#include <bits/stdc++.h>
#define endl "\n"
using namespace std;
using ll = long long;
struct Point{
ll x, y;
};
ll vp(Point a, Point b) {
return a.x * b.y - a.y * b.x;
}
ll sgn(Point a, Point b, Point c) {
// -1 if the order is A-B-C from left to right if B is the bottom point
// 1 or 0 otherwise
ll q = vp(Point{a.x - b.x, a.y - b.y}, Point{c.x - b.x, c.y - b.y});
return (q / abs(q));
}
bool operator<(Point a, Point b) {
return sgn(a, Point{0LL, 0LL}, b) == -1;
}
bool in_triangle(Point a, Point b, Point c, Point p) {
// assuming A-B-C
return (sgn(a, b, p) == -1 && sgn(c, b, p) == 1 && sgn(p, c, a) == -1);
}
bool cmp_hull(Point a, Point b) {
if (a.x == b.x) return a.y < b.y;
return a.x < b.x;
}
/*
Plan:
0. Sort all points by angle
1. Construct sqrt(n) convex hulls for all point sets
2. For each triangle, consider all sqrt(n) ranges of points already present
3. Check all points that are outside of the hulls manually
3.5 On both sides
4. For each complete range with a hull do a binary search on that hull:
5. Start with the leftmost (by the angle) point, end with the point anticlockwise on the convex hull
6. Check if the mid is in the triangle, if it is, then break. If we are moving further from the triangle by choosing a point to the right of the current one (cur_mid), then r = mid, else l = mid.
Claim: the total thing takes no more than 200 lines.
*/
vector<Point> points;
const ll sqrt_size = 1200;
signed main() {
ll n, m;
cin >> n >> m;
for (ll i = 0; i < n; i++) {
ll x, y;
cin >> x >> y;
points.push_back(Point{x, y});
}
sort(points.begin(), points.end()); // the comparator is there
vector<vector<Point>> hulls(n);
for (ll i = 0; i < n; i++) {
hulls[i / sqrt_size].push_back(points[i]);
}
for (ll i = 0; i < n; i++) {
if (hulls[i].empty()) continue;
vector<Point> hull;
sort(hulls[i].begin(), hulls[i].end(), cmp_hull);
for (auto p : hulls[i]) {
while (hull.size() > 1 && sgn(p, hull[(ll)hull.size() - 2], hull.back()) == -1) {
hull.pop_back();
}
hull.push_back(p);
}
hulls[i] = hull;
// top convex hull only!
}
// end of hull processing
for (ll trn = 0; trn < m; trn++) {
// current triangle
Point a, b;
cin >> a.x >> a.y >> b.x >> b.y;
if (sgn(a, Point{0LL, 0LL}, b) >= 0) swap(a, b);
ll left_start = n - 1, right_end = 0;
// left_start - leftmost point that is in the angle
// right_end - leftmost point after the angle
{
ll l = 0;
ll r = n;
while (r - l > 1) {
ll mid = (l + r) / 2;
if (sgn(a, Point{0LL, 0LL}, points[mid]) >= 0) {
l = mid;
} else {
r = mid;
}
}
left_start = l;
}
{
ll l = 0;
ll r = n;
while (r - l > 1) {
ll mid = (l + r) / 2;
if (sgn(b, Point{0LL, 0LL}, points[mid]) >= 0) {
l = mid;
} else {
r = mid;
}
}
right_end = r;
}
if (left_start >= right_end) {
cout << "N" << endl;
continue;
}
bool flag = false;
if (right_end - left_start <= sqrt_size) {
for (ll i = left_start; i < right_end; i++) {
if (in_triangle(a, Point{0LL, 0LL}, b, points[i])) {
flag = true;
break;
}
}
if (flag) {
cout << "Y" << endl;
} else {
cout << "N" << endl;
}
continue;
}
flag = false;
while (left_start % sqrt_size != 0) {
if (in_triangle(a, Point{0LL, 0LL}, b, points[left_start])) {
flag = true;
}
left_start++;
}
while (right_end > left_start && right_end % sqrt_size != 0) {
right_end--;
if (in_triangle(a, Point{0LL, 0LL}, b, points[right_end])) {
flag = true;
}
}
if (left_start == right_end) {
if (flag) {
cout << "Y" << endl;
} else {
cout << "N" << endl;
}
continue;
}
// assert(right_end % sqrt_size == 0);
assert(left_start % sqrt_size == 0);
flag = false;
for (ll i = left_start / sqrt_size; i < right_end / sqrt_size; i++) {
// convex hull processing
ll l = 0;
ll r = (ll)hulls[i].size();
while (r - l > 1) {
ll mid = (r + l) / 2;
if (in_triangle(a, Point{0LL, 0LL}, b, hulls[i][mid])) {
flag = true;
break;
}
if (mid + 1 == hulls[i].size() || !in_triangle(a, Point{0LL, 0LL}, b, hulls[i][mid + 1]) && sgn(hulls[i][mid + 1], a, hulls[i][mid]) == -1) {
r = mid;
} else {
l = mid;
}
}
if (flag) break;
}
if (flag) {
cout << "Y" << endl;
} else {
cout << "N" << endl;
}
}
return 0;
}
Compilation message
tri.cpp: In function 'int main()':
tri.cpp:208:21: warning: comparison of integer expressions of different signedness: 'll' {aka 'long long int'} and 'std::vector<Point>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
208 | if (mid + 1 == hulls[i].size() || !in_triangle(a, Point{0LL, 0LL}, b, hulls[i][mid + 1]) && sgn(hulls[i][mid + 1], a, hulls[i][mid]) == -1) {
| ~~~~~~~~^~~~~~~~~~~~~~~~~~
tri.cpp:208:98: warning: suggest parentheses around '&&' within '||' [-Wparentheses]
208 | if (mid + 1 == hulls[i].size() || !in_triangle(a, Point{0LL, 0LL}, b, hulls[i][mid + 1]) && sgn(hulls[i][mid + 1], a, hulls[i][mid]) == -1) {
| ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
5 ms |
344 KB |
Output is correct |
| 2 |
Correct |
6 ms |
348 KB |
Output is correct |
| 3 |
Incorrect |
98 ms |
2276 KB |
Output isn't correct |
| 4 |
Incorrect |
387 ms |
3784 KB |
Output isn't correct |
| 5 |
Incorrect |
755 ms |
6588 KB |
Output isn't correct |
| 6 |
Incorrect |
902 ms |
5568 KB |
Output isn't correct |
| 7 |
Incorrect |
1104 ms |
6788 KB |
Output isn't correct |
| 8 |
Incorrect |
452 ms |
5128 KB |
Output isn't correct |
| 9 |
Incorrect |
517 ms |
6160 KB |
Output isn't correct |
| 10 |
Incorrect |
584 ms |
6816 KB |
Output isn't correct |
