LG5367 "template" Cantor Cantor Expand Expand

Problem Description

LG5367

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answer

Cantor expansion formula:

\[ans=1+(\sum_{i=1}^{n}{a_i})\times(n-i)!\]

With Fenwick tree maintenance at \ (\ sum \) inside things, product maintenance prefix things behind.

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\(\mathrm{Code}\)

#include<bits/stdc++.h>
using namespace std;

template <typename Tp>
void read(Tp &x){
    x=0;char ch=1;int fh;
    while(ch!='-'&&(ch>'9'||ch<'0')) ch=getchar();
    if(ch=='-') ch=getchar(),fh=-1;
    else fh=1;
    while(ch>='0'&&ch<='9') x=(x<<1)+(x<<3)+ch-'0',ch=getchar();
    x*=fh;
}

#define int long long

const int maxn=1000007;
const int mod=998244353;

int n;
int times[maxn],a[maxn];

int c[maxn];
void add(int x,int k){
    while(x<=n){c[x]+=k;x+=((x)&(-x));}
}

int query(int x){
    int res=0;
    while(x){res+=c[x];x-=(x&(-x));}
    return res;
}

int ans;

signed main(){
    read(n);times[0]=1;
    for(int i=1;i<=n;i++){
        add(i,1);times[i]=times[i-1]*i%mod;
        read(a[i]);
    }
    for(int i=1;i<=n;i++){
        ans=(ans+(query(a[i])-1)*times[n-i]%mod)%mod;
        add(a[i],-1);
    }
    ans=(ans+1)%mod;
    printf("%lld\n",ans);
    return 0;
}