結果

問題 No.3277 Forever Monotonic Number
コンテスト
ユーザー hint908
提出日時 2025-09-19 22:33:44
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 700 ms / 4,000 ms
コード長 6,933 bytes
コンパイル時間 3,714 ms
コンパイル使用メモリ 297,320 KB
実行使用メモリ 7,716 KB
最終ジャッジ日時 2025-09-19 22:34:37
合計ジャッジ時間 8,141 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 1
other AC * 9
権限があれば一括ダウンロードができます

ソースコード

diff # 

// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")


#include<bits/stdc++.h>
using namespace std;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
template<class T> using V = vector<T>;
template<class T> using VV = V<V<T>>;
template<class T> using VVV = V<VV<T>>;
template<class T> using VVVV = VV<VV<T>>;
#define rep(i,n) for(ll i=0ll;(i)<(n);(i)++)
#define REP(i,a,n) for(ll i=(a);(i)<(n);(i)++)
#define rrep(i,n) for(ll i=(n)-1;(i)>=(0ll);(i)--)
#define RREP(i,a,n) for(ll i=(n)-1;(i)>=(a);(i)--)
const long long INF = (1LL << 60);
const long long mod99 = 998244353;
const long long mod107 = 1000000007;
const long long mod = mod99;
#define eb emplace_back
#define be(v) (v).begin(),(v).end()
#define all(v) (v).begin(),(v).end()
#define foa(i,v) for(auto& (i) : (v))
#define UQ(v) sort(be(v)), (v).erase(unique(be(v)), (v).end())
#define UQ2(v,cmp) sort(be(v)), (v).erase(unique(be(v),cmp), (v).end())
#define UQ3(v,cmp) sort(be(v),cmp), (v).erase(unique(be(v)), (v).end())
#define UQ4(v,cmp,cmp2) sort(be(v), cmp), (v).erase(unique(be(v),cmp2), (v).end())
#define LB(x,v) (lower_bound(be(v),(x))-(v).begin())
#define LB2(x,v,cmp) (lower_bound(be(v),(x),(cmp))-(v).begin())
#define UB(x,v) (upper_bound(be(v),(x))-(v).begin())
#define UB2(x,v,cmp) (upper_bound(be(v),(x),(cmp))-(v).begin())
#define dout()  cout << fixed << setprecision(20)
#define randinit() srand((unsigned)time(NULL))

template<class T, class U> bool chmin(T& t, const U& u) { if (t > u){ t = u; return 1;} return 0; }
template<class T, class U> bool chmax(T& t, const U& u) { if (t < u){ t = u; return 1;} return 0; }


ll Rnd(ll L=0, ll R=mod99){return rand()%(R-L)+L;}


VV<ll> matmul(VV<ll> v, VV<ll> w, ll p=(1ll<<60)){
    ll n1 = v.size();
    ll n2 = w.size();
    ll n3 = w[0].size();
    VV<ll> ret(n1, V<ll>(n3, 0));
    rep(i, n1) rep(j,n2) rep(k,n3) (ret[i][k] += v[i][j]*w[j][k]) %= p;
    return ret;
}

VV<ll> matpow(VV<ll> v, ll k, ll p){
    if(k == 1) return v;
    ll n = v.size();
    VV<ll> ret(n, V<ll>(n, 0));
    rep(i, n) ret[i][i] = 1;
    if(k == 0) return ret;
    
    VV<ll> w = matpow(v, k/2, p);
    w = matmul(w, w, p);
    if(k%2) w = matmul(w, v, p);
    
    return w;
    
}


struct Combination{
    vector<long long> fac, inv, finv;
    long long MOD;
    Combination(long long N = 200100, long long p = 998244353) : fac(N, 1), inv(N, 1), finv(N, 1), MOD(p){
        for(long long i = 2; i < N; i++){
            fac[i] = fac[i-1] * i % MOD;
            inv[i] = MOD - inv[MOD%i] * (MOD/i) % MOD;
            finv[i] = finv[i-1] * inv[i] % MOD;
        }
    }
    long long com(long long n, long long k){
        if(n < k) return 0;
        if(n < 0 || k < 0) return 0;
        return fac[n] * finv[k] % MOD * finv[n-k] % MOD;
    }
    
    long long per(long long n, long long k){
        if(n < k) return 0;
        if(n < 0 || k < 0) return 0;
        return fac[n] * finv[n-k] % MOD;
    }
};

long long modpow(long long n, long long k, long long p = mod){
    long long a = n % p;
    long long ans = 1;
    while(k != 0) {
        if(k & 1) ans = ans * a % p;
        k /= 2;
        a = a * a % p;
    }
    
    return ans;  
}

// n^(-1) ≡ b (mod p) となる b を求める
long long modinv(long long n, long long p = mod) { 
//    if(n == 1) return 1;
//    return p - modinv(p % n) * (p / n) % p;
    return modpow(n, p - 2, p);
}

// n^k ≡ b (mod p) となる最小の k を求める
long long modlog(long long n, long long b, long long p = mod){
  
    long long sqrt_p = sqrt(p);
    unordered_map<long long , long long> n_pow;
    long long memo = 1;
    
    for(long long i = 0; i < sqrt_p; i ++){
        if(!n_pow.count(memo)) n_pow[memo] = i;
        memo = memo * n % p; 
    }
    
    memo = modinv(memo, p);
    long long ans = 0;
    while(!n_pow.count(b)){
        if(ans >= p) return -1;
        ans += sqrt_p;
        b = b * memo % p;
    }
  
    ans += n_pow[b];
    return ans % (p - 1);

}

// ax + by = gcd(a, b) を満たす (x, y) が格納される
long long ext_gcd(long long a, long long b, long long &x, long long &y){
    if(b == 0){
        x = 1;
        y = 0;
        return a;
    }
    long long d = ext_gcd(b, a%b, y, x);
    y -= a/b*x;
    return d;
}


void solve(){
	ll m = 200;
	V<ll> ok(m, -1);
	rep(i, 10) ok[i] = 1;
	auto chk = [&](auto&&chk, ll n) -> ll {
		if(ok[n] >= 0) return ok[n];
		ll la = 10;
		ll s = 0;
		ll tmp = n;
		while(n){
			ll x = n%10;
			n /= 10;
			s += x;
			if(la < x) la = -1;
			else la = x;
		}
		n = tmp;
		if(la == -1) return ok[n] = 0;
		return ok[n] = chk(chk, s);
	};
	V<ll> nx(m+10, 201);
	for(ll i=m-1; i>=0; i--){
	    nx[i] = nx[i+1];
	    if(chk(chk, i)) nx[i] = i;
	}
	ll T;
	cin >> T;
	rep(t, T){
	    ll n;
	    cin >> n;
	    if(n == 0){
	        cout << 1 << '\n';
	        continue;
	    }
	    ll m = n+1;
	    V<ll> v;
	    while(m){
	        v.eb(m%10);
	        m /= 10;
	    }
	    m = n+1;
	    ll val = INF;
	    auto slv = [&](ll m) -> ll {
	        ll mm = m;
	        V<ll> v;
    	    while(m){
    	        v.eb(m%10);
    	        m /= 10;
    	    }
    	    m = mm;
    	    ll la = 0, f = 1, rest = 0;
    	    ll s = 0;
    	    for(ll i=v.size()-1; i>=0; i--){
    	        if(v[i] >= la and f) la = v[i];
    	        else{
    	            f = 0;
    	            v[i] = la;
    	        }
    	        s += v[i];
    	    }
    	    ll nxt = nx[s];
    	    if(v.size() * 9 < nxt){
    	        return INF;
    	    }
	        nxt -= s;
	        ll i = 0;
	        while(nxt){
	            if(nxt + v[i] <= 9){
	                v[i] += nxt;
	                nxt = 0;
	            }else{
	                nxt -= 9 - v[i];
	                v[i] = 9;
	            }
	            i++;
	        }
	        m = 0;
    	    while(!v.empty()){
    	        m = m*10 + v.back();
    	        v.pop_back();
    	    }
    	    return m;
	    };
	    chmin(val, slv(m));
	    m++;
	    rep(i, v.size()){
	        m += (9 - v[i]) * modpow(10, i, INF);
	       // cout << m << endl;
	        chmin(val, slv(m));
	    }
	    n ++;
	    m = val;
	    chmax(n, (m+8) / 9);
	   // cout << n << " " << m << endl;
	    ll ans = 0;
	    
	    if(n * 9 - 8 <= m){
	        ll r = m % 9;
	        ans += modpow(10, n, mod) * (r + 1);
	        ans -= 1;
	        ans %= mod;
	    }else{
	        ans += (modpow(10, n, mod) - 1) * modinv(9, mod);
	        ans %= mod;
	        m -= n;
	        ll r = m % 8;
	        ll keta = m / 8;
	        ans += (modpow(10, keta, mod) - 1) * 8 % mod * modinv(9, mod) % mod;
	        ans %= mod;
	        ans += modpow(10, keta, mod) * r;
	        ans %= mod;
	    }
	    ans %= mod;
	    ans += mod;
	    ans %= mod;
	    cout << ans << endl;
	}
	
	
}

int main(){
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    int t=1;
    // cin >> t;
    rep(i,t) solve();
}
0