#760618 (C++17) No.1936 Rational Approximation

提出ソース
結果

問題	No.1936 Rational Approximation
ユーザー	mtsd
提出日時	2022-05-13 22:14:25
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	2 ms / 2,000 ms
コード長	14,644 bytes
コンパイル時間	2,132 ms
コンパイル使用メモリ	208,624 KB
実行使用メモリ	6,944 KB
最終ジャッジ日時	2024-07-22 02:11:41
合計ジャッジ時間	2,711 ms
ジャッジサーバーID （参考情報）	judge4 / judge1
このコードへのチャレンジ
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テストケース

テストケース表示
入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 6,816 KB
testcase_01	AC	2 ms 6,940 KB
testcase_02	AC	1 ms 6,940 KB
testcase_03	AC	2 ms 6,940 KB
testcase_04	AC	2 ms 6,940 KB
testcase_05	AC	2 ms 6,944 KB
testcase_06	AC	2 ms 6,940 KB
testcase_07	AC	2 ms 6,940 KB
testcase_08	AC	2 ms 6,944 KB
testcase_09	AC	2 ms 6,940 KB
testcase_10	AC	2 ms 6,944 KB
testcase_11	AC	2 ms 6,944 KB
testcase_12	AC	2 ms 6,940 KB
testcase_13	AC	1 ms 6,944 KB
testcase_14	AC	2 ms 6,944 KB
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ソースコード

raw source code
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
#define inf 1000000007
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define fi first
#define se second
#define rep(i,n) for(int i = 0; i < (int)(n); ++i)
#define rrep(i,n) for(int i = (int)n-1; i >= 0; --i)
#define srep(i,a,b) for(int i = (int)a; i < (int)(b); ++i)
#define all(x) (x).begin(),(x).end()
#define SUM(v) accumulate(all(v), 0LL)
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end())
#define SZ(c) (int)(c).size()
template<typename T>
ostream& operator << (ostream& os, vector<T>& vec) {
    os << "{";
    for (int i = 0; i<(int)vec.size(); i++) {
        os << vec[i] << (i + 1 == (int)vec.size() ? "" : ", ");
    }
    os << "}";
    return os;
}
// pair出力
template<typename T, typename U>
ostream& operator << (ostream& os, pair<T, U> pair_var) {
    os << "(" << pair_var.first << ", " << pair_var.second << ")";
    return os;
}
// map出力
template<typename T, typename U>
ostream& operator << (ostream& os, map<T, U>& map_var) {
    os << "{";
    for(auto itr = map_var.begin(); itr != map_var.end(); itr++){
        os << "(" << itr->first << ", " << itr->second << ")";
        itr++;
        if(itr != map_var.end()) os << ", ";
        itr--;
    }
    os << "}";
    return os;
}
// set 出力
template<typename T>
ostream& operator << (ostream& os, set<T>& set_var) {
    os << "{";
    for(auto itr = set_var.begin(); itr != set_var.end(); itr++){
        os << (*itr);
        ++itr;
        if(itr != set_var.end()) os << ", ";
        itr--;
    }
    os << "}";
    return os;
}
// tuple 出力
template<int N,class Tuple>
void out(ostream &os,const Tuple &t){}
template<int N,class Tuple,class H,class ...Ts>
void out(ostream &os,const Tuple &t){
    if(N)os<<", ";
    os<<get<N>(t);
    out<N+1,Tuple,Ts...>(os,t);
}
template<class ...Ts>
ostream& operator<<(ostream &os, const tuple<Ts...> &t){
    os<<"(";
    out<0,tuple<Ts...>,Ts...>(os,t);
    os<<")";
    return os;
}
#define overload2(_1, _2, name, ...) name
#define vec(type, name, ...) vector<type> name(__VA_ARGS__)
#define VEC(type, name, size)                                                                                                                                  \
    vector<type> name(size);                                                                                                                                   \
    IN(name)
#define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define VV(type, name, h, w)                                                                                                                                   \
    vector<vector<type>> name(h, vector<type>(w));                                                                                                             \
    IN(name)
#define vvv(type, name, h, w, ...) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)                                                                                                                         \
    vector<vector<vector<vector<type>>>> name(a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
#define INT(...)                                                                                                                                               \
    int __VA_ARGS__;                                                                                                                                           \
    IN(__VA_ARGS__)
#define LL(...)                                                                                                                                                \
    ll __VA_ARGS__;                                                                                                                                            \
    IN(__VA_ARGS__)
#define STR(...)                                                                                                                                               \
    string __VA_ARGS__;                                                                                                                                        \
    IN(__VA_ARGS__)
#define CHR(...)                                                                                                                                               \
    char __VA_ARGS__;                                                                                                                                          \
    IN(__VA_ARGS__)
#define DBL(...)                                                                                                                                               \
    double __VA_ARGS__;                                                                                                                                        \
    IN(__VA_ARGS__)
int scan() { return getchar(); }
void scan(int &a) { cin >> a; }
void scan(long long &a) { cin >> a; }
void scan(char &a) { cin >> a; }
void scan(double &a) { cin >> a; }
void scan(string &a) { cin >> a; }
template <class T, class S> void scan(pair<T, S> &p) { scan(p.first), scan(p.second); }
template <class T> void scan(vector<T> &);
template <class T> void scan(vector<T> &a) {
    for(auto &i : a) scan(i);
}
template <class T> void scan(T &a) { cin >> a; }
void IN() {}
template <class Head, class... Tail> void IN(Head &head, Tail &...tail) {
    scan(head);
    IN(tail...);
}
const string YESNO[2] = {"NO", "YES"};
const string YesNo[2] = {"No", "Yes"};
const string yesno[2] = {"no", "yes"};
void YES(bool t = 1) { cout << YESNO[t] << endl; }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { cout << YesNo[t] << endl; }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { cout << yesno[t] << endl; }
void no(bool t = 1) { yes(!t); }
#ifdef LOCAL
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    cerr << " " << H;
    debug_out(T...);
}
#define dbg(...) \
    cerr << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl
#else
#define dbg(...) (void(0))
#define dump(x) (void(0))
#endif
template<typename A, typename T>
std::enable_if_t<std::is_convertible<T, A>::value> fill(A& array, const T& val)
{
    array = val;
}
template<typename A, typename T>
std::enable_if_t<!std::is_convertible<T, A>::value> fill(A& array, const T& val)
{
    for (auto& a : array) {
        fill(a, val);
    }
}
template <typename T, typename S> T ceil(T x, S y) {
    assert(y);
    return (y < 0 ? ceil(-x, -y) : (x > 0 ? (x + y - 1) / y : x / y));
}
template <typename T, typename S> T floor(T x, S y) {
    assert(y);
    return (y < 0 ? floor(-x, -y) : (x > 0 ? x / y : x / y - (x % y == 0 ? 0 : 1)));
}
vector<int> iota(int n) {vector<int> a(n);iota(all(a), 0);return a;}
template <class T> T POW(T x, int n) {T res = 1;for(; n; n >>= 1, x *= x){if(n & 1) res *= x;}return res;}
ll pow2(int i) { return 1LL << i; }
int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int lowbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
int lowbit(ll a) { return a == 0 ? 64 : __builtin_ctzll(a); }
// int allbit(int n) { return (1 << n) - 1; }
ll allbit(ll n) { return (1LL << n) - 1; }
int popcount(signed t) { return __builtin_popcount(t); }
int popcount(ll t) { return __builtin_popcountll(t); }
bool ispow2(int i) { return i && (i & -i) == i; }


template <class S> void fold_in(vector<S> &v) {}
template <typename Head, typename... Tail, class S> void fold_in(vector<S> &v, Head &&a, Tail &&...tail) {
    for(auto e : a) v.emplace_back(e);
    fold_in(v, tail...);
}
template <class S> void renumber(vector<S> &v) {}
template <typename Head, typename... Tail, class S> void renumber(vector<S> &v, Head &&a, Tail &&...tail) {
    for(auto &&e : a) e = lb(v, e);
    renumber(v, tail...);
}
template <class S, class... Args> void zip(vector<S> &head, Args &&...args) {
    vector<S> v;
    fold_in(v, head, args...);
    sort(all(v)), v.erase(unique(all(v)), v.end());
    renumber(v, head, args...);
}
template<class T> inline bool chmax(T &a, T b){
    if(a<b){
        a = b;
        return true;
    }
    return false;
}
template<class T> inline bool chmin(T &a, T b){
    if(a>b){
        a = b;
        return true;
    }
    return false;
}

template<typename T> class Rational {
private:
    static Rational make(const T& x, const T& y){
        Rational m; return m.num = x, m.den = y, m;
    }
public:
    friend ostream& operator<<(ostream& os, const Rational& rn) {
        return (os << rn.num << " / " << rn.den);
    }
    Rational& operator=(T val){ return *this = Rational(val); }
    bool operator<(const Rational& val) const { return num*val.den < den*val.num; }
    bool operator<(const T val) const { return *this < Rational(val); }
    friend bool operator<(const T val1, const Rational& val2){ return Rational(val1) < val2; }
    bool operator>(const Rational& val) const { return val < *this; }
    bool operator>(const T val) const { return *this > Rational(val); }
    friend bool operator>(const T val1, const Rational& val2){ return Rational(val1) > val2; }
    bool operator<=(const Rational& val) const { return !(*this > val); }
    bool operator<=(const T val) const { return *this <= Rational(val); }
    friend bool operator<=(const T val1, const Rational& val2){ return Rational(val1) <= val2; }
    bool operator>=(const Rational& val) const { return !(*this < val); }
    bool operator>=(const T val) const { return *this >= Rational(val); }
    friend bool operator>=(const T val1, const Rational& val2){ return Rational(val1) >= val2; }
    bool operator==(const Rational& val) const { return num*val.den == den*val.num; }
    bool operator==(const T val) const { return *this == Rational(val); }
    friend bool operator==(const T val1, const Rational& val2){ return Rational(val1) == val2; }
    bool operator!=(const Rational& val) const { return !(*this == val); }
    bool operator!=(const T val) const { return *this != Rational(val); }
    friend bool operator!=(const T val1, const Rational& val2){ return Rational(val1) != val2; }
    explicit operator bool() const noexcept { return num; }
    bool operator!() const noexcept { return !static_cast<bool>(*this); }
    Rational operator+() const { return *this; }
    Rational operator-() const { return make(-num, den); }
    friend Rational abs(const Rational& val){ return make(abs(val.num), val.den); }
    Rational operator+(const Rational& val) const { return make(num*val.den+val.num*den, den*val.den); }
    Rational operator+(T val) const { return *this + Rational(val); }
    friend Rational operator+(T a, const Rational& b){ return b + a; }
    Rational& operator+=(const Rational& val){ return *this = *this + val; }
    Rational& operator+=(const T& val){ return *this = *this + val; }
    Rational& operator++(){ return *this += 1; }
    Rational operator++(int){ return make(num + den, den); }
    Rational operator-(const Rational& val) const { return make(num*val.den-val.num*den, den*val.den); }
    Rational operator-(T val) const { return *this - Rational(val); }
    friend Rational operator-(T a, const Rational& b){ return Rational(a) - b; }
    Rational& operator-=(const Rational& val){ return *this = *this - val; }
    Rational& operator-=(const T& val){ return *this = *this - val; }
    Rational& operator--(){ return *this -= 1; }
    Rational operator--(int){ return make(num - den, den); }
    Rational operator*(const Rational& val) const { return make(num*val.num, den*val.den); }
    Rational operator*(T val) const { return *this * Rational(val); }
    friend Rational operator*(T a, const Rational& b){ return b * a; }
    Rational& operator*=(const Rational& val){ return *this = *this * val;}
    Rational& operator*=(const T& val){ return *this = *this * val; }
    Rational operator/(const Rational& val) const { return make(num*val.den, den*val.num); }
    Rational operator/(T val) const { return *this / Rational(val); }
    friend Rational operator/(T a, const Rational& b){ return Rational(a) / b; }
    Rational& operator/=(const Rational& val){ return *this / val; }
    Rational& operator/=(const T& val){ return *this = *this / val; }

    T num, den;

    Rational(){}
    Rational(T num_) : num(num_), den(1){}
    Rational(T num_, T den_) : num(num_), den(den_){ if(den < 0) num = -num, den = -den; }
};

int main(){
    LL(P,Q);
    // 0/1 -   1/1
    Rational<ll> x(P,Q);
    auto calc = [&](auto&&f,Rational<ll> L,Rational<ll> R,bool ldown)->pair<Rational<ll>,Rational<ll>>{
        if(L.den+R.den>=Q)return MP(L,R);
        ll pL = L.num;
        ll pR = R.num;
        ll qL = L.den;
        ll qR = R.den;
        if(ldown){
            ll ok = 0;
            ll ng = ceil(Q-qR,qL);
            while(ng-ok>1){
                ll mid = (ok+ng)/2;
                Rational<ll> r(pL*mid+pR,qL*mid + qR);
                if(r < x){
                    ng = mid;
                }else{
                    ok = mid;
                }
            }
            // ng - x - ok
            if(ng==ceil(Q-qR,qL)){
                return f(f,L,Rational<ll>(pL*ok+pR,qL*ok + qR),false);
            }else{
                return f(f,Rational<ll>(pL*ng+pR,qL*ng + qR),Rational<ll>(pL*ok+pR,qL*ok + qR),false);
            }
        }else{
            ll ok = ceil(Q-qL,qR);
            ll ng = 0;
            while(ok-ng>1){
                ll mid = (ok+ng)/2;
                Rational<ll> r(pL+pR*mid,qL + qR*mid);
                if(r < x){
                    ng = mid;
                }else{
                    ok = mid;
                }
            }
            // ng - x - ok
            if(ok==ceil(Q-qL,qR)){
                return f(f,Rational<ll>(pL+pR*ng,qL + qR*ng),R,true);
            }else{
                return f(f,Rational<ll>(pR*ng+pL,qR*ng + qL),Rational<ll>(pR*ok+pL,qR*ok + qL),true);
            }
        }
    };
    auto res = calc(calc,Rational<ll>(0,1),Rational<ll>(1,1),true);
    dbg(res);
    cout << res.first.den + res.first.num + res.second.den + res.second.num << endl;
    return 0;
}
yukicoder

結果

テストケース

ソースコード
