LOJ6432 [PKUSC2018] 真实排名 【组合数】

题目分析：

做三个指针然后预处理阶乘就行。

题目代码：

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

const int maxn = 102000;

const int mod = 998244353;

int n,k;
struct node{
    int data,num;
}a[maxn];

int ans[maxn];

int fac[maxn],inv[maxn];

int fast_pow(int now,int pw){
    if(pw == 1)return now;
    int z = fast_pow(now,pw/2);
    z = (1ll*z*z)%mod;
    if(pw & 1) z = (1ll*z*now)%mod;
    return z;
}

void init(){
    fac[0] = 1;
    for(int i=1;i<=n;i++) fac[i] = (1ll*fac[i-1]*i) %mod;
    inv[n] = fast_pow(fac[n],mod-2);
    for(int i=n;i>=1;i--){
    inv[i-1] = (1ll*inv[i]*i)%mod;
    }
}

int C(int alpha,int beta){
    if(beta > alpha) return 0;
    return (((1ll*fac[alpha]*inv[beta])%mod)*(inv[alpha-beta]))%mod;
}

int cmp(node alpha,node beta){return alpha.data > beta.data;}

void read(){
    scanf("%d%d",&n,&k);
    for(int i=1;i<=n;i++) {
    scanf("%d",&a[i].data),a[i].num = i;
    }
    sort(a+1,a+n+1,cmp);
}

void work(){                       
    init();
    int pts = 1,ok = 1;
    while(pts <= n && a[pts].data*2 >= a[1].data) pts++;
    for(int i=1;i<=n;i++){
    int nxt = i; while(nxt+1<=n && a[nxt+1].data == a[i].data) nxt++;
    while(pts <= n && a[pts].data*2 >= a[i].data) pts++;
    int forw = n-(pts-nxt),res = C(forw,k);
    for(int j=i;j<=nxt;j++) ans[a[j].num] += res;
    while(ok <= nxt && a[ok].data >= a[nxt].data*2) ok++;
    int newm = k-(nxt-ok+1);
    if(newm >= 0){
        forw = n-(nxt-ok+1),res = C(forw,newm);
        for(int j=i;j<=nxt;j++) ans[a[j].num] += res,ans[a[j].num] %= mod;
    }
    i = nxt;
    }
    for(int i=1;i<=n;i++) if(a[i].data == 0) ans[a[i].num] = C(n,k);
    for(int i=1;i<=n;i++) printf("%d
",ans[i]);
}

int main(){
    read();
    work();
    return 0;
}