线段树——Ultra-QuickSort

题目网址：http://acm.hust.edu.cn/vjudge/contest/view.action?cid=109331#problem/A

Description

In this problem, you have to analyze a particular sorting algorithm. The algorithm processes a sequence of n distinct integers by swapping two adjacent sequence elements until the sequence is sorted in ascending order. For the input sequence 
9 1 0 5 4 ,
Ultra-QuickSort produces the output 
0 1 4 5 9 .
Your task is to determine how many swap operations Ultra-QuickSort needs to perform in order to sort a given input sequence.

Input

The input contains several test cases. Every test case begins with a line that contains a single integer n < 500,000 -- the length of the input sequence. Each of the the following n lines contains a single integer 0 ≤ a[i] ≤ 999,999,999, the i-th input sequence element. Input is terminated by a sequence of length n = 0. This sequence must not be processed.

Output

For every input sequence, your program prints a single line containing an integer number op, the minimum number of swap operations necessary to sort the given input sequence.

Sample Input

5
9
1
0
5
4
3
1
2
3
0

Sample Output

6
0

题意：输入n个数，相邻两个数可以交换位置进行从小到大排序，求最小交换次数。

解题思路：用线段树的思想将数组一半一半的划分成小的区间，最后划分为只有两个数的区间，这两个数进行比较交换位置，记录交换次数就。先进行前两个数的比较，然后扩大区间为（left，right），

可知（left，right）区间中，（left，center）和（center+1，right）区间里的数已经排好序，将（center+1，right）中的数一个一个与（left，center）中的数比较大小，用另一个数组记录
新的排序后的位置（相当于向前插入数），并记录交换次数。

#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
#include <cstdlib>
using namespace std;
int a[500010];
long long num;
int temp[500010];

void Merge(int arr[], int left, int center, int right)
{
    int i=left;
    int j=center+1;
    int k=0;
    while (i<=center&&j<=right)
    {
        ///可知（left，right）区间中，（left，center）和（center+1，right）区间里的数已经排好序
        if (arr[i] > arr[j])
        {
            temp[k++] = arr[j++];///
            num+= center+1-i;
        }
        else
            temp[k++] = arr[i++];///记录小的数，以便得到排序后新的序列；
    }
    while (i <= center) ///
        temp[k++] = arr[i++];
    while (j <= right)  ///这个和上个while语句两个while语句记录了原数组交换次序后的新的数组；
        temp[k++] = arr[j++];
    for (i = left, k = 0; i <= right; i++, k++)///将array[]数组变为新的数组；
        arr[i] = temp[k];
}

void mergeSort(int arr[], int left, int right)
{
    if (left<right)
    {
        int center = (left + right) / 2;
        mergeSort(arr, left, center);     ///
        mergeSort(arr, center + 1, right);///将数组划分为两个区间；
        Merge(arr, left, center, right);  ///将这个区间里的数进行排序；
    }
}

int main()
{
   int n;
   while(scanf("%d",&n)&&n)
   {
      num=0;
      for(int i=0;i<n;i++)
      scanf("%d",&a[i]);
      mergeSort(a,0,n-1);
      printf("%lld\n",num);
   }
}