結果

問題 No.1936 Rational Approximation
ユーザー DemystifyDemystify
提出日時 2022-05-13 22:29:57
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 7,644 bytes
コンパイル時間 2,280 ms
コンパイル使用メモリ 204,484 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-07-22 02:35:27
合計ジャッジ時間 3,015 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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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
5,248 KB
testcase_01 AC 2 ms
5,376 KB
testcase_02 AC 2 ms
5,376 KB
testcase_03 AC 2 ms
5,376 KB
testcase_04 AC 2 ms
5,376 KB
testcase_05 AC 2 ms
5,376 KB
testcase_06 AC 2 ms
5,376 KB
testcase_07 AC 2 ms
5,376 KB
testcase_08 AC 2 ms
5,376 KB
testcase_09 AC 2 ms
5,376 KB
testcase_10 AC 2 ms
5,376 KB
testcase_11 AC 2 ms
5,376 KB
testcase_12 AC 2 ms
5,376 KB
testcase_13 AC 2 ms
5,376 KB
testcase_14 AC 2 ms
5,376 KB
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ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
// --------------------------------------------------------
#define FOR(i,l,r) for (ll i = (l); i < (r); ++i)
#define RFOR(i,l,r) for (ll i = (r)-1; (l) <= i; --i)
#define REP(i,n) FOR(i,0,n)
#define RREP(i,n) RFOR(i,0,n)
#define ALL(c) (c).begin(), (c).end()
#define RALL(c) (c).rbegin(), (c).rend()
#define SORT(c) sort(ALL(c))
#define RSORT(c) sort(RALL(c))
#define MIN(c) *min_element(ALL(c))
#define MAX(c) *max_element(ALL(c))
#define COUNT(c,v) count(ALL(c),(v))
#define SZ(c) ((ll)(c).size())
#define BIT(b,i) (((b)>>(i)) & 1)
#define PCNT(b) __builtin_popcountll(b)
#define P0(i) (((i) & 1) == 0)
#define P1(i) (((i) & 1) == 1)
#define LB(c,v) distance((c).begin(), lower_bound(ALL(c), (v)))
#define UB(c,v) distance((c).begin(), upper_bound(ALL(c), (v)))
#define UQ(c) SORT(c), (c).erase(unique(ALL(c)), (c).end())
#define elif else if
#ifdef _LOCAL
    #define debug_bar cerr << "--------------------\n";
    #define debug(x) cerr << "l." << __LINE__ << " : " << #x << " = " << (x) << '\n'
    #define debug_pair(x) cerr << "l." << __LINE__ << " : " << #x << " = (" << x.first << "," << x.second << ")\n";
    template<class T> void debug_line(const vector<T>& ans, int l, int r, int L = 0) { cerr << "l." << L << " :"; for (int i = l; i < r; i++) { cerr << ' ' << ans[i]; } cerr << '\n'; }
#else
    #define cerr if (false) cerr
    #define debug_bar
    #define debug(x)
    #define debug_pair(x)
    template<class T> void debug_line([[maybe_unused]] const vector<T>& ans, [[maybe_unused]] int l, [[maybe_unused]] int r, [[maybe_unused]] int L = 0) {}
#endif
template<class... T> void input(T&... a) { (cin >> ... >> a); }
void print() { cout << '\n'; }
template<class T> void print(const T& a) { cout << a << '\n'; }
template<class T, class... Ts> void print(const T& a, const Ts&... b) { cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; }
template<class T> void cout_line(const vector<T>& ans, int l, int r) { for (int i = l; i < r; i++) { if (i != l) { cout << ' '; } cout << ans[i]; } cout << '\n'; }
template<class T> bool chmin(T& a, const T b) { if (b < a) { a = b; return 1; } return 0; }
template<class T> bool chmax(T& a, const T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> T SUM(const vector<T>& A) { return accumulate(ALL(A), T(0)); }
template<class T> vector<T> cumsum(const vector<T>& A, bool offset = true) { int N = A.size(); vector<T> S(N+1, 0); for (int i = 0; i < N; i++) { S[i+1] = S[i] + A[i]; } if (not offset) { S.erase(S.begin()); } return S; }
ll mod(ll x, ll m) { assert(m != 0); return (x % m + m) % m; }
ll ceil(ll a, ll b) { if (b < 0) { return ceil(-a, -b); } assert(b > 0); return (a < 0 ? a / b : (a + b - 1) / b); }
ll floor(ll a, ll b) { if (b < 0) { return floor(-a, -b); } assert(b > 0); return (a > 0 ? a / b : (a - b + 1) / b); }
ll powint(ll x, ll n) { assert(n >= 0); if (n == 0) { return 1; }; ll res = powint(x, n>>1); res *= res; if (n & 1) { res *= x; } return res; }
pair<ll,ll> divmod(ll a, ll b) { assert(b != 0); ll q = floor(a, b); return make_pair(q, a - q * b); }
ll bitlen(ll b) { if (b <= 0) { return 0; } return (64LL - __builtin_clzll(b)); }
ll digit_len(ll n) { assert(n >= 0); if (n == 0) { return 1; } ll sum = 0; while (n > 0) { sum++; n /= 10; } return sum; }
ll digit_sum(ll n) { assert(n >= 0); ll sum = 0; while (n > 0) { sum += n % 10; n /= 10; } return sum; }
ll digit_prod(ll n) { assert(n >= 0); if (n == 0) { return 0; } ll prod = 1; while (n > 0) { prod *= n % 10; n /= 10; } return prod; }
ll xor_sum(ll x) { assert(0 <= x); switch (x % 4) { case 0: return x; case 1: return 1; case 2: return x ^ 1; case 3: return 0; } assert(false); }
string toupper(const string& S) { string T(S); for (int i = 0; i < (int)T.size(); i++) { T[i] = toupper(T[i]); } return T; }
string tolower(const string& S) { string T(S); for (int i = 0; i < (int)T.size(); i++) { T[i] = tolower(T[i]); } return T; }
int a2i(const char& c) { assert(islower(c)); return (c - 'a'); }
int A2i(const char& c) { assert(isupper(c)); return (c - 'A'); }
int d2i(const char& d) { assert(isdigit(d)); return (d - '0'); }
char i2a(const int& i) { assert(0 <= i && i < 26); return ('a' + i); }
char i2A(const int& i) { assert(0 <= i && i < 26); return ('A' + i); }
char i2d(const int& i) { assert(0 <= i && i <= 9); return ('0' + i); }
using P = pair<ll,ll>;
using VP = vector<P>;
using VVP = vector<VP>;
using VS = vector<string>;
using VVS = vector<VS>;
using VI = vector<int>;
using VVI = vector<VI>;
using VVVI = vector<VVI>;
using VLL = vector<ll>;
using VVLL = vector<VLL>;
using VVVLL = vector<VVLL>;
using VB = vector<bool>;
using VVB = vector<VB>;
using VVVB = vector<VVB>;
using VD = vector<double>;
using VVD = vector<VD>;
using VVVD = vector<VVD>;
using VLD = vector<ld>;
using VVLD = vector<VLD>;
using VVVLD = vector<VVLD>;
const ld EPS = 1e-10;
const ld PI  = acosl(-1.0);
constexpr ll MOD = 1000000007;
// constexpr ll MOD = 998244353;
constexpr int inf = (1 << 30) - 1;   // 1073741824 - 1
constexpr ll INF = (1LL << 62) - 1;  // 4611686018427387904 - 1
// --------------------------------------------------------
// #include <atcoder/all>
// using namespace atcoder;



// References:
//   <https://cp-algorithms.com/algebra/linear-diophantine-equation.html>
//   <https://codeforces.com/contest/710/submission/148530976>

// 線形ディオファントス方程式
// x + by = c の整数解の一つ (x_0, y_0) を求める
// 整数解が求まらなければ false を返す
//   - ★ a = 0 または b = 0 の場合、結果の取り扱いに注意！ ★
//   - O(log (a + b))
//   - 一般解（k は整数）
//       x = x_0 + k * (b / g)
//       y = y_0 - k * (a / g)
template <class T>
bool linear_diophantine_equation (T a, T b, T c, T& x_0, T& y_0, T& g) {
    auto extgcd = [](T a, T b, T& x, T& y) {
        auto _extgcd = [](auto&& self, T a, T b, T& x, T& y) -> T {
            if (b == 0) { x = 1; y = 0; return a; }
            T g = self(self, b, a % b, y, x);
            y -= (a / b) * x;
            return g;
        };
        T g = _extgcd(_extgcd, a, b, x, y);
        if (g < 0) { g = -g; x = -x; y = -y; }
        return g;
    };

    if (a == 0 && b == 0) {
        if (c != 0) { return false; }
        x_0 = y_0 = g = 0;
    } else if (a == 0) {
        if (c % b != 0) { return false; }
        x_0 = 0; y_0 = c / b; g = abs(b);
    } else if (b == 0) {
        if (c % a != 0) { return false; }
        x_0 = c / a; y_0 = 0; g = abs(a);
    } else {
        T x_g, y_g;
        g = extgcd(a, b, x_g, y_g);
        if (c % g) { return false; }
        x_0 = x_g * (c / g);
        y_0 = y_g * (c / g);
    }
    return true;
}


int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(15);

    ll P, Q; input(P, Q);

    auto func1 = [&]() -> pair<ll,ll> {
        ll a = -Q, b = P, c = 1;
        ll x_0, y_0, g;
        bool res = linear_diophantine_equation(a, b, c, x_0, y_0, g);
        assert(res);
        ll k = ceil(Q - y_0, Q) - 1;
        return {x_0 + k * Q, y_0 + k * P};
    };
    auto func2 = [&]() -> pair<ll,ll> {
        ll a = Q, b = -P, c = 1;
        ll x_0, y_0, g;
        bool res = linear_diophantine_equation(a, b, c, x_0, y_0, g);
        assert(res);
        ll k = ceil(Q - y_0, Q) - 1;
        return {x_0 + k * P, y_0 + k * Q};
    };

    auto [p_L, q_L] = func1();
    auto [p_R, q_R] = func2();
    debug_pair(make_pair(p_L, q_L));
    debug_pair(make_pair(p_R, q_R));

    ll ans = q_L + p_L + q_R + p_R;
    print(ans);

    return 0;
}
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