计数排序

Suppose we have an input array  consisting of  integers, each in the range . The counting-sortalgorithm sorts  using an auxiliary array  of counters. It outputs a sorted version of  as an auxiliary array .

The idea behind counting-sort is simple: For each , count the number of occurrences of  in and store this in . Now, after sorting, the output will look like  occurrences of 0, followed by occurrences of 1, followed by  occurrences of 2,..., followed by  occurrences of .

The first  loop in this code sets each counter  so that it counts the number of occurrences of  in . By using the values of  as indices, these counters can all be computed in  time with a single for loop. At this point, we could use  to fill in the output array  directly. However, this would not work if the elements of have associated data. Therefore we spend a little extra effort to copy the elements of  into .

The next  loop, which takes  time, computes a running-sum of the counters so that  becomes the number of elements in  that are less than or equal to . In particular, for every , the output array, , will have

Finally, the algorithm scans  backwards to place its elements, in order, into an output array . When scanning, the element  is placed at location  and the value  is decremented.

Theorem 11..7   The  method can sort an array  containing  integers in the set  in  time.

The counting-sort algorithm has the nice property of being stable; it preserves the relative order of equal elements. If two elements  and  have the same value, and  then  will appear before  in . This will be useful in the next section.

public class CountSort{    static  int[] countSort(int[] a,int k){        //k max element in array a        // the value of the element in a  server as the index for c , the key point        int[] c=new int[k];        for (int i = 0; i < a.length; i++)        {            c[a[i]]++;//same element in a will count the same element in c array        }        // from 1,not 0        for (int i = 1; i <k; i++)        {            c[i]+=c[i-1];        }        int[] b=new int[a.length];        for (int i=a.length-1; i >-1; i--)        {            //-- operation is to process the duplicate element, the value in array is changed. pay attention             b[--c[a[i]]]=a[i];        }        return b;    }        public static int getMax(int[] arr) {        int max = arr[0];        for (int i = 0; i < arr.length; i++) {            if (arr[i] > max)                max = arr[i];        }        return max;    }        public static void display(int[] R)    {        System.out.println();        for (int i = 0; i < R.length; i++)        {            System.out.print(R[i] + " ");        }    }    public static void main(String[] args)    {        int[] r = { 2,3,1,5,1,6,9,9 };        display(r);        int k=getMax(r)+1;        int[] b=countSort(r,k);        display(b);    }}