#include <bits/stdc++.h>
using namespace std;
template<class C>constexpr int sz(const C&c){return int(c.size());}
using ll=long long;using ld=long double;constexpr const char nl='\n',sp=' ';
using T = long double;
constexpr const T EPS = 1e-9;
bool lt(T a, T b) { return a + EPS < b; }
bool le(T a, T b) { return !lt(b, a); }
bool gt(T a, T b) { return lt(b, a); }
bool ge(T a, T b) { return !lt(a, b); }
bool eq(T a, T b) { return !lt(a, b) && !lt(b, a); }
bool ne(T a, T b) { return lt(a, b) || lt(b, a); }
int sgn(T a) { return lt(a, 0) ? -1 : lt(0, a) ? 1 : 0; }
struct eps_lt { bool operator () (T a, T b) const { return lt(a, b); } };
struct eps_le { bool operator () (T a, T b) const { return !lt(b, a); } };
struct eps_gt { bool operator () (T a, T b) const { return lt(b, a); } };
struct eps_ge { bool operator () (T a, T b) const { return !lt(a, b); } };
struct eps_eq {
bool operator () (T a, T b) const { return !lt(a, b) && !lt(b, a); }
};
struct eps_ne {
bool operator () (T a, T b) const { return lt(a, b) || lt(b, a); }
};
#define OP(op, U, a, x, y) pt operator op (U a) const { return pt(x, y); } \
pt &operator op##= (U a) { return *this = *this op a; }
#define CMP(op, body) bool operator op (pt p) const { return body; }
struct pt {
T x, y; constexpr pt(T x = 0, T y = 0) : x(x), y(y) {}
pt operator + () const { return *this; }
pt operator - () const { return pt(-x, -y); }
OP(+, pt, p, x + p.x, y + p.y) OP(-, pt, p, x - p.x, y - p.y)
OP(*, T, a, x * a, y * a) OP(/, T, a, x / a, y / a)
friend pt operator * (T a, pt p) { return pt(a * p.x, a * p.y); }
bool operator < (pt p) const { return eq(x, p.x) ? lt(y, p.y) : lt(x, p.x); }
CMP(<=, !(p < *this)) CMP(>, p < *this) CMP(>=, !(*this < p))
CMP(==, !(*this < p) && !(p < *this)) CMP(!=, *this < p || p < *this)
OP(*, pt, p, x * p.x - y * p.y, y * p.x + x * p.y)
OP(/, pt, p, (x * p.x + y * p.y) / (p.x * p.x + p.y * p.y),
(y * p.x - x * p.y) / (p.x * p.x + p.y * p.y))
};
#undef OP
#undef CMP
istream &operator >> (istream &stream, pt &p) { return stream >> p.x >> p.y; }
ostream &operator << (ostream &stream, pt p) {
return stream << p.x << ' ' << p.y;
}
pt conj(pt a) { return pt(a.x, -a.y); }
T dot(pt a, pt b) { return a.x * b.x + a.y * b.y; }
T cross(pt a, pt b) { return a.x * b.y - a.y * b.x; }
T norm(pt a) { return dot(a, a); }
T abs(pt a) { return sqrt(norm(a)); }
T arg(pt a) { return atan2(a.y, a.x); }
pt polar(T r, T theta) { return r * pt(cos(theta), sin(theta)); }
T distSq(pt a, pt b) { return norm(b - a); }
T dist(pt a, pt b) { return abs(b - a); }
T ang(pt a, pt b) { return arg(b - a); }
// sign of ang, area2, ccw: 1 if counterclockwise, 0 if collinear,
// -1 if clockwise
T ang(pt a, pt b, pt c) {
a -= b; c -= b; return arg(pt(dot(c, a), cross(c, a)));
}
// twice the signed area of triangle a, b, c
T area2(pt a, pt b, pt c) { return cross(b - a, c - a); }
int ccw(pt a, pt b, pt c) { return sgn(area2(a, b, c)); }
// a rotated theta radians around p
pt rot(pt a, pt p, T theta) { return (a - p) * pt(polar(T(1), theta)) + p; }
// rotated 90 degrees ccw
pt perp(pt a) { return pt(-a.y, a.x); }
struct Line {
pt v; T c;
// ax + by = c, left side is ax + by > c
Line(T a = 0, T b = 0, T c = 0) : v(b, -a), c(c) {}
// direction vector v with offset c
Line(pt v, T c) : v(v), c(c) {}
// points p and q
Line(pt p, pt q) : v(q - p), c(cross(v, p)) {}
T eval(pt p) const { return cross(v, p) - c; }
// sign of onLeft, dist: 1 if left of line, 0 if on line, -1 if right of line
int onLeft(pt p) const { return sgn(eval(p)); }
T dist(pt p) const { return eval(p) / abs(v); }
T distSq(pt p) const { T e = eval(p); return e * e / norm(v); }
// rotated 90 degrees ccw
Line perpThrough(pt p) const { return Line(p, p + perp(v)); }
Line translate(pt p) const { return Line(v, c + cross(v, p)); }
Line shiftLeft(T d) const { return Line(v, c + d * abs(v)); }
pt proj(pt p) const { return p - perp(v) * eval(p) / norm(v); }
pt refl(pt p) const { return p - perp(v) * T(2) * eval(p) / norm(v); }
// compares points by orthogonal projection (3 way comparison)
int cmpProj(pt p, pt q) const { return sgn(dot(v, p) - dot(v, q)); }
};
int lineLineIntersection(Line l1, Line l2, pt &res) {
T d = cross(l1.v, l2.v);
if (eq(d, 0)) return l2.v * l1.c == l1.v * l2.c ? 2 : 0;
res = (l2.v * l1.c - l1.v * l2.c) / d; return 1;
}
template <class T, class Cmp = less<T>>
vector<pair<T, T>> &maxDisjointIntervals(vector<pair<T, T>> &A,
Cmp cmp = Cmp()) {
sort(A.begin(), A.end(), [&] (const pair<T, T> &a, const pair<T, T> &b) {
return cmp(a.second, b.second);
});
int i = 0; for (int l = 0, r = 0, N = A.size(); l < N; l = r, i++) {
A[i] = A[l]; for (r = l + 1; r < N && !cmp(A[i].second, A[r].first); r++);
}
A.erase(A.begin() + i, A.end()); return A;
}
const bool FIRST = true, LAST = false;
template <const bool ISFIRST, class T, class F> T bsearch(T lo, T hi, F f) {
static_assert(is_integral<T>::value, "T must be integral");
hi--; while (lo <= hi) {
T mid = lo + (hi - lo) / 2;
if (f(mid) == ISFIRST) hi = mid - 1;
else lo = mid + 1;
}
return ISFIRST ? lo : hi;
}
int main() {
// freopen("in.txt", "r", stdin);
// freopen("out.txt", "w", stdout);
// freopen("err.txt", "w", stderr);
ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
int N;
ld H;
cin >> N >> H;
Line l(pt(0, H), pt(1, H));
vector<pt> P(N);
for (auto &&p : P) cin >> p;
vector<pair<T, T>> intervals;
for (int i = 2; i < N - 2; i += 2) intervals.emplace_back(0, 0);
vector<pt> hull;
for (int i = 1; i < N - 2; i++) {
if (i % 2) {
while (sz(hull) >= 2 && ccw(hull[sz(hull) - 2], hull[sz(hull) - 1], P[i]) >= 0) hull.pop_back();
hull.push_back(P[i]);
} else {
int j = bsearch<FIRST>(0, sz(hull) - 1, [&] (int k) {
return ccw(hull[k], hull[k + 1], P[i]) > 0;
});
pt p;
lineLineIntersection(l, Line(hull[j], P[i]), p);
intervals[i / 2 - 1].first = p.x;
}
}
hull.clear();
for (int i = N - 2; i >= 2; i--) {
if (i % 2) {
while (sz(hull) >= 2 && ccw(hull[sz(hull) - 2], hull[sz(hull) - 1], P[i]) <= 0) hull.pop_back();
hull.push_back(P[i]);
} else {
int j = bsearch<FIRST>(0, sz(hull) - 1, [&] (int k) {
return ccw(hull[k], hull[k + 1], P[i]) < 0;
});
pt p;
lineLineIntersection(l, Line(hull[j], P[i]), p);
intervals[i / 2 - 1].second = p.x;
}
}
cout << sz(maxDisjointIntervals(intervals, eps_lt())) << nl;
return 0;
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
6 ms |
1088 KB |
Output is correct |
| 2 |
Correct |
8 ms |
1072 KB |
Output is correct |
| 3 |
Correct |
7 ms |
1144 KB |
Output is correct |
| 4 |
Correct |
54 ms |
6628 KB |
Output is correct |
| 5 |
Correct |
55 ms |
6848 KB |
Output is correct |
| 6 |
Correct |
58 ms |
7024 KB |
Output is correct |
| 7 |
Correct |
525 ms |
58108 KB |
Output is correct |
| 8 |
Correct |
576 ms |
60160 KB |
Output is correct |
| 9 |
Correct |
655 ms |
62204 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
2 ms |
460 KB |
Output is correct |
| 2 |
Correct |
2 ms |
460 KB |
Output is correct |
| 3 |
Correct |
0 ms |
204 KB |
Output is correct |
| 4 |
Correct |
2 ms |
436 KB |
Output is correct |
| 5 |
Correct |
1 ms |
332 KB |
Output is correct |
| 6 |
Correct |
2 ms |
408 KB |
Output is correct |
| 7 |
Correct |
1 ms |
204 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
6 ms |
1088 KB |
Output is correct |
| 2 |
Correct |
8 ms |
1072 KB |
Output is correct |
| 3 |
Correct |
7 ms |
1144 KB |
Output is correct |
| 4 |
Correct |
54 ms |
6628 KB |
Output is correct |
| 5 |
Correct |
55 ms |
6848 KB |
Output is correct |
| 6 |
Correct |
58 ms |
7024 KB |
Output is correct |
| 7 |
Correct |
525 ms |
58108 KB |
Output is correct |
| 8 |
Correct |
576 ms |
60160 KB |
Output is correct |
| 9 |
Correct |
655 ms |
62204 KB |
Output is correct |
| 10 |
Correct |
2 ms |
460 KB |
Output is correct |
| 11 |
Correct |
2 ms |
460 KB |
Output is correct |
| 12 |
Correct |
0 ms |
204 KB |
Output is correct |
| 13 |
Correct |
2 ms |
436 KB |
Output is correct |
| 14 |
Correct |
1 ms |
332 KB |
Output is correct |
| 15 |
Correct |
2 ms |
408 KB |
Output is correct |
| 16 |
Correct |
1 ms |
204 KB |
Output is correct |
| 17 |
Correct |
530 ms |
59260 KB |
Output is correct |
| 18 |
Correct |
568 ms |
59020 KB |
Output is correct |
| 19 |
Correct |
61 ms |
6640 KB |
Output is correct |
| 20 |
Correct |
564 ms |
58240 KB |
Output is correct |
| 21 |
Correct |
57 ms |
6584 KB |
Output is correct |
| 22 |
Correct |
626 ms |
61940 KB |
Output is correct |
| 23 |
Correct |
1 ms |
304 KB |
Output is correct |
| 24 |
Correct |
576 ms |
61168 KB |
Output is correct |
| 25 |
Correct |
69 ms |
6828 KB |
Output is correct |
| 26 |
Correct |
631 ms |
62208 KB |
Output is correct |
| 27 |
Correct |
26 ms |
3508 KB |
Output is correct |
