326 lines
8.0 KiB
C++
326 lines
8.0 KiB
C++
#include <iostream>
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#include <fstream>
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#include <string>
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#include <cmath>
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#include <cstdlib>
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#include <ctime>
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#include <getopt.h>
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/*
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finds the area in a given set of points. all the arrays will be named points
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and i really don't feel like having this thing in several places in my code
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it's huge
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*/
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#define AREA(a,b,c) ( points[a].x * points[b].y + points[c].x * points[a].y + points[b].x * points[c].y - points[c].x * points[b].y - points[b].x * points[a].y - points[a].x * points[c].y )
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/* maximum size of coordinate plane */
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#define COORDMAX 500
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/* maximum number of points to compute */
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#define POINTMAX 5000
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using namespace std;
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ofstream out;
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/* the class that I will use to wrap a coordinate using oo design */
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class Point {
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public:
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short x, y;
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Point() {
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Reset();
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}
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Point ( short one, short two ) {
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x = one; y = two;
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}
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void Reset() {
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x = -1;
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y = -1;
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}
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double Slope ( const Point &end ) {
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double result = 0.0;
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result = ( this->y - end.y ) / ( this->x - end.x );
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return result;
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}
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/* overloaded C++ operators for various syntax simplifications */
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friend ostream& operator<< ( ostream &out, const Point &p ) {
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out << p.x << " " << p.y;
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return out;
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}
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friend ostream& operator<< ( ostream &out, const Point *p ) {
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out << p->x << " " << p->y;
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return out;
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}
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Point& operator= ( const Point &p ) {
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this->x = p.x;
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this->y = p.y;
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return *this;
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}
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Point& operator= ( const Point *p ) {
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this->x = p->x;
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this->y = p->y;
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return *this;
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}
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bool operator== ( const Point &p ) {
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return ( this->x == p.x && this->y == p.y );
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}
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bool operator!= ( const Point &p ) {
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return ( this->x != p.x && this->y != p.y );
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}
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};
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/*
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this function reads in all of the points in a file, up to POINTMAX in size
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since we don't include a size field in the input file
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*/
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Point *CreateByFile ( const char *name, long *size ) {
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ifstream infile ( name );
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Point *points;
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*size = 0;
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points = new Point[POINTMAX];
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if ( points == NULL ) {return NULL;}
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while ( !infile.eof() ) {
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short x = 0, y = 0;
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infile >> x;
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infile >> y;
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if ( x != 0 && y != 0 ) {
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points[*size].x = x;
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points[*size].y = y;
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(*size)++;
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}
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if ( *size >= POINTMAX ) {break;}
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}
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infile.close();
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return points;
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}
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/* this function creates an randomly sized array of Points randomly selected between 1 and COORDMAX */
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Point *CreateByRandom ( long *size, bool flag ) {
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Point *hull;
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srand ( time ( NULL ) );
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if ( !flag )
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*size = rand() % POINTMAX + 1;
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hull = new Point[*size];
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if ( hull == NULL )
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return hull;
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for ( long count = 0; count < *size; count++ ) {
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hull[count].x = rand() % COORDMAX + 1;
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hull[count].y = rand() % COORDMAX + 1;
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}
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return hull;
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}
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/* this function checks two coordinates against a set of Points for an edge */
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bool ConvexHullContains ( Point *points, long size, long first, long second ) {
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long count = 0;
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double d = 0.0;
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bool above = false, below = false;
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/* check all the points. points may or may not be sorted */
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for ( count = 0; count < size; count++ ) {
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/* don't check the checking points */
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if ( count == first || count == second ) {continue;}
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/* area from the book algorithm */
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d = AREA(first, second, count);
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/*
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one side or the other. it doesn't matter.
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by setting one flag and not the other, you can check to see which
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side of the line the points are on; only on *one* side of the line.
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*/
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if ( d > 0.0 ) {
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if ( below ) {return false;}
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above = true;
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}
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else if ( d < 0.0 ) {
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if ( above ) {return false;}
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below = true;
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}
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/*
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not really sure about this one. doesn't work otherwise.
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i don't know why the area would be zero, but it gives me strange
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hulls if i don't do this
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*/
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else
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return false;
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}
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/* finished the 'gauntlet' of checks, we have a winner */
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return true;
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}
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/*
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Brute Force convex hull smashing. Figures out which points are on the edge
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by generating all possible permutations of the point set
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*/
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void SmashHull ( Point *points, long size, bool *mark ) {
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long hullpoint = 0, count = 0, firsty = -1;
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/* blindly adds any points that are on the edge to the mark array */
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for ( hullpoint = 0; hullpoint < size; hullpoint++ ) {
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for ( count = 0; count < size; count++ ) {
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if ( hullpoint == count ) {continue;}
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if ( ConvexHullContains ( points, size, hullpoint, count ) ) {mark[hullpoint] = true;}
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}
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}
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/* this doesn't really output the points in order, but it does a generally decent job */
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long b = 0;
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for ( count = 0; count < size; count++ ) {b += points[count].y;}
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double t = b / size;
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for ( count = 0; count < size; count++ ) {
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if ( mark[count] && points[count].y >= t )
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out << points[count] << endl;
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}
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for ( count = size - 1; count >= 0 ; count-- ) {
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if ( mark[count] && points[count].y < t )
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out << points[count] << endl;
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}
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}
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/*
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a recursive function that determines the convex hull of a point set using
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a method similar to quicksort
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*/
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void QuickHull ( Point *points, long left, long right, bool *mark, bool flag ) {
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long count = 0, maxindex = 0;
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double area = 0.0, maxarea = 0.0;
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for ( count = left; count < right; count++ ) {
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area = AREA( left, right, count );
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if ( (area > maxarea && flag) || (area < maxarea && !flag) ) {maxarea = area;maxindex = count;}
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}
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if ( maxindex > 0 ) {
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mark[maxindex] = true;
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if ( flag ) {
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QuickHull ( points, left, maxindex, mark, flag );
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out << points[maxindex] << endl;
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QuickHull ( points, maxindex, right, mark, flag );
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}
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else {
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QuickHull ( points, maxindex, right, mark, flag );
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out << points[maxindex] << endl;
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QuickHull ( points, left, maxindex, mark, flag );
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}
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}
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}
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/*
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this is a C qsort compatible comparison function
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returns -1 when a < b, 1 when a > b, and 0 when a == b
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*/
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int ComparePoints ( const void *a, const void *b ) {
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Point *one = (Point *)a;
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Point *two = (Point *)b;
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if ( one->x < two->x ) {return -1;}
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else if ( one->x > two->x ) {return 1;}
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else {
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if ( one->y < two->y ) {return -1;}
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else if ( one->y > two->y ) {return 1;}
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else {return 0;}
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}
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}
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int main ( int argc, char **argv ) {
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Point *x = NULL;
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short firsty = -1;
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bool algorithm = false, comparative = false, outputflag = true;
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int arg = 0, argindex = 0;
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long size = 0, count = 0, t = 0;
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char *outputname = NULL, *inputname = NULL;
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/* hooray for getopt */
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struct option longopts[] = {
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{"p", 1, NULL, 'p'},
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{"b", 0, NULL, 'b'},
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{"i", 1, NULL, 'i'},
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{"o", 1, NULL, 'o'},
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{"h", 0, NULL, 'h'},
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{"help", 0, NULL, 'h'},
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{"?", 0, NULL, 'h'}
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};
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while ( 1 ) {
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arg = getopt_long ( argc, argv, "p:bi:o:h", longopts, &argindex );
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if ( arg == -1 ) {break;}
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switch ( arg ) {
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case 'p':
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comparative = true;
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size = atol ( optarg );
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break;
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case 'b':
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algorithm = true;
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break;
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case 'i':
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inputname = optarg;
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break;
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case 'o':
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outputname = optarg;
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outputflag = false;
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break;
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case 'h':
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cout << "Usage: " << argv[0] << " [options] --i <infile> --o <outfile>" << endl;
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cout << "\tOptions" << endl;
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cout << "\t--b\tChanges algorithm to brute force (default is quickhull)" << endl;
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cout << "\t--p\tSpecifies problem size of random generation" << endl;
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exit ( 0 );
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break;
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default:
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break;
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}
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}
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/* end getopt */
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if ( outputflag ) {
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outputname = new char[ strlen( argv[0] ) + 5 ];
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strcpy ( outputname, argv[0] );
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strcat ( outputname, ".out" );
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}
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out.open ( outputname );
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if ( inputname == NULL ) {x = CreateByRandom ( &size, comparative );}
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else {x = CreateByFile ( inputname, &size );}
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/* sort and output the point set */
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qsort ( x, size, sizeof( Point ), &ComparePoints );
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for ( count = 0; count < size; count++ ) {out << x[count] << endl;}
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out << endl;
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/* calculate convex hull and output results as they are found */
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bool result[size];
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for ( count = 0; count < size; count++ ) {result[count] = false;}
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result[0] = true;result[size - 1] = true;
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if ( algorithm ) {
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SmashHull ( x, size, result );
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}
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else {
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out << x[0] << endl;
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QuickHull ( x, 0, size - 1, result, true );
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out << x[size - 1] << endl;
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QuickHull ( x, 0, size - 1, result, false );
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}
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out.close();
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delete [] x;
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if ( outputflag ) {delete [] outputname;}
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return 0;
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}
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