poj2299--B - Ultra-QuickSort（线段树，离散化）

Ultra-QuickSort

Time Limit: 7000MS		Memory Limit: 65536K
Total Submissions: 41215		Accepted: 14915

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：求出最小交换次数，使得数组变得有序（由小到大）。  也就是求出逆序数，这个题归并排序，树状数组，线段树又可以解，可以当做练手用

使用线段树解的话，因为给出的数值很大，所以需要离散化，一开始直接使用map果断的超时了，只能想一个更简便的离散的方法，使用结构体存下一开始的值k和它初始的序号（id1），sort对k进行排序，得到新的序号（id2），通过id1直接改变给出的数组，变为id2，这样只用n + logn的时间就可以离散完成，（注意要判断重复的值，重复的值共享一个id2）。至于线段树部分就是一个模板

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
#define LL __int64
#define maxn 600000
#define lmin 1
#define rmax n
#define lson l,(l+r)/2,rt<<1
#define rson (l+r)/2+1,r,rt<<1|1
#define root lmin,rmax,1
#define now l,r,rt
#define int_now LL l,LL r,LL rt
struct node{
    LL id1 , id2 ;
    LL k ;
}p[maxn] ;
LL cl[maxn<<2] , a[maxn] ;
bool cmp(node a,node b)
{
    return a.k < b.k ;
}
void push_up(int_now)
{
    cl[rt] = cl[rt<<1] + cl[rt<<1|1] ;
}
void update(LL i,int_now)
{
    if( i < l || i > r )
        return ;
    if( i == l && i==r )
    {
        cl[rt]++ ;
        return ;
    }
    update(i,lson);
    update(i,rson);
    push_up(now);
    return ;
}
LL query(int ll,int rr,int_now)
{
    if( ll > r || rr < l )
        return 0;
    if( ll <= l && r <= rr )
        return cl[rt] ;
    return query(ll,rr,lson) + query(ll,rr,rson);
}
int main()
{
    LL i , n , m , l , r , x , num ;
    while(scanf("%I64d", &m) && m)
    {
        for(i = 0 ; i < m ; i++)
        {
            scanf("%I64d", &a[i]);
            p[i].k = a[i] ;
            p[i].id1 = i ;
        }
        sort(p,p+m,cmp);
        int temp = -1 ;
        n = 0 ;
        for(i = 0 ; i < m ; i++)
        {
            if( p[i].k == temp )
                p[i].id2 = n ;
            else
            {
                p[i].id2 = ++n ;
                temp = p[i].k ;
            }
        }
        for(i = 0 ; i < m ; i++)
            a[ p[i].id1 ] = p[i].id2 ;
        memset(cl,0,sizeof(cl));
        num = 0 ;
        for(i = 0 ; i < m ; i++)
        {
            num += (i - query(1,a[i],root));
            update(a[i],root);
        }
        printf("%I64d\n", num);
    }
    return 0;
}