#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 |
6 ms |
344 KB |
Output is correct |
| 2 |
Correct |
6 ms |
348 KB |
Output is correct |
| 3 |
Incorrect |
99 ms |
2296 KB |
Output isn't correct |
| 4 |
Incorrect |
382 ms |
3660 KB |
Output isn't correct |
| 5 |
Incorrect |
756 ms |
6592 KB |
Output isn't correct |
| 6 |
Incorrect |
895 ms |
5476 KB |
Output isn't correct |
| 7 |
Incorrect |
1138 ms |
6940 KB |
Output isn't correct |
| 8 |
Incorrect |
459 ms |
5312 KB |
Output isn't correct |
| 9 |
Incorrect |
510 ms |
6240 KB |
Output isn't correct |
| 10 |
Incorrect |
571 ms |
6384 KB |
Output isn't correct |
