Java排序算法 归并排序

归并排序（Merge）是将两个（或两个以上）有序表合并成一个新的有序表，即把待排序序列分为若干个子序列，每个子序列是有序的。然后再把有序子序列合并为整体有序序列。

归并排序是建立在归并操作上的一种有效的排序算法。该算法是采用分治法（Divide and Conquer）的一个非常典型的应用。 将已有序的子序列合并，得到完全有序的序列；即先使每个子序列有序，再使子序列段间有序。若将两个有序表合并成一个有序表，称为2-路归并。

归并排序算法稳定，数组需要O(n)的额外空间，链表需要O(log(n))的额外空间，时间复杂度为O(nlog(n))，算法不是自适应的，不需要对数据的随机读取。

工作原理：

1、申请空间，使其大小为两个已经排序序列之和，该空间用来存放合并后的序列

2、设定两个指针，最初位置分别为两个已经排序序列的起始位置

3、比较两个指针所指向的元素，选择相对小的元素放入到合并空间，并移动指针到下一位置

4、重复步骤3直到某一指针达到序列尾

5、将另一序列剩下的所有元素直接复制到合并序列尾

代码实现：

1. public<wbr></wbr>void<wbr>mergeSort(){<wbr><wbr><wbr></wbr></wbr></wbr></wbr>
2. long[]<wbr>workSpace<wbr>=<wbr></wbr></wbr></wbr>new<wbr></wbr>long[nElems];<wbr><wbr><wbr></wbr></wbr></wbr>
3. recMergeSort(workSpace,0,nElems-1);<wbr><wbr><wbr></wbr></wbr></wbr>
4. }<wbr><wbr><wbr></wbr></wbr></wbr>
5. private<wbr></wbr>void<wbr>recMergeSort(</wbr>long[]<wbr>workSpace,<wbr></wbr></wbr>int<wbr>lowerBound,<wbr></wbr></wbr>int<wbr>upperBound){<wbr><wbr><wbr></wbr></wbr></wbr></wbr>
6. if(lowerBound<wbr>==<wbr>upperBound){<wbr><wbr><wbr></wbr></wbr></wbr></wbr></wbr>
7. return;<wbr><wbr><wbr></wbr></wbr></wbr>
8. }<wbr><wbr><wbr></wbr></wbr></wbr>
9. else{<wbr><wbr><wbr></wbr></wbr></wbr>
10. int<wbr>mid=(lowerBound+upperBound)/</wbr>2;<wbr><wbr><wbr></wbr></wbr></wbr>
11. recMergeSort(workSpace,<wbr>lowerBound,<wbr>mid);<wbr><wbr><wbr></wbr></wbr></wbr></wbr></wbr>
12. recMergeSort(workSpace,<wbr>mid+</wbr>1,<wbr>upperBound);<wbr><wbr><wbr></wbr></wbr></wbr></wbr>
13. merge(workSpace,<wbr>lowerBound,<wbr>mid+</wbr></wbr>1,<wbr>upperBound);<wbr><wbr><wbr></wbr></wbr></wbr></wbr>
14. }<wbr><wbr><wbr></wbr></wbr></wbr>
15. }<wbr><wbr><wbr></wbr></wbr></wbr>
16. private<wbr></wbr>void<wbr>merge(</wbr>long[]<wbr>workSpace,<wbr></wbr></wbr>int<wbr>lowPtr,<wbr></wbr></wbr>int<wbr>highPtr,<wbr></wbr></wbr>int<wbr>upperBound){<wbr><wbr><wbr></wbr></wbr></wbr></wbr>
17. int<wbr>j<wbr>=<wbr></wbr></wbr></wbr>0;<wbr><wbr><wbr></wbr></wbr></wbr>
18. int<wbr>lowerBound<wbr>=<wbr>lowPtr;<wbr><wbr><wbr></wbr></wbr></wbr></wbr></wbr></wbr>
19. int<wbr>mid<wbr>=<wbr>highPtr<wbr>-<wbr></wbr></wbr></wbr></wbr></wbr>1;<wbr><wbr><wbr></wbr></wbr></wbr>
20. int<wbr>n<wbr>=<wbr>upperBound-lowerBound+</wbr></wbr></wbr>1;<wbr><wbr><wbr></wbr></wbr></wbr>
21. while(lowPtr<=mid&&highPtr<=upperBound){<wbr><wbr><wbr></wbr></wbr></wbr>
22. if(theArray[lowPtr]<theArray[highPtr]){<wbr><wbr><wbr></wbr></wbr></wbr>
23. workSpace[j++]=theArray[lowPtr++];<wbr><wbr><wbr></wbr></wbr></wbr>
24. }<wbr><wbr><wbr></wbr></wbr></wbr>
25. else{<wbr><wbr><wbr></wbr></wbr></wbr>
26. workSpace[j++]=theArray[highPtr++];<wbr><wbr><wbr></wbr></wbr></wbr>
27. }<wbr><wbr><wbr></wbr></wbr></wbr>
28. }<wbr><wbr><wbr></wbr></wbr></wbr>
29. while(lowPtr<=mid){<wbr><wbr><wbr></wbr></wbr></wbr>
30. workSpace[j++]<wbr>=<wbr>theArray[lowPtr++];<wbr><wbr><wbr></wbr></wbr></wbr></wbr></wbr>
31. }<wbr><wbr><wbr></wbr></wbr></wbr>
32. while(highPtr<=upperBound){<wbr><wbr><wbr></wbr></wbr></wbr>
33. workSpace[j++]<wbr>=<wbr>theArray[highPtr++];<wbr><wbr><wbr></wbr></wbr></wbr></wbr></wbr>
34. }<wbr><wbr><wbr></wbr></wbr></wbr>
35. for(j=0;j<n;j++){<wbr><wbr><wbr></wbr></wbr></wbr>
36. theArray[lowerBound+j]=workSpace[j];<wbr><wbr><wbr></wbr></wbr></wbr>
37. }<wbr><wbr><wbr></wbr></wbr></wbr>
38. }<wbr><wbr></wbr></wbr>

归并排序是比较稳定的排序.即相等的元素的顺序不会改变.如输入记录 1(1) 3(2) 2(3) 2(4) 5(5) (括号中是记录的关键字)时输出的 1(1) 2(3) 2(4) 3(2) 5(5) 中的2 和 2 是按输入的顺序.这对要排序数据包含多个信息而要按其中的某一个信息排序,要求其它信息尽量按输入的顺序排列时很重要.这也是它比快速排序优势的地方.