結果

問題 No.2744 Power! or +1
ユーザー au7777
提出日時 2024-08-18 14:02:12
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 4,881 bytes
コンパイル時間 4,662 ms
コンパイル使用メモリ 245,668 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-08-18 14:02:19
合計ジャッジ時間 5,929 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
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ファイルパターン 結果
sample AC * 2
other AC * 5 WA * 4
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ソースコード

diff #
プレゼンテーションモードにする

#include <bits/stdc++.h>
#include <atcoder/all>
typedef long long int ll;
using namespace std;
typedef pair<ll, ll> P;
using namespace atcoder;
template<typename T> using min_priority_queue = priority_queue<T, vector<T>, greater<T>>;
#define USE998244353
#ifdef USE998244353
const ll MOD = 998244353;
using mint = modint998244353;
#else
const ll MOD = 1000000007;
using mint = modint1000000007;
#endif
#pragma region //使いがち
const int MAX = 2000001;
long long fac[MAX], finv[MAX], inv[MAX];
void COMinit() {
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    for (int i = 2; i < MAX; 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(int n, int k){
    if (n < k) return 0;
    if (n < 0 || k < 0) return 0;
    return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}
ll gcd(ll x, ll y) {
   if (y == 0) return x;
   else if (y > x) {
       return gcd (y, x); 
   }
   else return gcd(x % y, y);
}
ll lcm(ll x, ll y) {
   return x / gcd(x, y) * y;
}
ll pow_ll(ll x, ll n) {
    if (n == 0) return 1;
    if (n % 2) {
        return pow_ll(x, n - 1) * x;
    }
    else {
        ll tmp = pow_ll(x, n / 2);
        return tmp * tmp;
    }
}
// floor(a^(1/k))
ll floor_root(ll a, ll k) {
    assert(a >= 0);
    assert(k >= 1);
    if (a == 0) return 0;
    if (k == 1) return a;
    // 大体の値
    ll x = (ll)pow(a, 1.0 / k);
    // 増やす
    while ((pow_ll(x + 1, k)) <= a) {
        x++;
    }
    // 減らす
    while ((pow_ll(x, k)) > a) {
        x--;
    }
    return x;
}
ll keta(ll num, ll arity) {
    ll ret = 0;
    while (num) {
        num /= arity;
        ret++;
    }
    return ret;
}
// k進数で見た時のi桁目の数を返す (一番下は0桁目)
ll keta_num(ll num, ll i, ll k) {
    return (num / pow_ll(k, i)) % k;
}
ll ceil(ll n, ll m) {
    // n > 0, m > 0
    ll ret = n / m;
    if (n % m) ret++;
    return ret;
}
void compress(vector<ll>& v) {
    // [3 5 5 6 1 1 10 1] -> [1 2 2 3 0 0 4 0] 
    vector<ll> u = v;
    sort(u.begin(), u.end());
    u.erase(unique(u.begin(),u.end()),u.end());
    map<ll, ll> mp;
    for (int i = 0; i < u.size(); i++) {
        mp[u[i]] = i;
    }
    for (int i = 0; i < v.size(); i++) {
        v[i] = mp[v[i]];
    }
}
vector<pair<ll, ll> > prime_factorize(ll N) {
    vector<pair<ll, ll> > res;
    for (ll a = 2; a * a <= N; ++a) {
        if (N % a != 0) continue;
        ll ex = 0; // 指数
        // 割れる限り割り続ける
        while (N % a == 0) {
            ++ex;
            N /= a;
        }
        // その結果を push
        res.push_back({a, ex});
    }
    // 最後に残った数について
    if (N != 1) res.push_back({N, 1});
    return res;
}
#pragma endregion
// xを何乗したらnの倍数になるか(divはnの素因数分解)
ll calc(vector<P>& div, ll x) {
    ll ans = 0;
    for (auto pa : div) {
        ll p = pa.first;
        ll a = pa.second;
        ll cnt = 0;
        while (x % p == 0) {
            x /= p;
            cnt++;
        }
        if (cnt == 0) return -1;
        ans = max(ans, ceil(a, cnt));
    }
    return ans;
}
// k!がnの倍数になる最小のkを求める
ll get_num(ll n) {
    ll x = n;
    for (ll i = 1; i <= n; i++) {
        x /= gcd(x, i);
        if (x == 1) return i;
    }
    return 0;
}
// x^k <= nを満たす最大のkを求める
ll get_pow(ll x, ll n) {
    if (x == 1) return 1e18;
    ll k = 1;
    ll cur = x;
    while (cur <= n / k) {
        k++;
        cur *= x;
    }
    return k;
}
int main() {
    ll n, a, b, c;
    cin >> n >> a >> b >> c;
    ll INF = 1e18;
    vector<ll> dis(n + 1, INF);
    dis[1] = 0;
    auto v = prime_factorize(n);
    ll bound = get_num(n);
    cerr << bound << endl;
    for (ll i = 1; i < n; i++) {
        // 操作1
        dis[i + 1] = min(dis[i + 1], dis[i] + a);
        // 操作2
        ll max_k = min(get_pow(INF, b), get_pow(n, i));
        for (ll k = 2; k <= max_k; k++) {
            dis[pow_ll(i, k)] = min(dis[pow_ll(i, k)], dis[i] + pow_ll(b, k));
        }
        // Nの倍数になる場合もOK
        ll k_reach = calc(v, i);
        if (k_reach != -1) {
            if (k_reach <= get_pow(INF, b)) {
                dis[n] = min(dis[n], dis[i] + k_reach * b);
            }
        }
        // 操作3
        ll cur = 1;
        for (ll j = 1; j <= i; j++) {
            cur *= j;
            if (cur > n) break;
        }
        if (cur <= n) {
            dis[cur] = min(dis[cur], dis[i] + c);
        }
        else {
            // 怪しい
            dis[n] = min(dis[n], dis[i] + 2 * c);
        }
        // Nの倍数になる場合
        if (i >= bound) {
            dis[n] = min(dis[n], dis[i] + c);
        }
    }
    cout << dis[n] << endl;
    return 0;
}
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