51NOD-01019 逆序数

Posted 2020-09-20 ONION_CYC

【算法】离散化+树状数组(求逆序对)

【题解】经典，原理是统计在i之前插入的且值≤i的个数，然后答案就是i-getsum(i)

#include<cstdio>
#include<algorithm>
#include<cstring>
#define lowbit(x) x&(-x)
using namespace std;
const int maxn=50010;
int A[maxn],ord[maxn],a[maxn],b[maxn],n,s;
bool cmp(int x,int y)
{return a[x]<a[y];}
void insert(int x)
{
    for(int i=x;i<=s;i+=lowbit(i))A[i]++;
}
int getsum(int x)
{
    int ans=0;
    for(int i=x;i>=1;i-=lowbit(i))ans+=A[i];
    return ans;
}
int main()
{
    scanf("%d",&n);
    for(int i=1;i<=n;i++)
    {
        scanf("%d",&a[i]);
        ord[i]=i;
    }
    sort(ord+1,ord+n+1,cmp);
    s=1;b[ord[1]]=1;
    for(int i=2;i<=n;i++)b[ord[i]]=a[ord[i]]==a[ord[i-1]]?s:++s;
    int ans=0;
    for(int i=1;i<=n;i++)
    {
        insert(b[i]);
        ans+=i-getsum(b[i]);
    }
    printf("%d",ans);
    return 0;
}    

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