#include <bits/stdc++.h>
#define endl "\n"
using namespace std;
struct Point{
int x, y;
};
int vp(Point a, Point b) {
return a.x * b.y - a.y * b.x;
}
int 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
int 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 int sqrt_size = 600;
int main() {
int n, m;
cin >> n >> m;
for (int i = 0; i < n; i++) {
int 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 (int i = 0; i < n; i++) {
hulls[i / sqrt_size].push_back(points[i]);
}
for (int 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[(int)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 (int 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) == 1) swap(a, b);
int left_start = n - 1, right_end = 0;
// left_start - leftmost point that is in the angle
// right_end - leftmost point after the angle
int l = -1;
int r = n - 1;
while (r - l > 1) {
int mid = (l + r) / 2;
if (sgn(a, Point{0, 0}, points[mid]) >= 0) {
l = mid;
} else {
r = mid;
}
}
left_start = r;
l = 0;
r = n;
while (r - l > 1) {
int mid = (l + r) / 2;
if (sgn(b, Point{0, 0}, points[mid]) >= 0) {
l = mid;
} else {
r = mid;
}
}
right_end = r;
if (l >= r) {
cout << "N" << endl;
continue;
}
bool flag = false;
if (right_end - left_start <= sqrt_size) {
for (int i = left_start; i < right_end; i++) {
if (in_triangle(a, Point{0, 0}, 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{0, 0}, b, points[left_start])) {
flag = true;
}
left_start++;
}
while (right_end - 1 > left_start && right_end % sqrt_size != 0) {
right_end--;
if (in_triangle(a, Point{0, 0}, b, points[right_end])) {
flag = true;
}
}
flag = false;
for (int i = left_start / sqrt_size; i < right_end / sqrt_size; i++) {
// convex hull processing
int l = 0;
int r = (int)hulls[i].size();
while (r - l > 1) {
int mid = (r + l) / 2;
if (in_triangle(a, Point{0, 0}, b, hulls[i][mid])) {
flag = true;
break;
}
if (mid + 1 == hulls[i].size() || !in_triangle(a, Point{0, 0}, b, hulls[i][mid + 1]) && sgn(hulls[i][mid + 1], a, hulls[i][mid]) == -1) {
r = mid;
} else {
l = mid;
}
}
for (int j = (l - 3 + hulls[i].size()) % hulls[i].size(); j <= (r + 3 + hulls[i].size()) % hulls[i].size(); j++) {
if (in_triangle(a, Point{0, 0}, b, hulls[i][j])) {
flag = true;
break;
}
}
if (flag) break;
}
if (flag) {
cout << "Y" << endl;
} else {
cout << "N" << endl;
}
}
return 0;
}
Compilation message
tri.cpp: In function 'int main()':
tri.cpp:191:21: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<Point>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
191 | if (mid + 1 == hulls[i].size() || !in_triangle(a, Point{0, 0}, b, hulls[i][mid + 1]) && sgn(hulls[i][mid + 1], a, hulls[i][mid]) == -1) {
| ~~~~~~~~^~~~~~~~~~~~~~~~~~
tri.cpp:191:94: warning: suggest parentheses around '&&' within '||' [-Wparentheses]
191 | if (mid + 1 == hulls[i].size() || !in_triangle(a, Point{0, 0}, b, hulls[i][mid + 1]) && sgn(hulls[i][mid + 1], a, hulls[i][mid]) == -1) {
| ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
tri.cpp:198:67: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<Point>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
198 | for (int j = (l - 3 + hulls[i].size()) % hulls[i].size(); j <= (r + 3 + hulls[i].size()) % hulls[i].size(); j++) {
| ~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Incorrect |
3 ms |
344 KB |
Output isn't correct |
| 2 |
Incorrect |
3 ms |
348 KB |
Output isn't correct |
| 3 |
Incorrect |
92 ms |
1776 KB |
Output isn't correct |
| 4 |
Incorrect |
160 ms |
2760 KB |
Output isn't correct |
| 5 |
Incorrect |
327 ms |
4984 KB |
Output isn't correct |
| 6 |
Incorrect |
292 ms |
4232 KB |
Output isn't correct |
| 7 |
Incorrect |
368 ms |
5060 KB |
Output isn't correct |
| 8 |
Incorrect |
290 ms |
4220 KB |
Output isn't correct |
| 9 |
Incorrect |
320 ms |
4552 KB |
Output isn't correct |
| 10 |
Incorrect |
356 ms |
5072 KB |
Output isn't correct |
