結果

問題 No.1383 Numbers of Product
ユーザー rniya
提出日時 2021-02-07 21:24:43
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,002 ms / 2,000 ms
コード長 5,625 bytes
コンパイル時間 2,047 ms
コンパイル使用メモリ 199,132 KB
最終ジャッジ日時 2025-01-18 14:25:36
ジャッジサーバーID
（参考情報） 		judge2 / judge3
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ファイルパターン 結果
sample AC * 2
other AC * 51
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 # 

#define LOCAL
#include <bits/stdc++.h>
using namespace std;
#pragma region Macros
typedef long long ll;
typedef __int128_t i128;
typedef unsigned int uint;
typedef unsigned long long ull;
#define ALL(x) (x).begin(), (x).end()

template <typename T> istream& operator>>(istream& is, vector<T>& v) {
    for (T& x : v) is >> x;
    return is;
}
template <typename T> ostream& operator<<(ostream& os, const vector<T>& v) {
    for (int i = 0; i < (int)v.size(); i++) {
        os << v[i] << (i + 1 == (int)v.size() ? "" : " ");
    }
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const pair<T, U>& p) {
    os << '(' << p.first << ',' << p.second << ')';
    return os;
}
template <typename T, typename U, typename V> ostream& operator<<(ostream& os, const tuple<T, U, V>& t) {
    os << '(' << get<0>(t) << ',' << get<1>(t) << ',' << get<2>(t) << ')';
    return os;
}
template <typename T, typename U, typename V, typename W> ostream& operator<<(ostream& os, const tuple<T, U, V, W>& t) {
    os << '(' << get<0>(t) << ',' << get<1>(t) << ',' << get<2>(t) << ',' << get<3>(t) << ')';
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const map<T, U>& m) {
    os << '{';
    for (auto itr = m.begin(); itr != m.end();) {
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr != m.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const unordered_map<T, U>& m) {
    os << '{';
    for (auto itr = m.begin(); itr != m.end();) {
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr != m.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const set<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const multiset<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const unordered_set<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const deque<T>& v) {
    for (int i = 0; i < (int)v.size(); i++) {
        os << v[i] << (i + 1 == (int)v.size() ? "" : " ");
    }
    return os;
}

void debug_out() { cerr << '\n'; }
template <class Head, class... Tail> void debug_out(Head&& head, Tail&&... tail) {
    cerr << head;
    if (sizeof...(Tail) > 0) cerr << ", ";
    debug_out(move(tail)...);
}
#ifdef LOCAL
#define debug(...)                                                                   \
    cerr << " ";                                                                     \
    cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \
    cerr << " ";                                                                     \
    debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

template <typename T> T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; }
template <typename T> T lcm(T x, T y) { return x / gcd(x, y) * y; }

template <class T1, class T2> inline bool chmin(T1& a, T2 b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template <class T1, class T2> inline bool chmax(T1& a, T2 b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
#pragma endregion

const int INF = 1e9;
const long long IINF = 1e18;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const char dir[4] = {'D', 'R', 'U', 'L'};
const long long MOD = 1000000007;
// const long long MOD = 998244353;

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    ll N, K, M;
    cin >> N >> K >> M;

    // Bは高々20とかまで
    // 先にB>=3での表し方がM-1かMになるものをチェックして、それがB=2で表せるかチェック
    // M=1のときはM>=2として表せるものを計算して除く

    unordered_map<ll, int> mp;
    for (int B = 3; B <= 20; B++) {
        for (int A = 1;; A++) {
            ll prod = 1;
            bool ok = true;
            for (int i = 0; i < B; i++) {
                ll nxt = K * i + A;
                if (2 * N / prod <= nxt) {
                    ok = false;
                    break;
                }
                prod *= nxt;
            }
            if (!ok) break;
            if (prod > N) break;
            mp[prod]++;
        }
    }

    auto check = [&](ll x) {
        int lb = 0, ub = INF + 10;
        while (ub - lb > 1) {
            int mid = (lb + ub) >> 1;
            (2 * N / (K + mid) <= mid || (K + mid) * mid >= x ? ub : lb) = mid;
        }
        return 2 * N / (K + ub) > ub && (K + ub) * ub == x;
    };

    int ans = 0, sum = 0;
    for (auto p : mp) {
        bool ok = check(p.first);
        sum += ok;
        if (p.second != M - 1 && p.second != M) continue;
        int cur = p.second;
        cur += check(p.first);
        ans += (cur == M);
    }

    if (M == 1) {
        int lb = 0, ub = INF + 10;
        while (ub - lb > 1) {
            int mid = (ub + lb) >> 1;
            (2 * N / (K + mid) <= mid || (K + mid) * mid > N ? ub : lb) = mid;
        }
        ans += lb - sum;
    }

    cout << ans << '\n';
    return 0;
}
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