【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。

 import java.util.Scanner;
 public class Main {

     public static void main(String[] args) {
         // TODO Auto-generated method stub

         Scanner in = new Scanner(System.in);
         int n = in.nextInt();
         int[] arr = new int[n];
         for(int i = 0;i < n;i++)
             arr[i] = in.nextInt();
         MergeSort(arr,0,arr.length-1);
         /*
         for(int i = 0;i < arr.length;i++)
             System.out.print(arr[i]);
             */
         System.out.print(total);
     }
     private static void MergeSort(int[] arr,int begin,int end){
         if(begin >= end)
             return;
         int mid = (begin+end)/2;
         MergeSort(arr, begin, mid);
         MergeSort(arr, mid+1, end);
         merge(arr, begin, end);
     }
     public static long total = 0;
     private static void merge(int[] arr,int begin,int end){
         int belement = 0;
         int mid = (begin+end)/2;
         int p1 = begin;
         int p2 = mid+1;
         int count = 0;
         int[] sorted = new int[end-begin+1];

         while(p1 <= mid && p2 <= end){
             if(arr[p1] > arr[p2]){
                 sorted[count] = arr[p2];
                 p2++;
                 count++;
                 belement++;
                 //System.out.println(belement);
             }else{
                 total += belement;
                 sorted[count] = arr[p1];
                 p1++;
                 count++;
             }
         }

         while(p1 <= mid){
             sorted[count] = arr[p1];
             count++;
             p1 ++;
             total += belement;
         }

         while(p2 <= end){
             sorted[count] = arr[p2];
             count ++;
             p2++;
         }

         for(int i = begin;i <= end;i++)
             arr[i] = sorted[i-begin];
     }

 }