【hihocoder】三十九周：二分.归并排序之逆序对

就是用归并排序求数组中得逆序对。假设数组为a:[2 4 5],和b:[1 3]，那么在这一次归并的时候逆序对这样求,belement表示当前result数组中b数组对应的元素个数,total表示逆序对的个数：

a:[2 4 5]  b:[1 3]   result{}

a:[2 4 5]  b[3]       result{1}              belement = 1;

a:[4 5]  b[3]          result{1 2}           belement = 1;        total = total + belement = 1;

a:[4 5]  b[]       　  result{1 2 3}        belement = 2;        total = 1;

a:[5]  b[]               result{1 2 3 4}     belement = 2;        total = total + belement = 3

a:[]  b[]                 result{1 2 3 4 5}  belement = 2;        total = total + belement = 5

所以数组2 4 5 1 3的逆序数总共有5个。

JAVA版本代码如下：注意total要设置成long型防止溢出。

 1 import java.util.Scanner;

 2 public class Main {

 3 

 4     public static void main(String[] args) {

 5         // TODO Auto-generated method stub

 6         

 7         Scanner in = new Scanner(System.in);

 8         int n = in.nextInt();

 9         int[] arr = new int[n];

10         for(int i = 0;i < n;i++)

11             arr[i] = in.nextInt();

12         MergeSort(arr,0,arr.length-1);

13         /*

14         for(int i = 0;i < arr.length;i++)

15             System.out.print(arr[i]);

16             */

17         System.out.print(total);

18     }

19     private static void MergeSort(int[] arr,int begin,int end){

20         if(begin >= end)

21             return;

22         int mid = (begin+end)/2;

23         MergeSort(arr, begin, mid);

24         MergeSort(arr, mid+1, end);

25         merge(arr, begin, end);

26     }

27     public static long total = 0;

28     private static void merge(int[] arr,int begin,int end){

29         int belement = 0;

30         int mid = (begin+end)/2;

31         int p1 = begin;

32         int p2 = mid+1;

33         int count = 0;

34         int[] sorted = new int[end-begin+1];

35         

36         while(p1 <= mid && p2 <= end){

37             if(arr[p1] > arr[p2]){

38                 sorted[count] = arr[p2];

39                 p2++;

40                 count++;

41                 belement++;        

42                 //System.out.println(belement);

43             }else{

44                 total += belement;

45                 sorted[count] = arr[p1];

46                 p1++;

47                 count++;

48             }

49         }

50         

51         while(p1 <= mid){

52             sorted[count] = arr[p1];

53             count++;

54             p1 ++;

55             total += belement;

56         }

57         

58         while(p2 <= end){

59             sorted[count] = arr[p2];

60             count ++;

61             p2++;

62         }

63         

64         for(int i = begin;i <= end;i++)

65             arr[i] = sorted[i-begin];

66     }

67     

68 }

View Code