/*	convex-hull.c

	Compute convex hulls of points in the plane by the Gries/Graham scan.
*/

/* Copyright 2003-2020 by Steven S. Skiena; all rights reserved.
Permission is granted for use in non-commerical applications
provided this copyright notice remains intact and unchanged.

These programs appear in my books:

"The Algorithm Design Manual" by Steven Skiena, second edition, Springer,
London 2008.  See out website www.algorist.com for additional information
or https://www.amazon.com/exec/obidos/ASIN/1848000693/thealgorith01-20

"Programming Challenges: The Programming Contest Training Manual"
by Steven Skiena and Miguel Revilla, Springer-Verlag, New York 2003.
See our website www.programming-challenges.com for additional information,
or http://www.amazon.com/exec/obidos/ASIN/0387001638/thealgorithmrepo/
*/


#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include "bool-old.h"

#include "geometry.h"

point first_point;  /* first hull point */

int leftlower();           // const void *, const void *);
int smaller_angle();       // const void *, const void *);

void sort_and_remove_duplicates(point in[], int *n) {
    int i;                  /* counter */
    int oldn;               /* number of points before deletion */
    int hole;               /* index marked for potential deletion */

    qsort(in, *n, sizeof(point), leftlower);

    oldn = *n;
    hole = 1;
    for (i = 1; i < oldn; i++) {
        if ((in[hole-1][X] == in[i][X]) && (in[hole-1][Y] == in[i][Y])) {
            (*n)--;
        } else {
            copy_point(in[i], in[hole]);
            hole = hole + 1;
        }
    }
    copy_point(in[oldn-1], in[hole]);
}

void convex_hull(point in[], int n, polygon *hull) {
    int i;          /* input counter */
    int top;        /* current hull size */

    if (n <= 3) { 		/* all points on hull! */
        for (i = 0; i < n; i++) {
            copy_point(in[i], hull->p[i]);
        }
        hull->n = n;
        return;
    }

    sort_and_remove_duplicates(in, &n);
    copy_point(in[0], (double*)&first_point);

    qsort(&in[1], n-1, sizeof(point), smaller_angle);

    copy_point(first_point, hull->p[0]);
    copy_point(in[1], hull->p[1]);

    copy_point(first_point, in[n]);	/* sentinel to avoid special case */
    top = 1;
    i = 2;

    while (i <= n) {
        if (cw(hull->p[top-1], hull->p[top], in[i])) {
            top = top-1;    /* top not on hull */
        } else {
            if (!collinear(hull->p[top - 1], hull->p[top], in[i])) {
                top = top+1;
            }
            copy_point(in[i], hull->p[top]);
            i = i + 1;
        }
    }
    hull->n = top;
}

int leftlower(const point *p1, const point *p2) {

    if ((*p1)[X] < (*p2)[X]) {
        return (-1);
    }

    if ((*p1)[X] > (*p2)[X]) {
        return (1);
    }

    if ((*p1)[Y] < (*p2)[Y]) {
        return (-1);
    }

    if ((*p1)[Y] > (*p2)[Y]) {
        return (1);
    }

    return(0);
}

int smaller_angle(point *p1, point *p2) {
    if (collinear(first_point, *p1, *p2)) {
        if (distance(first_point, *p1) <= distance(first_point, *p2)) {
            return(-1);
        } else {
            return(1);
        }
    }

    if (ccw(first_point, *p1, *p2)) {
        return(-1);
    } else {
        return(1);
    }
}

int main(void){
    point in[MAXPOLY];      /* input points */
    polygon hull;           /* convex hull */
    int n;                  /* number of points */
    int i;                  /* counter */

    scanf("%d", &n);
    for (i = 0; i < n; i++) {
        scanf("%lf %lf", &in[i][X], &in[i][Y]);
    }

    convex_hull(in, n, &hull);

    print_polygon(&hull);
}