# barcode in ssrs 2008 The secondary sorting method at line 8 is called a counting sort or tally sort. in Java Drawing EAN / UCC - 13 in Java The secondary sorting method at line 8 is called a counting sort or tally sort.

The secondary sorting method at line 8 is called a counting sort or tally sort.
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Theorem 14.18 The radix sort runs in O(n) time. The algorithm has WIDTH iterations and processes all n elements on each iteration three times. Thus, the running time is proportional to WIDTH*n and is a constant. Although O(n) is theoretically better than O(n lgn), the radix sort is rarely faster than the O(n lgn) sorting algorithms (merge sort, quick sort, and heap sort). That is because it has a lot of overhead extracting digits and copying arrays. THE BUCKET SORT The bucket sort is another distribution sort. It distributes the elements into buckets according to some coarse grain criterion and then applies another sorting algorithm to each bucket. It is similar to the quick sort in that all the elements in bucket i are greater than or equal to all the elements in bucket i 1 and less than or equal to all the elements in bucket i+1. Whereas quick sort partitions the sequence into two buckets, the bucket sort partitions the sequence into n buckets.
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Algorithm 14.11 The Bucket Sort (Precondition: s = {s0 . . . sn 1} is a sequence of n ordinal values with known minimum value min and maximum value max.) (Postcondition: the sequence s is sorted.) 1. Initialize an array of n buckets (collections). 2. Repeat step 3 for each si in the sequence. 3. Insert si into bucket j, where j = rn , r = (si min)/(max + 1 min). 4. Sort each bucket. 5. Repeat step 6 for j from 0 to n 1. 6. Add the elements of bucket j sequentially back into s. EXAMPLE 14.14 Sorting U.S. Social Security Numbers with the Bucket Sort.
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Suppose you have 1000 nine-digit identification numbers. Set up 1000 arrays of type int and then distribute the numbers using the formula j = rn , r = (si min)/(max + 1 min) = (si 0)/(109 + 1 0) si /109. So, for example, the identification number 666666666 would be inserted into bucket number j where j = rn = (666666666/109)(103) = 666.666666 = 666. Similarly, identification number 123456789 would be inserted into bucket number 123, and identification number 666543210 would be inserted into bucket 666. (See Figure 14.6.) Then each bucket would be sorted. Note that the number of elements in each bucket will average 1, so the choice of sorting algorithm will not affect the running time. Finally, the elements are copied back into s, starting with bucket number 0.
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Figure 14.6 Tracing the bucket sort
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EXAMPLE 14.15 The Bucket Sort
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public static void sort(int[] a) { // POSTCONDITION: a[0] <= a[1] <= ... <= a[a.length-1]; int min = min(a); int max = max(a); int n = a.length; Bucket[] bucket = new Bucket[n]; // step 1 for (int j=0; j<n; j++) { bucket[j] = new Bucket(); } for (int i=0; i<n; i++) { // step 2 int j = n*(a[i] - min)/(max + 1 - min); bucket[j].add(a[i]); // step 3 } int i=0; for (int j=0; j<n; j++) { Bucket bj=bucket[j]; bj.sort(); // step 4 for (int k=0; k<bj.size(); k++) { // step 5 a[i++] = bj.get(k); } } } private static int min(int[] a) { int min = a[0]; for (int ai: a) { if (ai < min) { min = ai; } } return min; } private static int max(int[] a) { int max = a[0]; for (int ai: a) { if (ai > max) { max = ai; } } return max; }
This program requires the implementation of this interface:
public interface Bucket { public void add(int x); public int get(int k); public int size(); } // appends x to end of bucket // returns element k from bucket // returns the number of elements
For example:
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private static class Bucket extends java.util.ArrayList<Integer> { void sort() { java.util.Arrays.sort(this.toArray()); } }