#1143140 (C++23) No.1936 Rational Approximation

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結果

問題	No.1936 Rational Approximation
コンテスト
ユーザー	WhiteKnight
提出日時	2026-01-08 05:01:28
言語	C++23 (gcc 15.2.0 + boost 1.89.0)
結果	AC
実行時間	2 ms / 2,000 ms
コード長	16,647 bytes
記録記録タグの例: 初AC ショートコード純ショートコード純主流ショートコード最速実行時間
コンパイル時間	2,494 ms
コンパイル使用メモリ	213,760 KB
実行使用メモリ	7,852 KB
最終ジャッジ日時	2026-01-08 05:01:32
合計ジャッジ時間	2,887 ms
ジャッジサーバーID （参考情報）	judge1 / judge2
このコードへのチャレンジ
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ファイルパターン	結果
sample	AC * 1
other	AC * 14
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ソースコード

raw source code

#include <cstdio>
#include <vector>
#include <iostream>
#include <deque>
#include <queue>
#include <tuple>
#include <map>
#include <set>
#include <algorithm>
#include <string>
#include <iomanip>
#include <bit>
#include <numeric>
#include <cassert>
#include <functional>

using namespace std;

//Integer-Related

typedef long long i64;
typedef unsigned long long ui64;

//vector-Related

template<typename T>
using vv = vector<vector<T>>;
template<typename T>
using vvv = vector<vector<vector<T>>>;
typedef vector<i64> vi64;
typedef vector<bool> vbool;
typedef vv<i64> vvi64;
typedef vv<bool> vvbool;
typedef vvv<i64> vvvi64;
typedef vvv<bool> vvvbool;
typedef pair<i64, i64> pi64;

typedef vector<string> vstr;

//これで最大値優先
template<typename Val_T, typename Pred = less<Val_T>>
using prque = priority_queue<Val_T, vector<Val_T>, Pred>;



//set-Related

#include <unordered_set>
typedef set<i64> si64;
typedef multiset<i64> msi64;
typedef unordered_set<i64> usi64;



//Calculation-Related

inline i64 rm(const i64 l, const i64 r) {
    i64 val = l % r;
    if (val >= 0) {
        return val;
    }
    else {
        return val + r;
    }
}

template<typename T>
T r_accumulate(const vector<T>& vec) {
    return std::accumulate(vec.begin(), vec.end(), T{});
}

template <typename T>
void r_insert(vector<T>& to, vector<T>& from) {
    ranges::copy(from, back_inserter(to));
}

constexpr std::string repeater3030(const std::string& s, int number) {
    std::string cur = "";
    for (i64 i = 0; i < number; i++)
    {
        cur += s;
    }
    return cur;
}

constexpr std::string repeater3030(const char& c, int number) {
    string s(1, c);
    return repeater3030(s, number);
}

constexpr i64 pow_i64(i64 base, i64 exp) {
    i64 res = 1LL;
    while (exp > 0LL)
    {
        if (exp & 1) {
            res *= base;
        }
        exp >>= 1LL;
        base *= base;
    }
    return res;
}

template<typename T>
T eqmin(T& a, T b) {
    a = min(a, b);
    return a;
}

template<typename T>
T eqmax(T& a, T b) {
    a = max(a, b);
    return a;
}



//Output-Related

template <typename T, typename U>
std::ostream& operator<<(std::ostream& os, const std::pair<T, U>& p) {
    os << "(" << p.first << ", " << p.second << ")";
    return os;
}

template<typename T>
inline void output(const T elem) {
    std::cout << elem << std::endl;
}

#ifndef __INTELLISENSE__
template<typename T1, typename T2>
inline void output(const pair<T1, T2> elem) {
    std::cout << "(" << elem.first << "," << elem.second << ")" << std::endl;
}

template<typename T>
inline void output(const vector<T>& vec) {
    for (T elem : vec) {
        std::cout << elem << " ";
    }
    std::cout << std::endl;
}

template<typename T>
inline void output(const vector<vector<T>>& vvec) {
    for (vector<T> vec : vvec) {
        std::cout << "(";
        for (T elem : vec) {
            std::cout << elem << " ";
        }
        std::cout << ")";
    }
    std::cout << std::endl;
}

template<typename T>
inline void output(const vector<vector<vector<T>>>& vvvec) {
    for (vector<vector<T>> vvec : vvvec)
    {
        std::cout << "[";
        for (vector<T> vec : vvec) {
            std::cout << "(";
            for (T elem : vec) {
                std::cout << elem << " ";
            }
            std::cout << ")";
        }
        std::cout << "]" << std::endl;
    }
}
#endif

template<typename T>
inline void output_iter(const T& iter) {
    for (auto&& elem : iter)
    {
        std::cout << elem << " ";
    }
    std::cout << std::endl;
}

/**
 * ACLibrary-fewnwicktree
 * Ref : https://atcoder.github.io/ac-library/master/document_ja/
 */


/**
 * ACLibrary-internaltypetraits
 * Ref : https://atcoder.github.io/ac-library/master/document_ja/
 */

#include <type_traits>

namespace atcoder {

namespace internal {

#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value,
                              __uint128_t,
                              unsigned __int128>;

template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
                                                  is_signed_int128<T>::value ||
                                                  is_unsigned_int128<T>::value,
                                              std::true_type,
                                              std::false_type>::type;

template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                 std::is_signed<T>::value) ||
                                                    is_signed_int128<T>::value,
                                                std::true_type,
                                                std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value,
    make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value,
                              std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;

#else

template <class T> using is_integral = typename std::is_integral<T>;

template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
                                              std::make_unsigned<T>,
                                              std::common_type<T>>::type;

#endif

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

}  // namespace internal

}  // namespace atcoder



namespace atcoder {

// Reference: https://en.wikipedia.org/wiki/Fenwick_tree
template <class T> struct fenwick_tree {
    using U = internal::to_unsigned_t<T>;

  public:
    fenwick_tree() : _n(0) {}
    explicit fenwick_tree(int n) : _n(n), data(n) {}

    void add(int p, T x) {
        assert(0 <= p && p < _n);
        p++;
        while (p <= _n) {
            data[p - 1] += U(x);
            p += p & -p;
        }
    }

    T sum(int l, int r) {
        assert(0 <= l && l <= r && r <= _n);
        return sum(r) - sum(l);
    }

  private:
    int _n;
    std::vector<U> data;

    U sum(int r) {
        U s = 0;
        while (r > 0) {
            s += data[r - 1];
            r -= r & -r;
        }
        return s;
    }
};

}  // namespace atcoder


/**
 * ACLibrary-segtree
 * Ref : https://atcoder.github.io/ac-library/master/document_ja/
 */


/**
 * ACLibrary-internalbit
 * Ref : https://atcoder.github.io/ac-library/master/document_ja/
 */

#ifdef _MSC_VER
#include <intrin.h>
#endif

#if __cplusplus >= 202002L
#endif

namespace atcoder {

namespace internal {

#if __cplusplus >= 202002L

using std::bit_ceil;

#else

// @return same with std::bit::bit_ceil
unsigned int bit_ceil(unsigned int n) {
    unsigned int x = 1;
    while (x < (unsigned int)(n)) x *= 2;
    return x;
}

#endif

// @param n `1 <= n`
// @return same with std::bit::countr_zero
int countr_zero(unsigned int n) {
#ifdef _MSC_VER
    unsigned long index;
    _BitScanForward(&index, n);
    return index;
#else
    return __builtin_ctz(n);
#endif
}

// @param n `1 <= n`
// @return same with std::bit::countr_zero
constexpr int countr_zero_constexpr(unsigned int n) {
    int x = 0;
    while (!(n & (1 << x))) x++;
    return x;
}

}  // namespace internal

}  // namespace atcoder



namespace atcoder {

#if __cplusplus >= 201703L

template <class S, auto op, auto e> struct segtree {
    static_assert(std::is_convertible_v<decltype(op), std::function<S(S, S)>>,
                  "op must work as S(S, S)");
    static_assert(std::is_convertible_v<decltype(e), std::function<S()>>,
                  "e must work as S()");

#else

template <class S, S (*op)(S, S), S (*e)()> struct segtree {

#endif

  public:
    segtree() : segtree(0) {}
    explicit segtree(int n) : segtree(std::vector<S>(n, e())) {}
    explicit segtree(const std::vector<S>& v) : _n(int(v.size())) {
        size = (int)internal::bit_ceil((unsigned int)(_n));
        log = internal::countr_zero((unsigned int)size);
        d = std::vector<S>(2 * size, e());
        for (int i = 0; i < _n; i++) d[size + i] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }

    void set(int p, S x) {
        assert(0 <= p && p < _n);
        p += size;
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    S get(int p) const {
        assert(0 <= p && p < _n);
        return d[p + size];
    }

    S prod(int l, int r) const {
        assert(0 <= l && l <= r && r <= _n);
        S sml = e(), smr = e();
        l += size;
        r += size;

        while (l < r) {
            if (l & 1) sml = op(sml, d[l++]);
            if (r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }
        return op(sml, smr);
    }

    S all_prod() const { return d[1]; }

    template <bool (*f)(S)> int max_right(int l) const {
        return max_right(l, [](S x) { return f(x); });
    }
    template <class F> int max_right(int l, F f) const {
        assert(0 <= l && l <= _n);
        assert(f(e()));
        if (l == _n) return _n;
        l += size;
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!f(op(sm, d[l]))) {
                while (l < size) {
                    l = (2 * l);
                    if (f(op(sm, d[l]))) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }

    template <bool (*f)(S)> int min_left(int r) const {
        return min_left(r, [](S x) { return f(x); });
    }
    template <class F> int min_left(int r, F f) const {
        assert(0 <= r && r <= _n);
        assert(f(e()));
        if (r == 0) return 0;
        r += size;
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!f(op(d[r], sm))) {
                while (r < size) {
                    r = (2 * r + 1);
                    if (f(op(d[r], sm))) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

  private:
    int _n, size, log;
    std::vector<S> d;

    void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
};

}  // namespace atcoder



using namespace atcoder;


/**
 * Graph一式
 * Author : WhiteKnight
 */

struct Dest {
    i64 to;
    i64 cost;
};

typedef vector<vector<Dest>> wgraphList;//Weighted,List
typedef vector<vector<i64>> sgraphList;//Simple,List
typedef vector<Dest> vedge;
typedef vvi64 wgraphMat;//Weighted,Matrix

wgraphList translate_simple_weight(sgraphList graph) {
    i64 N = graph.size();
    wgraphList res(N);
    for (i64 i = 0; i < N; i++)
    {
        for (auto&& e : graph[i])
        {
            res[i].push_back({e,1});
        }
    }
    return res;
}

//コストを無視し構造のみのグラフを返す
sgraphList translate_weight_simple(wgraphList graph){
    i64 N = graph.size();
    sgraphList res(N);
    for (i64 i = 0; i < N; i++)
    {
        for (auto&& e : graph[i])
        {
            res[i].push_back(e.to);
        }
    }
    return res;
}

template<i64 INF>
wgraphList translate_mat_list(wgraphMat graph){
    i64 N = graph.size();
    wgraphList res(N);
    for (i64 i = 0; i < N; i++)
    {
        for (i64 j = 0; j < N; j++)
        {
            if(graph[i][j] >= INF){
                continue;
            }
            res[i].push_back({ j,graph[i][j] });
        }
    }
    return res;
}

//Main Flow

/**
 * Stern-Brocot-Tree
 * Author: WhiteKnight
 */

struct Rational{
    i64 num;
    i64 dom;
};

struct SternBrocotTree{
private:
    //max_dom:included,val:included
    //first:左,second:右
    pair<Rational,Rational> get_nearest(i64 max_dom, Rational val){
        assert(val.dom > 0);
        assert(max_dom >= 1);
        Rational l = {0,1};
        Rational r = {1,0};
        Rational cur = {1,1};
        pair<Rational,Rational> res = { cur,cur };
        while (true)
        {
            if(cur.num*val.dom < val.num*cur.dom){
                //to right
                i64 dp_x = (cur.dom*val.num - cur.num*val.dom)/(r.num*val.dom - r.dom*val.num);
                if((cur.dom*val.num - cur.num*val.dom) != (r.num*val.dom - r.dom*val.num)){
                    dp_x++;
                }
                bool stopper = false;
                if(r.dom > 0){
                    stopper = (max_dom - cur.dom) / r.dom < dp_x;
                    eqmin(dp_x, (max_dom - cur.dom) / r.dom);
                }
                assert(dp_x >= 0);
                if(dp_x == 0){
                    break;
                }
                cur.num += dp_x * r.num;
                cur.dom += dp_x * r.dom;
                l.num = cur.num - r.num;
                l.dom = cur.dom - r.dom;
                if(stopper){
                    res.first = cur;
                    break;
                }else{
                    res.first = l;
                    res.second = cur;
                }
            }else if(cur.num*val.dom == val.num*cur.dom){
                res.first = cur;
                res.second = cur;
                return res;
            }else{
                //to left
                i64 dp_x = (cur.num*val.dom - val.num*cur.dom)/(val.num*l.dom-l.num*val.dom);
                if((cur.num*val.dom - val.num*cur.dom) != (val.num*l.dom-l.num*val.dom)){
                   dp_x++; 
                }
                bool stopper = (max_dom - cur.dom) / l.dom < dp_x;
                eqmin(dp_x, (max_dom - cur.dom) / l.dom);
                assert(dp_x >= 0);
                if(dp_x == 0){
                    break;
                }
                cur.num += dp_x * l.num;
                cur.dom += dp_x * l.dom;
                r.num = cur.num - l.num;
                r.dom = cur.dom - l.dom;
                if(stopper){
                    res.second = cur;
                    break;
                }else{
                    res.second = r;
                    res.first = cur;
                }
            }
        }
        return res;
    }

public:
    //max_dom:included,val:included
    Rational left_nearest(i64 max_dom, Rational val){
        auto res = get_nearest(max_dom,val);
        return res.first;
    }

    //max_dom:included,val:included
    Rational right_nearest(i64 max_dom, Rational val){
        auto res = get_nearest(max_dom,val);
        return res.second;
    }
};

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << setprecision(15);
    i64 P, Q;
    cin >> P >> Q;
    SternBrocotTree sbt;
    auto R = sbt.right_nearest(Q-1,{P,Q});
    auto L = sbt.left_nearest(Q-1,{P,Q});
    output(R.dom+R.num+L.dom+L.num);
    return 0;
}
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結果

ソースコード
