poj-2299 Ultra-QuickSort 归并排序求逆序数

最新推荐文章于 2021-10-09 14:23:30 发布

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最新推荐文章于 2021-10-09 14:23:30 发布

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分类专栏： POJ 排序

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本文介绍了一个特定的排序算法Ultra-QuickSort，并通过计算输入序列的逆序数来确定完成排序所需的最少交换操作次数。使用归并排序算法实现逆序数的计算。

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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

Sample Output

6
0

题意：给一组数，求这组数的逆序数。逆序数：对于n个不同的元素，先规定各元素之间有一个标准次序（例如n个不同的自然数，可规定从小到大为标准次序），于是在这n个元素的任一排列中，当某两个元素的先后次序与标准次序不同时，就说有1个逆序。一个排列中所有逆序总数叫做这个排列的逆序数。例如9 1 0 5 4的逆序数为4+1+1+0=6。

用归并排序可以计算逆序数。

#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#define INF 0x3f3f3f3f

using namespace std;

long long ans;
int arr[500010],t[500010];
void mergearray(int a[],int l,int mid,int r)
{
    int i=l,j=mid+1;
    int k=l;
    while (i<=mid&&j<=r)
    {
        if(a[i]<=a[j])
            t[k++]=a[i++];
        else{
            t[k++]=a[j++];
            ans += mid-i+1;
        }
    }
    while (i<=mid)
        t[k++]=a[i++];
    while (j<=r)
        t[k++]=a[j++];
    for (int i=l;i<=r;i++)
        a[i]=t[i];
}
void msort(int a[],int l,int r)
{
    if (l<r)
    {
        int mid=(l+r)/2;
        msort(a,l,mid);
        msort(a,mid+1,r);
        mergearray(a,l,mid,r);
    }
}

int main()
{
    int n;
    while (scanf("%d",&n),n)
    {
        ans=0;
        for (int i=1;i<=n;i++)
        {
            scanf("%d",&arr[i]);
        }
        msort(arr,1,n);
        printf("%lld\n",ans);
    }
    return 0;
}