#include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(10); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector &vec, int len) { vec.resize(len); } template void ndarray(vector &vec, int len, Args... args) { vec.resize(len); for (auto &v : vec) ndarray(v, args...); } template void ndfill(V &x, const T &val) { x = val; } template void ndfill(vector &vec, const T &val) { for (auto &v : vec) ndfill(v, val); } template bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; } template bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; } template pair operator+(const pair &l, const pair &r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair &l, const pair &r) { return make_pair(l.first - r.first, l.second - r.second); } template vector srtunq(vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template istream &operator>>(istream &is, vector &vec) { for (auto &v : vec) is >> v; return is; } template ostream &operator<<(ostream &os, const vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } #if __cplusplus >= 201703L template istream &operator>>(istream &is, tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template ostream &operator<<(ostream &os, const tuple &tpl) { std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os; } #endif template ostream &operator<<(ostream &os, const deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const pair &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; } template ostream &operator<<(ostream &os, const map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL #define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl #else #define dbg(x) #endif // Nonrecursive Segment Tree (point-update, range-get) // - Conditions for operations: // - merge_data: [TDATA, TDATA] -> TDATA, e(x, y) == e(y, x) // - data2ret: [TDATA, TQUERY] -> TRET // - merge_ret: [TRET, TRET] -> TRET, g(defaultRET, x) == x, g(x, y) = g(y, x) // - commutability f(e(x, y), q) == g(f(x, q), f(y, q)) template struct NonrecursiveSegmentTree { int N; TRET defaultRET; virtual TDATA merge_data(const TDATA &, const TDATA &) = 0; virtual TRET data2ret(const TDATA &, const TQUERY &) = 0; virtual TRET merge_ret(const TRET &, const TRET &) = 0; std::vector data; inline TDATA& at(int i) { return data[i]; } inline void _merge(int i) { at(i) = merge_data(at(i << 1), at((i << 1) + 1)); } void initialize(const std::vector &seq, TRET RET_ZERO) { N = seq.size(); defaultRET = RET_ZERO; data = seq; data.insert(data.end(), seq.begin(), seq.end()); for (int i = N - 1; i; i--) _merge(i); } NonrecursiveSegmentTree() = default; void update(int pos, const TDATA &x) { assert(pos >= 0 and pos < N); at(pos + N) = x; for (int i = pos + N; i > 1;) i >>= 1, _merge(i); } // [l, r), 0-indexed TRET get(int l, int r, TQUERY query = NULL) { assert(l >= 0 and r <= N); TRET retl = defaultRET, retr = defaultRET; l += N, r += N; while (l < r) { if (l & 1) retl = merge_ret(retl, data2ret(data[l++], query)); if (r & 1) retr = merge_ret(data2ret(data[--r], query), retr); l >>= 1, r >>= 1; } return merge_ret(retl, retr); } // Calculate smallest r that satisfies g(f(x_l, q), ..., f(x_{r - 1}, q)) >= threshold // Assumption: Monotonicity of g(x_l, ..., x_r) about r (l: fixed) // Complexity: O(log N) int binary_search(int l, const TRET &threshold, TQUERY query = NULL) { std::stack rs; l += N; int r = N * 2; TRET retl = defaultRET; if (threshold <= retl) return l - N; while (l < r) { if (l & 1) { TRET ret_tmp = merge_ret(retl, data2ret(data[l], query)); if (threshold <= ret_tmp) { while (l * 2 < N * 2) { ret_tmp = merge_ret(retl, data2ret(data[l * 2], query)); if (threshold <= ret_tmp) l *= 2; else retl = ret_tmp, l = l * 2 + 1; } return l - N; } l++; retl = ret_tmp; } if (r & 1) rs.push(--r); l >>= 1, r >>= 1; } while (!rs.empty()) { l = rs.top(); rs.pop(); TRET ret_tmp = merge_ret(retl, data2ret(data[l], query)); if (threshold <= ret_tmp) { while (l * 2 < N * 2) { ret_tmp = merge_ret(retl, data2ret(data[l * 2], query)); if (threshold <= ret_tmp) l *= 2; else retl = ret_tmp, l = l * 2 + 1; } return l - N; } retl = ret_tmp; } return N; } }; using Float = long double; struct T { int deg_out; Float dx, dy; }; const Float PI = acosl(-1.0l); struct SegmentTree : public NonrecursiveSegmentTree { using SegTree = NonrecursiveSegmentTree; T merge_data(const T &vl, const T &vr) override { Float rad = vl.deg_out / 360.0 * PI * 2; Float dx = vl.dx + cosl(rad) * vr.dx - sinl(rad) * vr.dy; Float dy = vl.dy + sinl(rad) * vr.dx + cosl(rad) * vr.dy; return T{(vl.deg_out + vr.deg_out + 720) % 360, dx, dy}; }; T data2ret(const T &v, const bool &q) override { return v; } T merge_ret(const T &vl, const T &vr) override { return merge_data(vl, vr); }; SegmentTree(const std::vector &seq, T defaultmin) : SegTree::NonrecursiveSegmentTree() { SegTree::initialize(seq, defaultmin); }; }; int main() { int N, Q; cin >> N >> Q; vector vec(N + 1); vector deg_now(N + 1, 0); vector len_now(N + 1, 1); len_now[0] = 0; FOR(i, 1, N + 1) vec[i].dx = 1; SegmentTree tree(vec, vec[0]); while (Q--) { int q, i, x; cin >> q >> i; if (q == 0) { cin >> x; i--; deg_now[i] = x; vec[i].deg_out = deg_now[i]; tree.update(i, vec[i]); } if (q == 1) { cin >> x; vec[i].dx /= len_now[i]; vec[i].dy /= len_now[i]; len_now[i] = x; vec[i].dx *= len_now[i]; vec[i].dy *= len_now[i]; tree.update(i, vec[i]); } if (q == 2) { auto ret = tree.get(0, i + 1); cout << ret.dx << ' ' << ret.dy << '\n'; } } }