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#include <iostream>
#include <math.h>
#include <algorithm>
#include <vector>
using namespace std;
struct A{ //stores the pairs of points
int x;
int y;
};
int N;
int sx=10000,sy=10000; //Coordinates of the smallest point.
vector <A> mass;
int used[100];
bool CMP(A i,A j) //Which point is bigger by sin
{
if((i.xsx)/(sqrt(pow(i.xsx,2)+pow(i.ysy,2)))>(j.xsx)/(sqrt(pow(j.xsx,2)+pow(j.ysy,2))))
return 1;
else return 0;
}
// Function that calculates the absolute value
// of a double type.
double MyAbs(double num)
{
double inv = num * 1;
return (num <= 0) ? inv : num;
}
// Function that calculates the area.
//Given vector of points in the XY plane.
double CalcArea(vector<pair<double, double > > list)
{
double area = 0; // Total Area
double diff = 0; // Difference Of Y{i + 1}  Y{i  1}
unsigned int last = list.size()  1; // Size Of Vector  1
//That loop goes to all points from 2 to n1.
for(unsigned int i = 1; i < last; i++)
{
diff =list[i + 1].second  list[i  1].second;
area += list[i].first * diff;
}
//Now we consider the points 1 and n.
diff = list[1].second  list[last].second;
area += list[0].first * diff; //
diff = list[0].second  list[last  1].second;
area += list[last].first * diff;
/* Calculate The Final Answer */
area = 0.5 * MyAbs(area);
return area; // Return The Area
}
int main()
{
N=5;
double it;
int i;
for(i=1;i<=N;i++)
{ A temp;
cin>>temp.x>>temp.y;
mass.push_back(temp);
if(sy>mass[mass.size()1].y)
{
it=mass.size()1;
sy=mass[mass.size()1].y;
sx=mass[mass.size()1].x;
}
if(mass[mass.size()1].y==sy&&mass[mass.size()1].x<sx)
{
it=mass.size()1;
sx=mass[mass.size()1].x;
}
}
mass.erase(mass.begin()+it);
sort(mass.begin(),mass.end(),CMP);
cout<<endl<<endl<<endl<<endl;
for(i=0;i<mass.size();i++)
cout<<mass[i].x<<" "<<mass[i].y<<endl;//Here it outputs the points which creates the external
//line of the polygon.
vector<A> stack;
A temp;
temp.x=sx;
temp.y=sy;
stack.push_back(temp);
stack.push_back(mass[0]);
for(i=1;i<mass.size();i++)
{
int x1,x2,x3,y1,y2,y3;
int status=0;
while(status==0)
{
x3=mass[i].x;
y3=mass[i].y;
x1=stack[stack.size()2].x;
y1=stack[stack.size()2].y;
x2=stack[stack.size()1].x;
y2=stack[stack.size()1].y;
if((x1*y3+y1*x2+x3*y2)(x2*y3+y2*x1+x3*y1)>0)
stack.pop_back();
else
{
stack.push_back(mass[i]);
status=1;
}
}
}
for(i=0;i<stack.size();i++)
cout<<stack[i].x<<" "<<stack[i].y<<endl;
double x = 0;
double y = 0;
vector< pair<double, double> > v;
int mm=mass.size();
int nn=stack.size();
while(stack.size() > 0)
{
for (i=0;i<=stack.size();i++)
v.push_back(make_pair(x[i], y[i]));// here I want to push back the pairs x and y into V
nn; //which goes ti the function that computes the area.
}
while(mass.size() > 0)
{
for (i=0;i<=mass.size();i++)
v.push_back(make_pair(x[i], y[i]));// here I want to push back the pairs x and y into V
mm; //which goes ti the function that computes the area.
}
cout<<"The Area Of The Polygon Is: " << CalcArea(v) <<endl;
system ("pause");
return 0;
}
 