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#define PROBLEM "https://judge.yosupo.jp/problem/aplusb" #include "my_template.hpp" #include "geo/base.hpp" #include "geo/convex_hull.hpp" #include "geo/convex_polygon.hpp" #include "geo/incremental_convexhull.hpp" #include "random/base.hpp" using P = Point<ll>; void test() { int N = RNG(3, 10); vc<P> point(N); FOR(i, N) point[i] = P(RNG(-5, 5), RNG(-5, 5)); auto I = ConvexHull(point); point = rearrange(point, I); N = len(point); if (N <= 2) return; ConvexPolygon<ll> X(point); FOR(x, -10, 11) FOR(y, -10, 11) { P p(x, y); pair<int, int> ans = {infty<int>, -infty<int>}; FOR(i, N) { chmin(ans.fi, p.dot(point[i])); } FOR(i, N) { chmax(ans.se, p.dot(point[i])); } auto [mi, i] = X.min_dot(p); auto [ma, j] = X.max_dot(p); assert(ans.fi == mi && ans.se == ma); assert(mi == p.dot(point[i])); assert(ma == p.dot(point[j])); } } void solve() { int a, b; cin >> a >> b; cout << a + b << "\n"; } signed main() { FOR(10000) test(); solve(); return 0; }
#line 1 "test/1_mytest/max_dot.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/aplusb" #line 1 "my_template.hpp" #if defined(LOCAL) #include <my_template_compiled.hpp> #else // https://codeforces.com/blog/entry/96344 #pragma GCC optimize("Ofast,unroll-loops") // いまの CF だとこれ入れると動かない? // #pragma GCC target("avx2,popcnt") #include <bits/stdc++.h> using namespace std; using ll = long long; using u8 = uint8_t; using u16 = uint16_t; using u32 = uint32_t; using u64 = uint64_t; using i128 = __int128; using u128 = unsigned __int128; using f128 = __float128; template <class T> constexpr T infty = 0; template <> constexpr int infty<int> = 1'010'000'000; template <> constexpr ll infty<ll> = 2'020'000'000'000'000'000; template <> constexpr u32 infty<u32> = infty<int>; template <> constexpr u64 infty<u64> = infty<ll>; template <> constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000; 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; } template <typename T, typename... Vectors> void concat(vc<T> &first, const Vectors &... others) { vc<T> &res = first; (res.insert(res.end(), others.begin(), others.end()), ...); } #endif #line 3 "test/1_mytest/max_dot.test.cpp" #line 2 "geo/base.hpp" template <typename T> struct Point { T x, y; Point() : x(0), y(0) {} template <typename A, typename B> Point(A x, B y) : x(x), y(y) {} template <typename A, typename B> Point(pair<A, B> p) : x(p.fi), y(p.se) {} Point operator+=(const Point p) { x += p.x, y += p.y; return *this; } Point operator-=(const Point p) { x -= p.x, y -= p.y; return *this; } Point operator+(Point p) const { return {x + p.x, y + p.y}; } Point operator-(Point p) const { return {x - p.x, y - p.y}; } bool operator==(Point p) const { return x == p.x && y == p.y; } bool operator!=(Point p) const { return x != p.x || y != p.y; } Point operator-() const { return {-x, -y}; } Point operator*(T t) const { return {x * t, y * t}; } Point operator/(T t) const { return {x / t, y / t}; } bool operator<(Point p) const { if (x != p.x) return x < p.x; return y < p.y; } T dot(const Point& other) const { return x * other.x + y * other.y; } T det(const Point& other) const { return x * other.y - y * other.x; } double norm() { return sqrtl(x * x + y * y); } double angle() { return atan2(y, x); } Point rotate(double theta) { static_assert(!is_integral<T>::value); double c = cos(theta), s = sin(theta); return Point{c * x - s * y, s * x + c * y}; } Point rot90(bool ccw) { return (ccw ? Point{-y, x} : Point{y, -x}); } }; #ifdef FASTIO template <typename T> void rd(Point<T>& p) { fastio::rd(p.x), fastio::rd(p.y); } template <typename T> void wt(Point<T>& p) { fastio::wt(p.x); fastio::wt(' '); fastio::wt(p.y); } #endif // A -> B -> C と進むときに、左に曲がるならば +1、右に曲がるならば -1 template <typename T> int ccw(Point<T> A, Point<T> B, Point<T> C) { T x = (B - A).det(C - A); if (x > 0) return 1; if (x < 0) return -1; return 0; } template <typename REAL, typename T, typename U> REAL dist(Point<T> A, Point<U> B) { REAL dx = REAL(A.x) - REAL(B.x); REAL dy = REAL(A.y) - REAL(B.y); return sqrt(dx * dx + dy * dy); } // ax+by+c template <typename T> struct Line { T a, b, c; Line(T a, T b, T c) : a(a), b(b), c(c) {} Line(Point<T> A, Point<T> B) { a = A.y - B.y, b = B.x - A.x, c = A.x * B.y - A.y * B.x; } Line(T x1, T y1, T x2, T y2) : Line(Point<T>(x1, y1), Point<T>(x2, y2)) {} template <typename U> U eval(Point<U> P) { return a * P.x + b * P.y + c; } template <typename U> T eval(U x, U y) { return a * x + b * y + c; } // 同じ直線が同じ a,b,c で表現されるようにする void normalize() { static_assert(is_same_v<T, int> || is_same_v<T, long long>); T g = gcd(gcd(abs(a), abs(b)), abs(c)); a /= g, b /= g, c /= g; if (b < 0) { a = -a, b = -b, c = -c; } if (b == 0 && a < 0) { a = -a, b = -b, c = -c; } } bool is_parallel(Line other) { return a * other.b - b * other.a == 0; } bool is_orthogonal(Line other) { return a * other.a + b * other.b == 0; } }; template <typename T> struct Segment { Point<T> A, B; Segment(Point<T> A, Point<T> B) : A(A), B(B) {} Segment(T x1, T y1, T x2, T y2) : Segment(Point<T>(x1, y1), Point<T>(x2, y2)) {} bool contain(Point<T> C) { T det = (C - A).det(B - A); if (det != 0) return 0; return (C - A).dot(B - A) >= 0 && (C - B).dot(A - B) >= 0; } Line<T> to_Line() { return Line(A, B); } }; template <typename REAL> struct Circle { Point<REAL> O; REAL r; Circle(Point<REAL> O, REAL r) : O(O), r(r) {} Circle(REAL x, REAL y, REAL r) : O(x, y), r(r) {} template <typename T> bool contain(Point<T> p) { REAL dx = p.x - O.x, dy = p.y - O.y; return dx * dx + dy * dy <= r * r; } }; #line 2 "geo/convex_hull.hpp" #line 4 "geo/convex_hull.hpp" // allow_180=true で同一座標点があるとこわれる // full なら I[0] が sorted で min になる template <typename T, bool allow_180 = false> vector<int> ConvexHull(vector<Point<T>>& XY, string mode = "full", bool sorted = false) { assert(mode == "full" || mode == "lower" || mode == "upper"); ll N = XY.size(); if (N == 1) return {0}; if (N == 2) { if (XY[0] < XY[1]) return {0, 1}; if (XY[1] < XY[0]) return {1, 0}; return {0}; } vc<int> I(N); if (sorted) { FOR(i, N) I[i] = i; } else { I = argsort(XY); } if constexpr (allow_180) { FOR(i, N - 1) assert(XY[i] != XY[i + 1]); } auto check = [&](ll i, ll j, ll k) -> bool { T det = (XY[j] - XY[i]).det(XY[k] - XY[i]); if constexpr (allow_180) return det >= 0; return det > T(0); }; auto calc = [&]() { vector<int> P; for (auto&& k: I) { while (P.size() > 1) { auto i = P[P.size() - 2]; auto j = P[P.size() - 1]; if (check(i, j, k)) break; P.pop_back(); } P.eb(k); } return P; }; vc<int> P; if (mode == "full" || mode == "lower") { vc<int> Q = calc(); P.insert(P.end(), all(Q)); } if (mode == "full" || mode == "upper") { if (!P.empty()) P.pop_back(); reverse(all(I)); vc<int> Q = calc(); P.insert(P.end(), all(Q)); } if (mode == "upper") reverse(all(P)); while (len(P) >= 2 && XY[P[0]] == XY[P.back()]) P.pop_back(); return P; } #line 2 "geo/convex_polygon.hpp" #line 5 "geo/convex_polygon.hpp" // n=2 は現状サポートしていない template <typename T> struct ConvexPolygon { using P = Point<T>; int n; vc<P> point; ConvexPolygon(vc<P> point_) : n(len(point_)), point(point_) { assert(n >= 3); FOR(i, n) { int j = nxt_idx(i), k = nxt_idx(j); assert((point[j] - point[i]).det(point[k] - point[i]) >= 0); } } // 比較関数 comp(i,j) template <typename F> int periodic_min_comp(F comp) { int L = 0, M = n, R = n + n; while (1) { if (R - L == 2) break; int L1 = (L + M) / 2, R1 = (M + R + 1) / 2; if (comp(L1 % n, M % n)) { R = M, M = L1; } elif (comp(R1 % n, M % n)) { L = M, M = R1; } else { L = L1, R = R1; } } return M % n; } int nxt_idx(int i) { return (i + 1 == n ? 0 : i + 1); } int prev_idx(int i) { return (i == 0 ? n - 1 : i - 1); } // 中:1, 境界:0, 外:-1. test した. int side(P p) { int L = 1, R = n - 1; T a = (point[L] - point[0]).det(p - point[0]); T b = (point[R] - point[0]).det(p - point[0]); if (a < 0 || b > 0) return -1; // p は 0 から見て [L,R] 方向 while (R - L >= 2) { int M = (L + R) / 2; T c = (point[M] - point[0]).det(p - point[0]); if (c < 0) R = M, b = c; else L = M, a = c; } T c = (point[R] - point[L]).det(p - point[L]); T x = min({a, -b, c}); if (x < 0) return -1; if (x > 0) return 1; // on triangle p[0]p[L]p[R] if (p == point[0]) return 0; if (c != 0 && a == 0 && L != 1) return 1; if (c != 0 && b == 0 && R != n - 1) return 1; return 0; } // return {min, idx}. test した. pair<T, int> min_dot(P p) { int idx = periodic_min_comp([&](int i, int j) -> bool { return point[i].dot(p) < point[j].dot(p); }); return {point[idx].dot(p), idx}; } // return {max, idx}. test した. pair<T, int> max_dot(P p) { int idx = periodic_min_comp([&](int i, int j) -> bool { return point[i].dot(p) > point[j].dot(p); }); return {point[idx].dot(p), idx}; } // p から見える範囲. p 辺に沿って見えるところも見えるとする. test した. // 多角形からの反時計順は [l,r] だが p から見た偏角順は [r,l] なので注意 pair<int, int> visible_range(P p) { int a = periodic_min_comp([&](int i, int j) -> bool { return ((point[i] - p).det(point[j] - p) < 0); }); int b = periodic_min_comp([&](int i, int j) -> bool { return ((point[i] - p).det(point[j] - p) > 0); }); if ((p - point[a]).det(p - point[prev_idx(a)]) == T(0)) a = prev_idx(a); if ((p - point[b]).det(p - point[nxt_idx(b)]) == T(0)) b = nxt_idx(b); return {a, b}; } // 線分が「内部と」交わるか // https://codeforces.com/contest/1906/problem/D bool check_cross(P A, P B) { FOR(2) { swap(A, B); auto [a, b] = visible_range(A); if ((point[a] - A).det(B - A) >= 0) return 0; if ((point[b] - A).det(B - A) <= 0) return 0; } return 1; } vc<T> AREA; // point[i,...,j] (inclusive) の面積 T area_between(int i, int j) { assert(0 <= i && i < n); assert((0 <= j && j < n) || (i <= j && j < i + n)); if (i > j) j += n; if (AREA.empty()) build_AREA(); return AREA[j] - AREA[i] + (point[j % n].det(point[i])); } void build_AREA() { AREA.resize(2 * n); FOR(i, n) AREA[n + i] = AREA[i] = point[i].det(point[nxt_idx(i)]); AREA = cumsum<T>(AREA); } }; #line 2 "geo/incremental_convexhull.hpp" // 下側凸包 template <typename T, bool strict = true> struct IncrementalConvexHull_Lower { using P = Point<T>; set<P> S; IncrementalConvexHull_Lower() {} int size() { return len(S); } template <typename ADD_V, typename RM_V, typename ADD_E, typename RM_E> void add(Point<T> p, ADD_V add_v, RM_V rm_v, ADD_E add_e, RM_E rm_e) { int s = side(p); if (strict && s >= 0) return; if (!strict && s > 0) return; // 点追加 add_v(p); S.insert(p); vc<P> left; { auto it = S.find(p); while (it != S.begin()) { --it; if (left.empty()) { left.eb(*it); continue; } auto a = *it; auto b = left.back(); T det = (b - a).det(p - a); if (strict && det > 0) break; if (!strict && det >= 0) break; left.eb(a); } } vc<P> right; { auto it = S.find(p); while (1) { ++it; if (it == S.end()) break; if (right.empty()) { right.eb(*it); continue; } auto a = right.back(); auto b = *it; T det = (a - p).det(b - p); if (strict && det > 0) break; if (!strict && det >= 0) break; right.eb(b); } } // 点削除 if (len(left) > 1) { S.erase(next(S.find(left.back())), S.find(p)); } if (len(right) > 1) { S.erase(next(S.find(p)), S.find(right.back())); } FOR(i, len(left) - 1) rm_v(left[i]); FOR(i, len(right) - 1) rm_v(right[i]); // 辺削除 if (len(left) && len(right)) { auto a = left[0], b = right[0]; rm_e(a, b); } FOR(i, len(left) - 1) { auto a = left[i + 1], b = left[i]; rm_e(a, b); } FOR(i, len(right) - 1) { auto a = right[i], b = right[i + 1]; rm_e(a, b); } // 辺追加 if (len(left)) { add_e(left.back(), p); } if (len(right)) { add_e(p, right.back()); } } // 中:1, 境界:0, 外:-1 int side(Point<T> p) { auto r = S.lower_bound(p); if (r == S.begin()) { // 全部 p 以上 if (len(S) && (*r) == p) return 0; return -1; } if (r == S.end()) { // p は max より大きい return -1; } auto l = prev(r); auto p1 = *l, p2 = *r; T det = (p - p1).det(p2 - p1); if (det == 0) return 0; return (det > 0 ? -1 : 1); } }; template <typename T, bool strict = true> struct Incremental_ConvexHull { using P = Point<T>; IncrementalConvexHull_Lower<T, strict> LOWER, UPPER; int cnt_E; T det_sum; bool is_empty; Incremental_ConvexHull() : cnt_E(0), det_sum(0), is_empty(1) {} int size() { return cnt_E; } bool empty() { return is_empty; } template <typename REAL> REAL area() { return det_sum * 0.5; } T area_2() { return det_sum; } template <typename ADD_V, typename RM_V, typename ADD_E, typename RM_E> void add(Point<T> p, ADD_V add_v, RM_V rm_v, ADD_E add_e, RM_E rm_e) { is_empty = 0; LOWER.add( p, add_v, rm_v, [&](Point<T> a, Point<T> b) { add_e(a, b); ++cnt_E; det_sum += a.det(b); }, [&](Point<T> a, Point<T> b) { rm_e(a, b); --cnt_E; det_sum -= a.det(b); }); UPPER.add( -p, [&](Point<T> p) { add_v(-p); }, [&](Point<T> p) { rm_v(-p); }, [&](Point<T> a, Point<T> b) { add_e(-a, -b); ++cnt_E; det_sum += a.det(b); }, [&](Point<T> a, Point<T> b) { rm_e(-a, -b); --cnt_E; det_sum -= a.det(b); }); } void add(Point<T> p) { add( p, [](Point<T> p) {}, [](Point<T> p) {}, [](Point<T> s, Point<T> t) {}, [](Point<T> s, Point<T> t) {}); } // 中:1、境界:0、外:-1 int side(Point<T> p) { int a = LOWER.side(p); int b = UPPER.side(-p); if (a == 0 || b == 0) return 0; return min(a, b); } }; #line 2 "random/base.hpp" u64 RNG_64() { static u64 x_ = u64(chrono::duration_cast<chrono::nanoseconds>(chrono::high_resolution_clock::now().time_since_epoch()).count()) * 10150724397891781847ULL; x_ ^= x_ << 7; return x_ ^= x_ >> 9; } u64 RNG(u64 lim) { return RNG_64() % lim; } ll RNG(ll l, ll r) { return l + RNG_64() % (r - l); } #line 9 "test/1_mytest/max_dot.test.cpp" using P = Point<ll>; void test() { int N = RNG(3, 10); vc<P> point(N); FOR(i, N) point[i] = P(RNG(-5, 5), RNG(-5, 5)); auto I = ConvexHull(point); point = rearrange(point, I); N = len(point); if (N <= 2) return; ConvexPolygon<ll> X(point); FOR(x, -10, 11) FOR(y, -10, 11) { P p(x, y); pair<int, int> ans = {infty<int>, -infty<int>}; FOR(i, N) { chmin(ans.fi, p.dot(point[i])); } FOR(i, N) { chmax(ans.se, p.dot(point[i])); } auto [mi, i] = X.min_dot(p); auto [ma, j] = X.max_dot(p); assert(ans.fi == mi && ans.se == ma); assert(mi == p.dot(point[i])); assert(ma == p.dot(point[j])); } } void solve() { int a, b; cin >> a >> b; cout << a + b << "\n"; } signed main() { FOR(10000) test(); solve(); return 0; }