金色传说 Gym - 102174J （dp）

题目

https://cn.vjudge.net/problem/Gym-102174J

题意

中文题 

思路

dp

#include 
#include
using namespace std;
typedef long long ll;
const ll mod=998244353;
ll dp[500005];
ll dpp[500005];
ll a[500005];
ll qpow(ll x,ll n)
{
    ll ans = 1;
    while(n)
    {
        if(n % 2) ans = ans * x%mod;
        x = x*x%mod;
        n /= 2;
    }
    return ans;
}
ll ok(int x)
{
    ll qw = qpow(10,x);
    qw %= mod;
    ll ans = (qw*(qw-1)/2)%mod;
    return ans;
}
int main()
{
    int T;
    scanf("%d",&T);
    dp[1] = 0;
    dpp[1] = 10;
    a[1] = ok(1);
    for(int i = 2;i <= 500000;i++)
    {
        dp[i] = 2*dpp[i-1]%mod;
        dpp[i] = (10*dpp[i-1]%mod + 10*dp[i-1]%mod)%mod;
        a[i] = ok(i);
    }
    while(T--)
    {
        int n;
        scanf("%d",&n);
        ll ans = a[n];
        for(int i = 1;i <= n-2;i++)
        {
            ans = (ans + a[i]*dp[n-i]) % mod;
        }
        ans %= mod;
        printf("%lld\n",ans);
    }
    return 0;
}