#337518 (C++14) No.811 約数の個数の最大化

• 問題: No.811 約数の個数の最大化
• ユーザー: Tiramister
• 提出日時: 2019-04-12 21:33:06
• 言語: C++14 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 27 ms / 2,000 ms
• コード長: 6,909 bytes
• コンパイル時間: 1,218 ms
• コンパイル使用メモリ: 120,888 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-09-14 17:23:33
• 合計ジャッジ時間: 1,982 ms
• ジャッジサーバーID （参考情報）: judge4 / judge1

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	3 ms; 5,248 KB
testcase_01	AC	3 ms; 5,376 KB
testcase_02	AC	20 ms; 5,376 KB
testcase_03	AC	3 ms; 5,376 KB
testcase_04	AC	3 ms; 5,376 KB
testcase_05	AC	3 ms; 5,376 KB
testcase_06	AC	4 ms; 5,376 KB
testcase_07	AC	4 ms; 5,376 KB
testcase_08	AC	11 ms; 5,376 KB
testcase_09	AC	10 ms; 5,376 KB
testcase_10	AC	8 ms; 5,376 KB
testcase_11	AC	13 ms; 5,376 KB
testcase_12	AC	7 ms; 5,376 KB
testcase_13	AC	27 ms; 5,376 KB
testcase_14	AC	19 ms; 5,376 KB

ソースコード

// IO
#include <cstdio>
#include <iomanip>
#include <ios>
#include <iostream>

// algorithm
#include <algorithm>
#include <cmath>
#include <numeric>

// container
#include <vector>
#include <string>
#include <tuple>
#include <set>
#include <map>
#include <unordered_map>
#include <stack>
#include <queue>
#include <deque>

// others
#include <random>
#include <limits>
#include <functional>
#include <ctime>
#include <cassert>

// type alias
using lint = long long;
using ldouble = long double;
template <class T>
using greater_priority_queue = std::priority_queue<T, std::vector<T>, std::greater<T>>;

/* ----- class ----- */

template <class Cost = int>
struct Edge {
    int from, to;
    Cost cost;
    Edge(int from = -1, int to = -1, Cost cost = 1)
        : from(from), to(to), cost(cost){};

    bool operator<(const Edge<Cost>& e) const { return this->cost < e.cost; }
    bool operator>(const Edge<Cost>& e) const { return this->cost > e.cost; }
};

template <class Cost = int>
using Edges = std::vector<Edge<Cost>>;

template <class Cost = int>
class Graph {
public:
    int size;
    std::vector<std::vector<Edge<Cost>>> path;

    explicit Graph(int N = 0) : size(N), path(size) {}
    void span(int from, int to, Cost cost = 1) {
        path[from].push_back(Edge<Cost>(from, to, cost));
    }
    std::vector<Edge<Cost>>& operator[](int v) { return path[v]; }
};

/* ----- Output Functions for Debugging ----- */

template <class T>
std::ostream& operator<<(std::ostream& os, std::vector<T> v);
template <class T>
std::ostream& operator<<(std::ostream& os, std::set<T> v);
template <class L, class R>
std::ostream& operator<<(std::ostream& os, std::pair<L, R> p);
template <class K, class T>
std::ostream& operator<<(std::ostream& os, std::map<K, T> v);
template <class T>
std::ostream& operator<<(std::ostream& os, std::stack<T> s);
template <class T>
std::ostream& operator<<(std::ostream& os, std::queue<T> q);
template <class T>
std::ostream& operator<<(std::ostream& os, std::priority_queue<T> q);
template <class T>
std::ostream& operator<<(std::ostream& os, std::priority_queue<T, std::vector<T>, std::greater<T>> q);
template <class T>
std::ostream& operator<<(std::ostream& os, Edge<T> e);

template <class T>
std::ostream& operator<<(std::ostream& os, std::vector<T> v) {
    os << "[";
    for (auto vv : v) os << vv << ",";
    return os << "]";
}
template <class T>
std::ostream& operator<<(std::ostream& os, std::set<T> v) {
    os << "{";
    for (auto vv : v) os << vv << ",";
    return os << "}";
}
template <class L, class R>
std::ostream& operator<<(std::ostream& os, std::pair<L, R> p) {
    return os << "(" << p.first << "," << p.second << ")";
}
template <class K, class T>
std::ostream& operator<<(std::ostream& os, std::map<K, T> v) {
    os << "{";
    for (auto vv : v) os << vv << ",";
    return os << "}";
}
template <class T>
std::ostream& operator<<(std::ostream& os, std::stack<T> s) {
    os << "[";
    while (!s.empty()) {
        os << s.top() << ",";
        s.pop();
    }
    return os << "]";
}
template <class T>
std::ostream& operator<<(std::ostream& os, std::queue<T> q) {
    os << "[";
    while (!q.empty()) {
        os << q.front() << ",";
        q.pop();
    }
    return os << "]";
}
template <class T>
std::ostream& operator<<(std::ostream& os, std::priority_queue<T> q) {
    os << "{";
    while (!q.empty()) {
        os << q.top() << ",";
        q.pop();
    }
    return os << "}";
}
template <class T>
std::ostream& operator<<(std::ostream& os, std::priority_queue<T, std::vector<T>, std::greater<T>> q) {
    os << "{";
    while (!q.empty()) {
        os << q.top() << ",";
        q.pop();
    }
    return os << "}";
}
template <class T>
std::ostream& operator<<(std::ostream& os, Edge<T> e) {
    return os << "(" << e.from << "->" << e.to << ":" << e.cost << ")";
}

/* ----- Short Functions ----- */

template <class T>
inline T sq(T a) { return a * a; }

template <class T>
inline T iceil(T n, T d) { return (n + d - 1) / d; }

template <class T>
T gcd(T a, T b) {
    while (b > 0) {
        a %= b;
        std::swap(a, b);
    }
    return a;
}

template <class T, class U>
T ipow(T b, U n) {
    T ret = 1;
    while (n > 0) {
        if (n & 1) ret *= b;
        n >>= 1;
        b *= b;
    }
    return ret;
}

// 0-indexed
template <class T, class U>
inline T kthbit(T a, U k) { return (a >> k) & 1; }

template <class T, class U>
inline T mask(T a, U k) { return a & ((1 << k) - 1); }

template <class T>
std::map<T, int> compress(std::vector<T>& v) {
    std::sort(v.begin(), v.end());
    v.erase(std::unique(v.begin(), v.end()), v.end());

    std::map<T, int> rev;
    for (int i = 0; i < v.size(); ++i) rev[v[i]] = i;
    return rev;
}

template <class T>
T Vec(T v) { return v; }

template <class T, class... Ts>
auto Vec(size_t l, Ts... ts) {
    return std::vector<decltype(Vec<T>(ts...))>(l, Vec<T>(ts...));
}

/* ----- Constants ----- */

// const int INF = std::numeric_limits<int>::max() / 3;
// const ll INF = std::numeric_limits<ll>::max() / 3;
// const ld PI = acos(-1);
// const ld EPS = 1e-10;
// std::mt19937 mt(int(std::time(nullptr)));

class Prime {
    using lint = long long;

public:
    int MAX_V;
    std::vector<int> primes;
    std::vector<bool> isp;

    explicit Prime(int N) : MAX_V(N) {
        isp.assign(MAX_V + 1, true);
        isp[0] = isp[1] = false;
        for (int i = 2; i * i <= MAX_V; ++i) {
            if (isp[i]) {
                for (int j = i; i * j <= MAX_V; ++j) {
                    isp[i * j] = false;
                }
            }
        }
        for (int p = 2; p <= MAX_V; ++p) {
            if (isp[p]) primes.push_back(p);
        }
    }

    bool isprime(lint N) const {
        if (N <= MAX_V) return isp[N];
        for (lint p : primes) {
            if (p * p > N) break;
            if (N % p == 0) return false;
        }
        return true;
    }

    std::vector<std::pair<lint, int>> factorization(lint N) const {
        std::vector<std::pair<lint, int>> ret;
        for (lint p : primes) {
            if (p * p > N) break;
            if (N % p != 0) continue;
            int cnt = 0;
            while (N % p == 0) {
                N /= p;
                ++cnt;
            }
            ret.emplace_back(p, cnt);
        }
        if (N > 1) ret.emplace_back(N, 1);
        return ret;
    }
};

const Prime P(100010);

int main() {
    int N, K;
    std::cin >> N >> K;

    int ans = 0, maxf = 0;
    for (int n = 1; n < N; ++n) {
        int g = gcd(N, n);
        auto facts = P.factorization(g);
        int f = 0;
        for (auto p : facts) f += p.second;
        if (f < K) continue;

        facts = P.factorization(n);
        f = 1;
        for (auto p : facts) f *= (p.second + 1);

        if (maxf < f) {
            ans = n;
            maxf = f;
        }
    }

    std::cout << ans << std::endl;
    return 0;
}