advanced sorting algorithm for the radix sort we'll discuss the radix sort in terms of normal base- arithmeticwhich is easier to visualize howeveran efficient implementation of the radix sort would use base- arithmetic to take advantage of the computer' speed in bit manipulation we'll look at the radix sort rather than the similar but somewhat more complex radix-exchange sort the word radix means the base of system of numbers ten is the radix of the decimal system and is the radix of the binary system the sort involves examining each digit of the key separatelystarting with the (least significantdigit all the data items are divided into groupsaccording to the value of their digit these groups are then reassembledall the keys ending with go firstfollowed by all the keys ending in and so on up to we'll call these steps sub-sort in the second sub-sortall data is divided into groups againbut this time according to the value of their digit this must be done without changing the order of the previous sort that iswithin each of the groupsthe ordering of the items remains the same as it was after step the sub-sorts must be stable again the groups are recombinedthose with digit of firstthen those with digit of and so on up to this process is repeated for the remaining digits if some keys have fewer digits than otherstheir higher-order digits are considered to be here' an exampleusing seven data itemseach with three digits leading zeros are shown for clarity ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( /unsorted array /sorted on digit /sorted on digit /sorted on digit /sorted array the parentheses delineate the groups within each group the digits in the appropriate position are the same to convince yourself that this approach really workstry it on piece of paper with some numbers you make up designing program in practice the original data probably starts out in an ordinary array where should the groups gothere' problem with using another array or an array of