Convex Hull

struct point{
    int x, y;
};

point P[mx], C[mx], P0;

int triArea(point a, point b, point c) {
    return (a.x*(b.y-c.y) + b.x*(c.y-a.y) + c.x*(a.y-b.y));
}

int sqDist(point a, point b) {
    return ((a.x-b.x)*(a.x-b.x) + (a.y-b.y)*(a.y-b.y));
}

int cross(point a, point b, point c) {
   return ((b.x-a.x)*(c.x-b.x) + (b.y-a.y)*(c.y-b.y));
}

bool comp(point a, point b) {
    int d = triArea(P0, a, b);
    if(d < 0) return false;
    if(!d && sqDist(P0, a) > sqDist(P0, b)) return false;
    return true;
}

inline bool normal(point a, point b) {
    return ((a.x==b.x) ? a.y < b.y : a.x < b.x);
}

bool issame(point a, point b) {
    return (a.x == b.x && a.y == b.y);
}

int makeUnique(int np) {
    sort(&P[0], &P[np], normal);
    np = unique(&P[0], &P[np], issame) - P;
    return np;
}

int convexHull(int np) {
    if(np<=2) {
        for(int i=0;i<np;i++){
            C[i] = P[i];
        }
        return np;
    }

    int i, j, nc, pos = 0;
    for(i = 1; i < np; i++)
        if(P[i].y<P[pos].y || (P[i].y==P[pos].y && P[i].x<P[pos].x))
            pos = i;
    swap(P[0], P[pos]);
    P0 = P[0];
    sort(&P[1], &P[np], comp);
    for(i = 0; i < 3; i++) C[i] = P[i];
    for(i = j = 3; i < np; i++) {
        while(triArea(C[j-2], C[j-1], P[i]) < 0) j--;
        C[j++] = P[i];
    }
    return nc = j;
}

int compress(int nc) {
    int i, j, d;
    C[nc] = C[0];
    for(i=j=1; i < nc; i++) {
        d = triArea2(C[j-1], C[i], C[i+1]);
        if(d || (!d && issame(C[j-1], C[i+1]))) C[j++] = C[i];
    }
    return nc = j;
}