poj2299——Ultra-QuickSort

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：

给定一个长度为n（n<=500000）的序列a，如果只允许进行比较和交换相邻两个数的操作，求至少需要多少次交换才能把a从小到大排序。

Solution：

容易发现每次交换和比较相邻的两个数使序列有序，就是冒泡排序，而冒泡排序的最少操作数就是序列中的逆序数对的个数，所以本题转换为求序列中的逆序对的个数。于是就可以用树状数组求啦。由于本题数据较大，所以我们需要对数值离散化，然后排序，按倒序update并getsum求在它更新之前有多少个数在其前面，详细见我的树状数组详解的博客。

代码:

#include<bits/stdc++.h>
#define il inline
#define ll long long
using namespace std;
const int N=500005;
int aa[N],c[N],n;
struct node{
int v,order;
}a[N];
il bool cmp(node a,node b){return a.v<b.v;}
il void update(int t,int v)
{
    while(t<=n){
        c[t]+=v;
        t+=(t&-t);
    }
}
il int getsum(int t)
{
    int sum=0;
    while(t){
        sum+=c[t];
        t-=(t&-t);
    }
    return sum;
}
il int gi()
{
    int a=0;char x=getchar();bool f=0;
    while((x<'0'||x>'9')&&x!='-')x=getchar();
    if(x=='-')x=getchar(),f=1;
    while(x>='0'&&x<='9')a=a*10+x-48,x=getchar();
    return f?-a:a;
}
int main()
{
    while(1){
        n=gi();
        if(!n)return 0;
        memset(c,0,sizeof(c));
        for(int i=1;i<=n;i++)a[i].v=gi(),a[i].order=i;
        sort(a+1,a+n+1,cmp);
        for(int i=1;i<=n;i++)aa[a[i].order]=i;
        ll ans=0;
        for(int i=n;i>0;i--)update(aa[i],1),ans+=getsum(aa[i]-1);
        printf("%lld
",ans);
    }
}