hdu-5497 Inversion(滑动窗口+树状数组)

Posted 2020-08-11 LittlePointer

题目链接：

Inversion

Time Limit: 6000/3000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 1087    Accepted Submission(s): 323

Problem Description

You have a sequence {a1,a2,...,an} and you can delete a contiguous subsequence of length m. So what is the minimum number of inversions after the deletion.

 

 

Input

There are multiple test cases. The first line of input contains an integer T, indicating the number of test cases. For each test case:

The first line contains two integers n,m(1≤n≤105,1≤m<n) - the length of the seuqence. The second line contains n integers a1,a2,...,an(1≤ai≤n).

The sum of n in the test cases will not exceed 2×106.

 

 

Output

For each test case, output the minimum number of inversions.

 

 

Sample Input

2

3 1

1 2 3

4 2

4 1 3 2

 

 

Sample Output

0

1

 

题意：

有一个序列,然后你可以删除一个长度为mm的连续子序列. 问如何删除才能使逆序对最少.

思路：

也是套路,逆序对可以用树状数组求得,连续的可以使用滑动窗口,跟尺取法差不多啦;开了两个树状数组一个记录左边界之前的数,一个记录右边界后面的数,然后更新逆序对的数目,取最小就好了;

AC代码：

#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
const int maxn=1e5+10;
int sum1[maxn],sum2[maxn],n,m,a[maxn];
int lowbit(int x){return x&(-x);}
inline void update1(int x,int num)
{
    while(x<=n)
    {
        sum1[x]+=num;
        x+=lowbit(x);
    }
}
inline int query1(int x)
{
    int s=0;
    while(x)
    {
        s+=sum1[x];
        x-=lowbit(x);
    }
    return s;
}
inline void update2(int x,int num)
{
    while(x<=n)
    {
        sum2[x]+=num;
        x+=lowbit(x);
    }
} 
inline int query2(int x)
{
    int s=0;
    while(x)
    {
        s+=sum2[x];
        x-=lowbit(x);
    }
    return s;
}
int main()
{
    int t;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%d%d",&n,&m);
        for(int i=0;i<=n;i++)sum1[i]=sum2[i]=0;
        for(int i=1;i<=n;i++)scanf("%d",&a[i]);
        LL su=0;
        for(int i=n;i>0;i--)
        {
            su=su+query2(a[i]-1);
            update2(a[i],1);
        }
        LL ans=su,temp=su;int l,r=1;
        for(l=1;l<=n-m+1;l++)
        {
            while(r-l<m&&r<=n)
            {
                update2(a[r],-1);
                temp=temp-query2(a[r]-1);
                temp=temp-(l-1-query1(a[r]));
                r++;
            }
            ans=min(ans,temp);
            temp=temp+(l-1-query1(a[l]));
            temp=temp+query2(a[l]-1);
            update1(a[l],1);
        }
        printf("%lld\n",ans);
    }
    return 0;
}