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test/mytest/dyadic_rational.test.cpp
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- Last update: 2023-11-07 20:28:52+09:00
- Problem: https://judge.yosupo.jp/problem/aplusb
Depends on
my_template.hpp
Code
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#include "my_template.hpp"
#include "game/dyadic_rational.hpp"
void test() {
using X = Dyadic_Rational<ll>;
// 足し
assert(X(1) + X(2) == X(3));
assert(X(-3) + X(2) == X(-1));
assert(X(-3) + X(3) == X(0));
assert(X(3, 8) + X(1, 2) == X(7, 8));
assert(X(3, 8) + X(3, 8) == X(3, 4));
assert(X(3, 8) + X(-3, 8) == X(0));
assert(X(2, 8) + X(-1, 4) == X(0));
// 引き
assert(X(1) - X(2) == X(-1));
assert(X(-3) - X(2) == X(-5));
assert(X(-3) - X(3) == X(-6));
assert(X(3, 8) - X(1, 2) == X(-1, 8));
assert(X(3, 8) - X(3, 8) == X(0, 1));
assert(X(3, 8) - X(-3, 8) == X(3, 4));
assert(X(2, 8) - X(-1, 4) == X(1, 2));
// 不等号
assert(X(1) < X(2));
assert(X(-3) < X(2));
assert(X(-3) < X(3));
assert(X(3, 8) < X(1, 2));
assert(X(3, 8) == X(3, 8));
assert(X(3, 8) > X(-3, 8));
assert(X(2, 8) > X(-1, 4));
// {x|y}
assert(X::simplest(X(1), X(2)) == X(3, 2));
assert(X::simplest(X(-3), X(0)) == X(-1));
assert(X::simplest(X(1), X(5)) == X(2));
assert(X::simplest(X(-3), X(1)) == X(0));
assert(X::simplest(X(9, 16), X(5, 8)) == X(19, 32));
assert(X::simplest(X(1, 2), X(2, 1)) == X(1));
assert(X::simplest(X(1, 8), X(5, 8)) == X(1, 2));
assert(X::simplest(X(-91, 64), X(-41, 32)) == X(-11, 8));
assert(X::simplest(X(-3, 2), X(-1, 1)) == X(-5, 4));
}
void solve() {
int a, b;
cin >> a >> b;
cout << a + b << "\n";
}
signed main() {
test();
solve();
return 0;
}#line 1 "test/mytest/dyadic_rational.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#line 1 "my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;
template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;
using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
#define vv(type, name, h, ...) \
vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#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__))))
// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
#define FOR_subset(t, s) \
for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define stoi stoll
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T>
T floor(T a, T b) {
return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
T q = floor(x, y);
return {q, x - q * y};
}
template <typename T, typename U>
T SUM(const vector<U> &A) {
T sm = 0;
for (auto &&a: A) sm += a;
return sm;
}
#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()), x.shrink_to_fit()
template <typename T>
T POP(deque<T> &que) {
T a = que.front();
que.pop_front();
return a;
}
template <typename T>
T POP(pq<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(pqg<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(vc<T> &que) {
T a = que.back();
que.pop_back();
return a;
}
template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
if (check_ok) assert(check(ok));
while (abs(ok - ng) > 1) {
auto x = (ng + ok) / 2;
(check(x) ? ok : ng) = x;
}
return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
FOR(iter) {
double x = (ok + ng) / 2;
(check(x) ? ok : ng) = x;
}
return (ok + ng) / 2;
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
return (a > b ? a = b, 1 : 0);
}
// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
vc<int> A(S.size());
FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
return A;
}
template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
int N = A.size();
vector<T> B(N + 1);
FOR(i, N) { B[i + 1] = B[i] + A[i]; }
if (off == 0) B.erase(B.begin());
return B;
}
// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
vector<int> ids(len(A));
iota(all(ids), 0);
sort(all(ids),
[&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
return ids;
}
// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
vc<T> B(len(I));
FOR(i, len(I)) B[i] = A[I[i]];
return B;
}
#endif
#line 1 "game/dyadic_rational.hpp"
// a+b/2^M の形で持つ
template <typename INTEGER>
struct Dyadic_Rational {
using X = Dyadic_Rational;
INTEGER a, b;
static constexpr int M = std::numeric_limits<INTEGER>::digits - 2;
Dyadic_Rational(INTEGER a = 0) : a(a), b(0) {}
// x + y / z
Dyadic_Rational(INTEGER x, INTEGER y, INTEGER z) : a(x), b(y) {
auto [q, r] = divmod(b, z);
a += q;
b = r;
b *= (INTEGER(1) << M) / z;
}
// x/y
Dyadic_Rational(INTEGER x, INTEGER y) : Dyadic_Rational(0, x, y) {}
static X from_ab(INTEGER a, INTEGER b) {
X x(a);
x.b = b;
return x;
}
// 比較
bool operator==(X const& rhs) const { return (a == rhs.a && b == rhs.b); }
bool operator!=(X const& rhs) const { return !(*this == rhs); }
bool operator<(X const& rhs) const {
return (a < rhs.a) || (a == rhs.a && b < rhs.b);
}
bool operator<=(X const& rhs) const {
return (a < rhs.a) || (a == rhs.a && b <= rhs.b);
}
bool operator>(X const& rhs) const {
return (a > rhs.a) || (a == rhs.a && b > rhs.b);
}
bool operator>=(X const& rhs) const {
return (a > rhs.a) || (a == rhs.a && b >= rhs.b);
}
// 加法
friend X operator+(const X& x, const X& y) {
INTEGER a = x.a + y.a, b = x.b + y.b;
while (b >= INTEGER(1) << M) {
++a;
b -= INTEGER(1) << M;
}
return from_ab(a, b);
}
friend X operator-(const X& x, const X& y) {
INTEGER a = x.a - y.a, b = x.b - y.b;
while (b < 0) {
--a;
b += INTEGER(1) << M;
}
return from_ab(a, b);
}
friend X operator-(const X& x) {
INTEGER a = -x.a, b = -x.b;
while (b < 0) {
--a;
b += INTEGER(1) << M;
}
return from_ab(a, b);
}
X& operator+=(const X& x) { return (*this) = (*this) + x; }
X& operator-=(const X& x) { return (*this) = (*this) - x; }
static X simplest(const X& x, const X& y) {
assert(x < y);
if (y.a < 0) return -simplest(-y, -x);
{
INTEGER l = x.a + 1;
INTEGER r = (y.b == 0 ? y.a - 1 : y.a);
if (l <= 0 && 0 <= r) return X(0);
if (l <= r && 0 <= l) return X(l);
if (l <= r && r <= 0) return X(r);
}
INTEGER l = x.b + 1;
INTEGER r = (y.b == 0 ? (INTEGER(1) << M) - 1 : y.b - 1);
if (l == r) return from_ab(x.a, l);
int k = topbit(l ^ r);
r &= ~((INTEGER(1) << k) - 1);
return from_ab(x.a, r);
}
static constexpr X infinity() { return from_ab(INTEGER(1) << M, 0); }
string to_string() {
ll x = a, y = b, z = INTEGER(1) << M;
while (y % 2 == 0 && z % 2 == 0) { y /= 2, z /= 2; }
y += x * z;
return std::to_string(y) + "/" + std::to_string(z);
}
};
#line 4 "test/mytest/dyadic_rational.test.cpp"
void test() {
using X = Dyadic_Rational<ll>;
// 足し
assert(X(1) + X(2) == X(3));
assert(X(-3) + X(2) == X(-1));
assert(X(-3) + X(3) == X(0));
assert(X(3, 8) + X(1, 2) == X(7, 8));
assert(X(3, 8) + X(3, 8) == X(3, 4));
assert(X(3, 8) + X(-3, 8) == X(0));
assert(X(2, 8) + X(-1, 4) == X(0));
// 引き
assert(X(1) - X(2) == X(-1));
assert(X(-3) - X(2) == X(-5));
assert(X(-3) - X(3) == X(-6));
assert(X(3, 8) - X(1, 2) == X(-1, 8));
assert(X(3, 8) - X(3, 8) == X(0, 1));
assert(X(3, 8) - X(-3, 8) == X(3, 4));
assert(X(2, 8) - X(-1, 4) == X(1, 2));
// 不等号
assert(X(1) < X(2));
assert(X(-3) < X(2));
assert(X(-3) < X(3));
assert(X(3, 8) < X(1, 2));
assert(X(3, 8) == X(3, 8));
assert(X(3, 8) > X(-3, 8));
assert(X(2, 8) > X(-1, 4));
// {x|y}
assert(X::simplest(X(1), X(2)) == X(3, 2));
assert(X::simplest(X(-3), X(0)) == X(-1));
assert(X::simplest(X(1), X(5)) == X(2));
assert(X::simplest(X(-3), X(1)) == X(0));
assert(X::simplest(X(9, 16), X(5, 8)) == X(19, 32));
assert(X::simplest(X(1, 2), X(2, 1)) == X(1));
assert(X::simplest(X(1, 8), X(5, 8)) == X(1, 2));
assert(X::simplest(X(-91, 64), X(-41, 32)) == X(-11, 8));
assert(X::simplest(X(-3, 2), X(-1, 1)) == X(-5, 4));
}
void solve() {
int a, b;
cin >> a >> b;
cout << a + b << "\n";
}
signed main() {
test();
solve();
return 0;
}