【数据结构】——排序算法——2.2、快速排序
一、先上维基的图:
图二、快速排序实例
分类 | 排序算法 |
---|---|
数据结构 | 不定 |
最差时间复杂度 | |
最优时间复杂度 | |
平均时间复杂度 | |
最差空间复杂度 | 根据实现的方式不同而不同 |
二、描述
快速排序使用分治法(Divide and conquer)策略来把一个序列(list)分为两个子序列(sub-lists)。举个例子,军训时第一次集合,大家一时间混乱了,不知道怎么排,这时候教官随便抓了个人,说以该同学为基准,高的站左边,矮的站右边。此时,基本就把队伍分为高低两大阵营。那么,在每个小区间内,又进行同样的操作,迭代到每个区间内只有一个人,那么操作便结束了!
步骤为:
- 从数列中挑出一个元素,称为"基准"(pivot),
- 重新排序数列,所有元素比基准值小的摆放在基准前面,所有元素比基准值大的摆在基准的后面(相同的数可以到任一边)。在这个分区退出之后,该基准就处于数列的中间位置。这个称为分区(partition)操作。
- 递归地(recursive)把小于基准值元素的子数列和大于基准值元素的子数列排序。
递归的最底部情形,是数列的大小是零或一,也就是永远都已经被排序好了。虽然一直递归下去,但是这个算法总会退出,因为在每次的迭代(iteration)中,它至少会把一个元素摆到它最后的位置去。
三、Java程序
非wiki版:
- public class Qsorta {
- public static void qsort_asc(int source[],int low,int high){
- int i,j,x;
- if(low < high){
- i = low;
- j = high;
- x = source[i];
- while(i<j){
- while(i<j&& source[j]>x ){
- j--;
- }
- if(i<j){
- source[i] = source[j];
- i++;
- }
- while(i<j&& source[i] < x){
- i++;
- }
- if(i<j){
- source[j] = source[i];
- j--;
- }
- }
- source[i] = x;
- qsort_asc(source,low,i-1);
- qsort_asc(source,i+1,high);
- }
- }
- public static void main(String[] args){
- int[] a = {4,2,1,6,3,-5,85};
- int i;
- qsort_asc(a,a.length-1);
- for(i=0;i<a.length-1;i++)
- System.out.println("a" + i + " is "+a[i]);
- }
- }
wiki版:
- import java.util.Comparator;
- import java.util.Random;
- public class Quicksort {
- public static final Random RND = new Random();
- private static void swap(Object[] array,int i,int j) {
- Object tmp = array[i];
- array[i] = array[j];
- array[j] = tmp;
- }
- private static <E> int partition(E[] array,int begin,int end,Comparator<? super E> cmp) {
- int index = begin + RND.nextInt(end - begin + 1);
- E pivot = array[index];
- swap(array,index,end);
- for (int i = index = begin; i < end; ++ i) {
- if (cmp.compare(array[i],pivot) <= 0) {
- swap(array,index++,i);
- }
- }
- swap(array,end);
- return (index);
- }
- private static <E> void qsort(E[] array,Comparator<? super E> cmp) {
- if (end > begin) {
- int index = partition(array,begin,end,cmp);
- qsort(array,index - 1,index + 1,cmp);
- }
- }
- public static <E> void sort(E[] array,Comparator<? super E> cmp) {
- qsort(array,array.length - 1,cmp);
- }
- }
- /*
- * more efficient implements for quicksort. <br />
- * use left,center and right median value (@see #median()) for the pivot,and
- * the more efficient inner loop for the core of the algorithm.
- */
- class Sort {
- public static final int CUTOFF = 11;
- /**
- * quick sort algorithm. <br />
- *
- * @param arr an array of Comparable items. <br />
- */
- public static <T extends Comparable<? super T>> void quicksort( T[] arr ) {
- quickSort( arr,arr.length - 1 );
- }
- /**
- * get the median of the left,center and right. <br />
- * order these and hide the pivot by put it the end of
- * of the array. <br />
- *
- * @param arr an array of Comparable items. <br />
- * @param left the most-left index of the subarray. <br />
- * @param right the most-right index of the subarray.<br />
- * @return T
- */
- public static <T extends Comparable<? super T>> T median( T[] arr,int left,int right ) {
- int center = ( left + right ) / 2;
- if ( arr[left].compareTo( arr[center] ) > 0 )
- swapRef( arr,left,center );
- if ( arr[left].compareTo( arr[right] ) > 0 )
- swapRef( arr,right );
- if ( arr[center].compareTo( arr[right] ) > 0 )
- swapRef( arr,center,right );
- swapRef( arr,right - 1 );
- return arr[ right - 1 ];
- }
- /**
- * internal method to sort the array with quick sort algorithm. <br />
- *
- * @param arr an array of Comparable Items. <br />
- * @param left the left-most index of the subarray. <br />
- * @param right the right-most index of the subarray. <br />
- */
- private static <T extends Comparable<? super T>> void quickSort( T[] arr,int right ) {
- if ( left + CUTOFF <= right ) {
- //find the pivot
- T pivot = median( arr,right );
- //start partitioning
- int i = left,j = right - 1;
- for ( ; ; ) {
- while ( arr[++i].compareTo( pivot ) < 0 ) ;
- while ( arr[--j].compareTo( pivot ) > 0 ) ;
- if ( i < j )
- swapRef( arr,i,j );
- else
- break;
- }
- //swap the pivot reference back to the small collection.
- swapRef( arr,right - 1 );
- quickSort( arr,i - 1 ); //sort the small collection.
- quickSort( arr,i + 1,right ); //sort the large collection.
- } else {
- //if the total number is less than CUTOFF we use insertion sort instead (cause it much more efficient).
- insertionSort( arr,right );
- }
- }
- /**
- * method to swap references in an array.<br />
- *
- * @param arr an array of Objects. <br />
- * @param idx1 the index of the first element. <br />
- * @param idx2 the index of the second element. <br />
- */
- public static <T> void swapRef( T[] arr,int idx1,int idx2 ) {
- T tmp = arr[idx1];
- arr[idx1] = arr[idx2];
- arr[idx2] = tmp;
- }
- /**
- * method to sort an subarray from start to end
- * with insertion sort algorithm. <br />
- *
- * @param arr an array of Comparable items. <br />
- * @param start the begining position. <br />
- * @param end the end position. <br />
- */
- public static <T extends Comparable<? super T>> void insertionSort( T[] arr,int start,int end ) {
- int i;
- for ( int j = start + 1; j <= end; j++ ) {
- T tmp = arr[j];
- for ( i = j; i > start && tmp.compareTo( arr[i - 1] ) < 0; i-- ) {
- arr[ i ] = arr[ i - 1 ];
- }
- arr[ i ] = tmp;
- }
- }
- }