variable-length integer representations, then the representations of the numbers from 1 to 10 would be output as 1, 10, 2, 3, 4, 5, 6, 7, 8, 9, as if the shorter keys were left-justified and padded on the right with blank characters to make the shorter keys as long as the longest key for the purpose of determining sorted order.

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