#758851 (C++17) No.1932 動く点 P / Moving Point P

提出ソース
結果

問題	No.1932 動く点 P / Moving Point P
コンテスト
ユーザー	haruki_K
提出日時	2022-05-06 22:59:59
言語	C++17 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	943 ms / 6,000 ms
コード長	17,910 bytes
コンパイル時間	2,487 ms
コンパイル使用メモリ	208,296 KB
最終ジャッジ日時	2025-01-29 04:02:31
ジャッジサーバーID （参考情報）	judge4 / judge5
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 * 11
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ソースコード

raw source code
// >>> TEMPLATES
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
#define int ll
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rep1(i, n) for (int i = 1; i <= (int)(n); i++)
#define repR(i, n) for (int i = (int)(n)-1; i >= 0; i--)
#define rep1R(i, n) for (int i = (int)(n); i >= 1; i--)
#define loop(i, a, B) for (int i = a; i B; i++)
#define loopR(i, a, B) for (int i = a; i B; i--)
#define all(x) begin(x), end(x)
#define allR(x) rbegin(x), rend(x)
#define pb push_back
#define eb emplace_back
#define fst first
#define snd second
template <class Int> auto constexpr inf_ = numeric_limits<Int>::max()/2-1;
auto constexpr INF32 = inf_<int32_t>;
auto constexpr INF64 = inf_<int64_t>;
auto constexpr INF   = inf_<int>;
#ifdef LOCAL
#include "debug.hpp"
#define oj_local(x, y) (y)
#else
#define dump(...) (void)(0)
#define say(x) (void)(0)
#define debug if (0)
#define oj_local(x, y) (x)
#endif
template <class T, class Comp> struct pque : priority_queue<T, vector<T>, Comp> { vector<T> &data() { return this->c; } void clear() { this->c.clear(); } };
template <class T> using pque_max = pque<T, less<T>>;
template <class T> using pque_min = pque<T, greater<T>>;
template <class T, class = typename T::iterator, enable_if_t<!is_same<T, string>::value, int> = 0>
ostream& operator<<(ostream& os, T const& a) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; }
template <class T, size_t N, enable_if_t<!is_same<T, char>::value, int> = 0>
ostream& operator<<(ostream& os, const T (&a)[N]) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; }
template <class T, class = decltype(begin(declval<T&>())), class = typename enable_if<!is_same<T, string>::value>::type>
istream& operator>>(istream& is, T &a) { for (auto& x : a) is >> x; return is; }
template <class T, class S> ostream& operator<<(ostream& os, pair<T, S> const& p) { return os << p.first << " " << p.second; }
template <class T, class S> istream& operator>>(istream& is, pair<T, S>& p) { return is >> p.first >> p.second; }
struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup;
template <class F> struct FixPoint : private F {
    constexpr FixPoint(F&& f) : F(forward<F>(f)) {}
    template <class... T> constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward<T>(x)...); }
};
struct MakeFixPoint { template <class F> constexpr auto operator|(F&& f) const { return FixPoint<F>(forward<F>(f)); } };
#define MFP MakeFixPoint()|
#define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__)
template <class T, size_t d> struct vec_impl {
    using type = vector<typename vec_impl<T, d-1>::type>;
    template <class... U> static type make_v(size_t n, U&&... x) { return type(n, vec_impl<T, d-1>::make_v(forward<U>(x)...)); }
};
template <class T> struct vec_impl<T, 0> { using type = T; static type make_v(T const& x = {}) { return x; } };
template <class T, size_t d = 1> using vec = typename vec_impl<T, d>::type;
template <class T, size_t d = 1, class... Args> auto make_v(Args&&... args) { return vec_impl<T, d>::make_v(forward<Args>(args)...); }
template <class T> void quit(T const& x) { cout << x << endl; exit(0); }
template <class T, class U> constexpr bool chmin(T& x, U const& y) { if (x > (T)y) { x = (T)y; return true; } return false; }
template <class T, class U> constexpr bool chmax(T& x, U const& y) { if (x < (T)y) { x = (T)y; return true; } return false; }
template <class It> constexpr auto sumof(It b, It e) { return accumulate(b, e, typename iterator_traits<It>::value_type{}); }
template <class T> int sz(T const& x) { return x.size(); }
template <class C, class T> int lbd(C const& v, T const& x) { return lower_bound(begin(v), end(v), x)-begin(v); }
template <class C, class T> int ubd(C const& v, T const& x) { return upper_bound(begin(v), end(v), x)-begin(v); }
constexpr ll mod(ll x, ll m) { assert(m > 0); return (x %= m) < 0 ? x+m : x; }
constexpr ll div_floor(ll x, ll y) { assert(y != 0); return x/y - ((x^y) < 0 and x%y); }
constexpr ll div_ceil(ll x, ll y) { assert(y != 0); return x/y + ((x^y) > 0 and x%y); }
constexpr int dx[] = { 1, 0, -1, 0, 1, -1, -1, 1 };
constexpr int dy[] = { 0, 1, 0, -1, 1, 1, -1, -1 };
constexpr int popcnt(ll x) { return __builtin_popcountll(x); }
mt19937_64 seed_{random_device{}()};
template <class Int> Int rand(Int a, Int b) { return uniform_int_distribution<Int>(a, b)(seed_); }
i64 irand(i64 a, i64 b) { return rand<i64>(a, b); } // [a, b]
u64 urand(u64 a, u64 b) { return rand<u64>(a, b); } //
template <class It> void shuffle(It l, It r) { shuffle(l, r, seed_); }
template <class V> V &operator--(V &v) { for (auto &x : v) --x; return v; }
template <class V> V &operator++(V &v) { for (auto &x : v) ++x; return v; }
bool next_product(vector<int> &v, int m) {
    repR (i, v.size()) if (++v[i] < m) return true; else v[i] = 0;
    return false;
}
bool next_product(vector<int> &v, vector<int> const& s) {
    repR (i, v.size()) if (++v[i] < s[i]) return true; else v[i] = 0;
    return false;
}
template <class vec> int sort_unique(vec &v) {
    sort(begin(v), end(v));
    v.erase(unique(begin(v), end(v)), end(v));
    return v.size();
}
template <class It> auto prefix_sum(It l, It r) {
    vector<typename It::value_type> s = { 0 };
    while (l != r) s.emplace_back(s.back() + *l++);
    return s;
}
template <class It> auto suffix_sum(It l, It r) {
    vector<typename It::value_type> s = { 0 };
    while (l != r) s.emplace_back(*--r + s.back());
    reverse(s.begin(), s.end());
    return s;
}
template <class T> T pop(vector<T> &a) { auto x = a.back(); a.pop_back(); return x; }
template <class T, class V, class C> T pop(priority_queue<T, V, C> &a) { auto x = a.top(); a.pop(); return x; }
template <class T> T pop(queue<T> &a) { auto x = a.front(); a.pop(); return x; }
template <class T> T pop_front(deque<T> &a) { auto x = a.front(); a.pop_front(); return x; }
template <class T> T pop_back(deque<T> &a) { auto x = a.back(); a.pop_back(); return x; }
template <class T> T pop_front(set<T> &a) { auto x = *a.begin(); a.erase(a.begin()); return x; }
template <class T> T pop_back(set<T> &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; }
template <class T> T pop_front(multiset<T> &a) { auto it = a.begin(); auto x = *it; a.erase(it); return x; }
template <class T> T pop_back(multiset<T> &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; }
// <<<
// >>> Point
template <class T> constexpr bool equal(T x, T y) { return x == y; }
template <class T> struct Point {
    T x, y;
    constexpr Point() : x(0), y(0) {}
    constexpr Point(T x, T y) : x(x), y(y) {}
    constexpr Point(complex<T> const& z) : x(z.real()), y(z.imag()) {}
    constexpr pair<T, T> to_pair() const { return {x, y}; }
    constexpr Point inv() const { return {x/norm(), -y/norm()}; }
    constexpr Point conj() const { return {x, -y}; }
    constexpr T norm() const { return x*x + y*y; }
    constexpr Point rot90(int n = 1) const {
        n %= 4; if (n < 0) n += 4;
        if (n == 1) return *this * Point(0, 1);
        if (n == 2) return *this * (-1);
        if (n == 3) return *this * Point(0, -1);
        return *this;
    }
    constexpr Point operator+() const { return *this; }
    constexpr Point operator-() const { return {-x, -y}; }
    constexpr Point operator+(Point const& p) const { return {x+p.x, y+p.y}; }
    constexpr Point operator-(Point const& p) const { return {x-p.x, y-p.y}; }
    constexpr Point operator*(Point const& p) const { return {x*p.x-y*p.y, x*p.y+y*p.x}; }
    constexpr Point operator/(Point const& p) const { return *this * p.conj() / p.norm(); }
    constexpr Point operator*(T const& a) const { return {a*x, a*y}; }
    constexpr Point operator/(T const& a) const { return {x/a, y/a}; }
    constexpr Point& operator+=(Point const& p) { return *this = *this + p; }
    constexpr Point& operator-=(Point const& p) { return *this = *this - p; }
    constexpr Point& operator*=(Point const& p) { return *this = *this * p; }
    constexpr Point& operator/=(Point const& p) { return *this = *this / p; }
    constexpr Point& operator*=(T const& a) { return *this = *this * a; }
    constexpr Point& operator/=(T const& a) { return *this = *this / a; }
    constexpr friend Point operator*(T const& a, Point const& p) { return p*a; }
    constexpr friend Point operator/(T const& a, Point const& p) { return Point(a)/p; }
    constexpr T dot(Point const& q) const { return x*q.x + y*q.y; }
    constexpr T cross(Point const& q) const { return x*q.y - y*q.x; }
    constexpr T dot(Point const& p, Point const& q) const { return (p-*this).dot(q-*this); }
    constexpr T cross(Point const& p, Point const& q) const { return (p-*this).cross(q-*this); }
    // constexpr bool operator==(Point const& q) const { return sgn(x-q.x) == 0 && sgn(y-q.y) == 0; }
    constexpr bool operator==(Point const& q) const { return equal(x, q.x) and equal(y, q.y); }
    constexpr bool operator!=(Point const& q) const { return !operator==(q); }

    constexpr friend Point conj(Point const& p) { return p.conj(); }
    constexpr friend T norm(Point const& p) { return p.x*p.x + p.y*p.y; }
    constexpr friend T dot(Point const& p, Point const& q) { return p.dot(q); }
    constexpr friend T cross(Point const& p, Point const& q) { return p.cross(q); }
#ifdef LOCAL
    friend string to_s(Point const& p) { return to_s(p.to_pair()); }
#endif
    friend istream& operator>>(istream& is, Point& p) { return is >> p.x >> p.y; }
    friend ostream& operator<<(ostream& os, Point const& p) { return os << p.x << " " << p.y; }
};

// <<<
template <class T>
constexpr bool operator<(Point<T> const& p, Point<T> const& q) {
    return p.to_pair() < q.to_pair();
}
//using P = Point<int>;
constexpr int sgn(int x) { return x > 0 ? 1 : x < 0 ? -1 : 0; }

using Real = long double;
using P = Point<Real>;
constexpr Real eps = 1e-10;
constexpr int sgn(Real x) { return x > eps ? 1 : x < -eps ? -1 : 0; }
constexpr Real pi = acos(-1.0L);
constexpr Real to_rad(Real deg) { return Real(deg) * pi / 180; }
constexpr Real to_deg(Real rad) { return rad * 180 / pi; }
template <class T> constexpr T sq(T const& x) { return x*x; }
template <> constexpr bool equal<Real>(Real x, Real y) { return sgn(x-y) == 0; }
template <class T>
constexpr Real abs(Point<T> const& p) { return sqrt((Real)p.norm()); }
constexpr Point<Real> normalize(Point<Real> const& p) { return p/abs(p); }
// >>> segment tree

template <class Handler> struct Segtree : Handler {
    using Value = typename Handler::Value;
    using Handler::unit_value;  // () -> Value
    using Handler::merge; // (Value, Value) -> Value

    vector<Value> v;
    int n;

    Segtree() {}
    template <class... T> Segtree(T&&... x) { init(forward<T>(x)...); }

    template <class F, class = decltype(declval<F>()(0))>
    void init(int n, F gen)  {
        assert(n >= 0);
        this->n = n;
        v.resize(2*n, unit_value());
        for (int i = 0; i < n; i++) v[n+i] = gen(i);
        for (int i = n-1; i >= 1; i--) v[i] = merge(v[i<<1], v[i<<1|1]);
    }
    void init(int n) { init(n, [&](int) { return unit_value(); }); }
    void init(int n, Value const& x) { init(n, [&](int) { return x; }); }
    void init(vector<Value> const& v) { init(v.size(), [&](int i) { return v[i]; }); }
    int size() const { return n; }

    void set(int i, Value const& x) {
        assert(0 <= i); assert(i < size());
        i += n; v[i] = x;
        while (i >>= 1) v[i] = merge(v[i<<1], v[i<<1|1]);
    }
    Value operator[](int i) const { return get(i); }
    Value get(int i) const {
        assert(0 <= i); assert(i < size());
        return v[n + i];
    }
    // [l, r)
    Value get(int l, int r) const {
        assert(0 <= l); assert(l <= r); assert(r <= size());
        Value x = unit_value(), y = unit_value();
        for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
            if (l&1) x = merge(x, v[l++]);
            if (r&1) y = merge(v[--r], y);
        }
        return merge(x, y);
    }
    Value get_all() const { return get(0, size()); }
    template <class F> int max_right(int l, F f) {
        assert(0 <= l); assert(l <= size());
        assert(f(unit_value()));
        l += n;
        const int r = size() << 1;
        Value x = unit_value();
        while (true) {
            if (l == r) return size();
            int k = __builtin_ctz(l | 1 << __lg(r - l));
            auto y = merge(x, v[l >> k]);
            if (not f(y)) { l >>= k; break; }
            x = y, l += 1 << k;
        }
        while (l < size()) {
            auto y = merge(x, v[l <<= 1]);
            if (f(y)) x = y, l++;
        }
        return l - size();
    }
    template <class F> int min_left(int r, F f) {
        assert(0 <= r); assert(r <= size());
        assert(f(unit_value()));
        r += n;
        const int l = size();
        Value x = unit_value();
        while (true) {
            if (l == r) return 0;
            int k = __builtin_ctz(r | 1 << __lg(r - l));
            auto y = merge(v[(r >> k) - 1], x);
            if (not f(y)) { r >>= k; --r; break; }
            x = y, r -= 1 << k;
        }
        while (r < size()) {
            r = r << 1 | 1;
            auto y = merge(v[r], x);
            if (f(y)) x = y, r--;
        }
        return r + 1 - size();
    }
    vector<Value> dat() const {
        vector<Value> ret(size());
        for (int i = 0; i < size(); i++) ret[i] = get(i);
        return ret;
    }
};

// <<<
// >>> matrix (array)
// template <class T>
// decltype(T::one()) semi_ring_one(signed) { return T::one(); }
// template <class T>
// constexpr T semi_ring_one(long) { return 1; }
template <class T, size_t N, size_t M>
struct Matrix {
    int n = N, m = M;
    array<array<T, M>, N> a;
    Matrix() : a() {}
    Matrix(initializer_list<initializer_list<T>> init) {
        size_t i = 0;
        for (auto ls : init) {
            size_t j = 0;
            for (auto const& x : ls) {
                a[i][j] = x;
                j++;
            }
            assert((int)j == m);
            i++;
        }
        assert((int)i == n);
    }
    array<T, M> const& operator[](int i) const {
        assert(0 <= i); assert(i < n);
        return a[i];
    }
    array<T, M> & operator[](int i) {
        assert(0 <= i); assert(i < n);
        return a[i];
    }
    bool operator==(Matrix const& x) const {
        if (n != x.n || m != x.m) return false;
        rep (i, n) rep (j, m) if (a[i][j] != x[i][j]) return false;
        return true;
    }
    bool operator!=(Matrix const& x) const {
        return !(*this == x);
    }
	Matrix operator+() const { return *this; }
    Matrix operator+(Matrix const& x) const { return Matrix(*this) += x; }
    Matrix& operator+=(Matrix const& x) {
        assert(n == x.n); assert(m == x.m);
        rep (i, n) rep (j, m) a[i][j] += x[i][j];
        return *this;
    }
    template <size_t L>
    Matrix<T, N, L> operator*(Matrix<T, M, L> const& x) const {
        assert(m == x.n);
        Matrix<T, N, L> ret;
        rep (i, n) rep (j, m) rep (k, x.m) ret[i][k] += a[i][j] * x[j][k];
        return ret;
    }
    Matrix& operator*=(Matrix<T, M, M> const& x) {
        auto res = (*this)*x;
        swap(a, res.a);
        return *this;
    }
    Matrix operator*(T const& c) const { return Matrix(*this) *= c; }
    Matrix& operator*=(T const& c) {
        rep (i, n) rep (j, m) a[i][j] *= c;
        return *this;
    }
    friend Matrix operator*(T const& c, Matrix const& x) {
        Matrix ret = x;
        rep (i, x.n) rep (j, x.m) ret[i][j] = c*x[i][j];
        return ret;
    }
    static Matrix identity() {
        assert(N == M);
        Matrix ret;
        rep (i, N) ret[i][i] = P(1, 0);
        return ret;
    }
    Matrix pow(ll k) const {
        assert(n == m); assert(k >= 0);
        Matrix v = *this, r = Matrix::identity();
        for (; k > 0; k >>= 1, v *= v) if (k&1) r *= v;
        return r;
    }
#if 1
    Matrix operator-() const {
        Matrix x = *this;
        rep (i, n) rep (j, m) x[i][j] = -x[i][j];
        return x;
    }
    Matrix& operator-=(Matrix const& x) {
        assert(n == x.n); assert(m == x.m);
        rep (i, n) rep (j, m) a[i][j] -= x[i][j];
        return *this;
    }
    Matrix operator-(Matrix const& x) const { return Matrix(*this) -= x; }
    Matrix& operator/=(T const& c) {
        rep (i, n) rep (j, m) a[i][j] /= c;
        return *this;
    }
    Matrix operator/(T const& c) const {
        return Matrix(*this) /= c;
    }
#endif
    friend istream& operator>>(istream& is, Matrix& x) {
        rep (i, x.n) rep (j, x.m) is >> x[i][j];
        return is;
    }
#ifdef LOCAL
    friend string to_s(Matrix const& x) {
        string ret;
        rep (i, x.n) {
            ret += "\n(";
            rep (j, x.m) ret += " " + to_s(x[i][j]);
            ret += " )";
        }
        return ret += "\n";
    }
#endif
};

// <<<

struct M {
    using Value = Matrix<P, 2, 2>;
    static Value unit_value() { return Value::identity(); }
    static Value merge(Value const& x, Value const& y) {
        return y * x;
    }
};

int32_t main() {
    int n; cin >> n;
    Segtree<M> seg(n);
    rep (i, n) {
        Real p, q, r; cin >> p >> q >> r;
        P z(p, q);
        P rot = polar(Real(1), to_rad(r));
        M::Value A = {
            { rot, z-z*rot },
            { P(0, 0), P(1, 0) }
        };
        seg.set(i, A);
    }

    int q; cin >> q;
    while (q--) {
        int l, r; cin >> l >> r; --l;
        Real x, y; cin >> x >> y;
        dump(l, r, x, y);
        auto A = seg.get(l, r);
        P p(x, y);
        p = A[0][0]*p + A[0][1];
        cout << p.to_pair() << '\n';
    }

}
yukicoder

結果

ソースコード
