C++(clang++ 11.0.1) 解法, 执行用时: 895ms, 内存消耗: 106796K, 提交时间: 2023-07-14 22:11:43

#include<bits/stdc++.h>
#define int long long
using namespace std;
const int N = 2e6+5;
const int mod = 998244353;
unordered_map<int,int>mp;
int qpow(int a,int b){
    int res=1;
    while(b){
        if(b&1) res=res*a%mod;
        a=a*a%mod;
        b>>=1; 
    }
    return res;
}
int dfs(int n){
    if(mp.count(n)) return mp[n];
    int m=(1+n)>>1;
    return mp[n]=(dfs(m)+dfs(n-m)+n)%mod;
}
signed main(void){
    ios::sync_with_stdio(false);cin.tie(0);
    mp[1]=1;
    mp[2]=3;
    int T=1;
    cin>>T;
    while(T--){
        int n;
        cin>>n;
        cout<<dfs(n)*qpow(n,mod-2)%mod<<"\n"; 
    }       
    return 0;
}

pypy3 解法, 执行用时: 1842ms, 内存消耗: 193556K, 提交时间: 2023-07-14 22:54:57

from functools import lru_cache
from sys import stdin

input = stdin.readline

mod = 998244353


@lru_cache(None)
def f(n: int):
    res = n
    if n == 1:
        return 1
    if res >= mod:
        res -= mod
    m = (n + 1) // 2
    if m > 1:
        res += f(m)
        if res >= mod:
            res -= mod
    res += f(n - m)
    if res >= mod:
        res -= mod
    return res


for _ in range(int(input())):
    n = int(input())
    print(f(n) * pow(n, mod - 2, mod) % mod)

Python3 解法, 执行用时: 3870ms, 内存消耗: 241736K, 提交时间: 2023-07-20 20:59:30

from functools import cache
from sys import stdin
input = stdin.readline
mod=998244353
@cache
def dp(n:int):
    time=n
    if n==1:return 1
    if time>=mod:time-=mod
    m=(1+n)//2
    if m>1:
        time+=dp(m)
        if time>=mod: time-=mod
    time+=dp(n-m)
    if time >= mod: time -= mod
    return time
for  _ in range(int(input())):
    k=int(input())
    print(dp(k)*pow(k,mod-2,mod)%mod)