【笔记】康拓展开＆逆康拓展开

参考资料

OI-WIKI

代码

/*
 * 康拓展开树状数组优化O(nlogn)
 * 给一个排列，返回排列的排名
 */
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int MOD=1e9+7,N=1e5+5;
int sum[N],n,a[N];
ll jc[N];
int lowbit(int x){
    return x&-x;
}
void add(int x,int k){
    while(x <= n){
	sum[x]=sum[x]+k;
	x=x+lowbit(x);
    }
}
int getsum(int x){
    int ans=0;
    while(x>=1){
	ans=ans+sum[x];
	x=x-lowbit(x);
    }
    return ans;
}
void solve(){
    ll rank=1;
    for(int i=1;i<=n;i++){
	add(a[i],1);
	int k=getsum(a[i]-1);
	k=(a[i]-1)-k;
	rank = (rank + (k*jc[n-i])) %MOD;
    }
    printf("%lld
",rank);

}
int main(){
    jc[1]=1;
    for(int i=2;i<=N;i++){
	jc[i]=jc[i-1]*i%MOD;
    }
    int _;
    scanf("%d",&_);
    while(_--) {
	memset(sum,0,sizeof(sum));
	scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%d",&a[i]);
	solve();
    }
}