Data Structures and Algorithm Analysis - Computer Science at ...

Sec. 7.7 Binsort and Radix Sort 247First pass(on right digit)Initial List: 27 91 1 97 17 23 84 28 72 5 67 25Second pass(on left digit)001 5191 1117272223 2527 283233484455 255666772797 17 677728288849991 97Result of first pass: 91 1 72 23 84 5 25 27 97 17 67 28Result of second pass: 1 5 17 23 25 27 28 67 72 84 91 97Figure 7.17 An example of Radix Sort for twelve two-digit numbers in base ten.Two passes are required to sort the list.a large key range requires an unacceptably large array B. Thus, even the extendedBinsort is useful only for a limited key range.A further generalization to Binsort yields a bucket sort. Each bin is associatedwith not just one key, but rather a range of key values. A bucket sort assigns recordsto bins and then relies on some other sorting technique to sort the records withineach bin. The hope is that the relatively inexpensive bucketing process will putonly a small number of records in each bin, and that a “cleanup sort” within thebins will then be relatively cheap.There is a way to keep the number of bins and the related processing smallwhile allowing the cleanup sort to be based on Binsort. Consider a sequence ofrecords with keys in the range 0 to 99. If we have ten bins available, we can firstassign records to bins by taking their key value modulo 10. Thus, every key willbe assigned to the bin matching its rightmost decimal digit. We can then take theserecords from the bins in order and reassign them to the bins on the basis of theirleftmost (10’s place) digit (define values in the range 0 to 9 to have a leftmost digitof 0). In other words, assign the ith record from array A to a bin using the formulaA[i]/10. If we now gather the values from the bins in order, the result is a sortedlist. Figure 7.17 illustrates this process.