Poj 2299 - Ultra-QuickSort 离散化,树状数组,逆序对

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

Source

Waterloo local 2005.02.05

题意：给定n个数，只能交换相邻的两个元素，至少交换几次，成为递增序列。

题解：

明显要求序列的逆序对数目。。。

对于样例：

5

9 1 0 5 4

我们将其排序：

0 1 4 5 9

在每个位置上初始放为1.

1 1 1 1 1

然后，从原序列开始遍历。

先到9，我们把其排好序的位置拿出，即为5。

然后统计位置5之前有多少1。

1 1 1 1 1

————  > 4个  ans+=4

然后把5号位置放为0。

1 1 1 1 0

继续操作即可。。。

这个树状数组维护即可。。。

注意开long long和原序列排序后要去重。。。

 1 #include<bits/stdc++.h>
 2 using namespace std;
 3 #define MAXN 500010
 4 #define LL long long
 5 int n,BIT[MAXN],a[MAXN],aa[MAXN];
 6 int read()
 7 {
 8     int s=0,fh=1;char ch=getchar();
 9     while(ch<‘0‘||ch>‘9‘){if(ch==‘-‘)fh=-1;ch=getchar();}
10     while(ch>=‘0‘&&ch<=‘9‘){s=s*10+(ch-‘0‘);ch=getchar();}
11     return s*fh;
12 }
13 int Lowbit(int o){return o&(-o);}
14 void Update(int o,int o1)
15 {
16     while(o<=n)
17     {
18         BIT[o]+=o1;
19         o+=Lowbit(o);
20     }
21 }
22 int Sum(int o)
23 {
24     int sum=0;
25     while(o>0)
26     {
27         sum+=BIT[o];
28         o-=Lowbit(o);
29     }
30     return sum;
31 }
32 int main()
33 {
34     int tot,i,wz;
35     LL ans;
36     while(1)
37     {
38         n=read();if(n==0)break;
39         for(i=1;i<=n;i++){a[i]=read();aa[i]=a[i];}
40         memset(BIT,0,sizeof(BIT));
41         sort(a+1,a+n+1);
42         tot=unique(a+1,a+n+1)-(a+1);
43         for(i=1;i<=tot;i++)Update(i,1);
44         ans=0;
45         for(i=1;i<=n;i++)
46         {
47             wz=lower_bound(a+1,a+tot+1,aa[i])-a;
48             ans+=(LL)Sum(wz-1);
49             if(BIT[wz]!=0)Update(wz,-1);
50         }
51         printf("%lld\n",ans);
52     }
53     fclose(stdin);
54     fclose(stdout);
55     return 0;
56 }