advanced sorting among the keys themselves to sort the sequence of keys while these distribution algorithms are fastthey are not general purpose sorting algorithms in other wordsthey cannot be applied to just any sequence of keys typicallythese algorithms are used when the keys have certain characteristics and for specific types of applications radix sort radix sort is fast distribution sorting algorithm that orders keys by examining the individual components of the keys instead of comparing the keys themselves for examplewhen sorting integer keysthe individual digits of the keys are compared from least significant to most significant this is special purpose sorting algorithm but can be used to sort many types of keysincluding positive integersstringsand floating-point values the radix sort algorithm also known as bin sort can be traced back to the time of punch cards and card readers card readers contained number of bins in which punch cards could be placed after being read by the card reader to sort values punched on cards the cards were first separated into different bins based on the value in the ones column of each value the cards would then be collected such that the cards in the bin representing zero would be placed on topfollowed by the cards in the bin for oneand so on through nine the cards were then sorted againbut this time by the tens column the process continued until the cards were sorted by each digit in the largest value the final result was stack of punch cards with values sorted from smallest to largest algorithm description to illustrate how the radix sort algorithm worksconsider the array of values shown at the top of figure as with the card reader versionbins are used to store the various keys based on the individual column values since we are sorting positive integerswe will need ten binsone for each digit the process starts by distributing the values among the various bins based on the digits in the ones columnas illustrated in step (aof figure if keys have duplicate digits in the ones columnthe values are placed in the bins in the order that they occur within the list thuseach duplicate is placed behind the keys already stored in the corresponding binas illustrated by the keys in bins and after the keys have been distributed based on the least significant digitthey are gathered back into the arrayone bin at timeas illustrated in step (bof figure the keys are taken from each binwithout rearranging themand inserted into the array with those in bin zero placed at the frontfollowed by those in bin onethen bin twoand so on until all of the keys are back in the sequence at this pointthe keys are only partially sorted the process must be repeated againbut this time the distribution is based on the digits in the tens column after distributing the keys the second timeas illustrated in step (cof figure they