Convex Hull

cpp/convexHull.cpp

@@ -0,0 +1,64 @@
+struct pt{
+    long long x, y;
+    pt(){}
+    pt(long long _x, long long _y):x(_x), y(_y){}
+    pt operator+(const pt & p) const { return pt(x + p.x, y + p.y); }
+    pt operator-(const pt & p) const { return pt(x - p.x, y - p.y); }
+    long long cross(const pt & p) const { return x * p.y - y * p.x; }
+    long long dot(const pt & p) const { return x * p.x + y * p.y; }
+    long long cross(const pt & a, const pt & b) const { return (a - *this).cross(b - *this); }
+    long long dot(const pt & a, const pt & b) const { return (a - *this).dot(b - *this); }
+    long long sqrLen() const { return this->dot(*this); }
+};
+
+bool lexComp(const pt & l, const pt & r){
+    return l.x < r.x || (l.x == r.x && l.y < r.y);
+}
+
+int sgn(long long val){
+    return val > 0 ? 1 : (val == 0 ? 0 : -1);
+}
+
+vector<pt> seq;
+int n;
+
+bool pointInTriangle(pt a, pt b, pt c, pt point){
+    long long s1 = abs(a.cross(b, c));
+    long long s2 = abs(point.cross(a, b)) + abs(point.cross(b, c)) + abs(point.cross(c, a));
+    return s1 == s2;
+}
+
+void prepare(vector<pt> & points){
+    n = points.size();
+    int pos = 0;
+    for(int i = 1; i < n; i++){
+        if(lexComp(points[i], points[pos]))
+            pos = i;
+    }
+    rotate(points.begin(), points.begin() + pos, points.end());
+
+    n--;
+    seq.resize(n);
+    for(int i = 0; i < n; i++)
+        seq[i] = points[i + 1] - points[0];
+}
+
+bool pointInConvexPolygon(pt point){
+    if(seq[0].cross(point) != 0 && sgn(seq[0].cross(point)) != sgn(seq[0].cross(seq[n - 1])))
+        return false;
+    if(seq[n - 1].cross(point) != 0 && sgn(seq[n - 1].cross(point)) != sgn(seq[n - 1].cross(seq[0])))
+        return false;
+
+    if(seq[0].cross(point) == 0)
+        return seq[0].sqrLen() >= point.sqrLen();
+
+    int l = 0, r = n - 1;
+    while(r - l > 1){
+        int mid = (l + r)/2;
+        int pos = mid;
+        if(seq[pos].cross(point) >= 0)l = mid;
+        else r = mid;
+    }
+    int pos = l;
+    return pointInTriangle(seq[pos], seq[pos + 1], pt(0, 0), point);
+}