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test/mytest/incremental_ch.test.cpp
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- Last update: 2024-03-29 11:46:13+09:00
- Problem: https://judge.yosupo.jp/problem/aplusb
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Code
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#include "my_template.hpp"
#include "geo/incremental_convexhull.hpp"
// geocon2013 c sample より
void test() {
{
Incremental_ConvexHull<ll> X;
assert(X.area_2() == 0);
assert(X.side(Point<ll>(2, 2)) == -1);
assert(X.side(Point<ll>(1, 2)) == -1);
assert(X.side(Point<ll>(1, 1)) == -1);
assert(X.side(Point<ll>(2, 1)) == -1);
X.add(Point<ll>(1, 1));
assert(X.side(Point<ll>(2, 2)) == -1);
assert(X.side(Point<ll>(1, 2)) == -1);
assert(X.side(Point<ll>(1, 1)) == 0);
assert(X.side(Point<ll>(2, 1)) == -1);
X.add(Point<ll>(5, 1));
assert(X.area_2() == 0);
assert(X.side(Point<ll>(2, 2)) == -1);
assert(X.side(Point<ll>(1, 2)) == -1);
assert(X.side(Point<ll>(1, 1)) == 0);
assert(X.side(Point<ll>(2, 1)) == 0);
X.add(Point<ll>(1, 5));
assert(X.area_2() == 16);
assert(X.side(Point<ll>(2, 2)) == 1);
assert(X.side(Point<ll>(1, 2)) == 0);
assert(X.side(Point<ll>(1, 1)) == 0);
assert(X.side(Point<ll>(2, 1)) == 0);
}
{
Incremental_ConvexHull<ll> X;
X.add(Point<ll>(2, 1));
X.add(Point<ll>(4, 1));
X.add(Point<ll>(6, 1));
assert(X.side(Point<ll>(1, 1)) == -1);
assert(X.side(Point<ll>(3, 1)) == 0);
assert(X.side(Point<ll>(5, 1)) == 0);
assert(X.side(Point<ll>(7, 1)) == -1);
}
}
void solve() {
int a, b;
cin >> a >> b;
cout << a + b << "\n";
}
signed main() {
test();
solve();
return 0;
}#line 1 "test/mytest/incremental_ch.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 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 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+(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(Point other) { return x * other.x + y * other.y; }
T det(Point other) { 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};
}
};
#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>
REAL dist(Point<T> A, Point<T> B) {
A = A - B;
T p = A.dot(A);
return sqrt(REAL(p));
}
// 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) {
static_assert(is_integral<T>::value);
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;
}
};
template <typename T>
struct Polygon {
vc<Point<T>> points;
T a;
template <typename A, typename B>
Polygon(vc<pair<A, B>> pairs) {
for (auto&& [a, b]: pairs) points.eb(Point<T>(a, b));
build();
}
Polygon(vc<Point<T>> points) : points(points) { build(); }
int size() { return len(points); }
template <typename REAL>
REAL area() {
return a * 0.5;
}
template <enable_if_t<is_integral<T>::value, int> = 0>
T area_2() {
return a;
}
bool is_convex() {
FOR(j, len(points)) {
int i = (j == 0 ? len(points) - 1 : j - 1);
int k = (j == len(points) - 1 ? 0 : j + 1);
if ((points[j] - points[i]).det(points[k] - points[j]) < 0) return false;
}
return true;
}
private:
void build() {
a = 0;
FOR(i, len(points)) {
int j = (i + 1 == len(points) ? 0 : i + 1);
a += points[i].det(points[j]);
}
if (a < 0) {
a = -a;
reverse(all(points));
}
}
};
#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 4 "test/mytest/incremental_ch.test.cpp"
// geocon2013 c sample より
void test() {
{
Incremental_ConvexHull<ll> X;
assert(X.area_2() == 0);
assert(X.side(Point<ll>(2, 2)) == -1);
assert(X.side(Point<ll>(1, 2)) == -1);
assert(X.side(Point<ll>(1, 1)) == -1);
assert(X.side(Point<ll>(2, 1)) == -1);
X.add(Point<ll>(1, 1));
assert(X.side(Point<ll>(2, 2)) == -1);
assert(X.side(Point<ll>(1, 2)) == -1);
assert(X.side(Point<ll>(1, 1)) == 0);
assert(X.side(Point<ll>(2, 1)) == -1);
X.add(Point<ll>(5, 1));
assert(X.area_2() == 0);
assert(X.side(Point<ll>(2, 2)) == -1);
assert(X.side(Point<ll>(1, 2)) == -1);
assert(X.side(Point<ll>(1, 1)) == 0);
assert(X.side(Point<ll>(2, 1)) == 0);
X.add(Point<ll>(1, 5));
assert(X.area_2() == 16);
assert(X.side(Point<ll>(2, 2)) == 1);
assert(X.side(Point<ll>(1, 2)) == 0);
assert(X.side(Point<ll>(1, 1)) == 0);
assert(X.side(Point<ll>(2, 1)) == 0);
}
{
Incremental_ConvexHull<ll> X;
X.add(Point<ll>(2, 1));
X.add(Point<ll>(4, 1));
X.add(Point<ll>(6, 1));
assert(X.side(Point<ll>(1, 1)) == -1);
assert(X.side(Point<ll>(3, 1)) == 0);
assert(X.side(Point<ll>(5, 1)) == 0);
assert(X.side(Point<ll>(7, 1)) == -1);
}
}
void solve() {
int a, b;
cin >> a >> b;
cout << a + b << "\n";
}
signed main() {
test();
solve();
return 0;
}