finding the number of integer points under a triangle, square and circle
for circle i have tried to check for all points within radius distance from center.For square, i test for all points from bottom-left-corner to upper-right-corner and for triangle i test the signs of determinants as suggested here. I get correct answer while i enter individual values ie either 1 cirlce or 1 square or 1 triangle , but not when there are >1 of them. Eg for the case:
C 10 10 3
S 9 8 4
T 7 9 10 8 8 10
where C is circle, S is square and T is triangle,and (10,10) is center of circle with radius 3. (9,8) is the left-most corner of square of side 4 and (7,9),(10,8) and (8,10) are the three vertices of the triangle , the total distinct points covered by them is 34 but i am getting 37.
Here's what i've tried:
typedef pair<int,int> point;
set<point>myset;
set<point>::iterator it;
int findDeter(int x1,int y1,int x2,int y2,int x0,int y0)
{
int ret = x1*(y2-y0)-y1*(x2-x0)+(x2*y0-x0*y2)
-x2*(y1-y0)+y2*(x1-x0)-(x1*y0-x0*y1)
+x0*(y1-y2)-y0*(x1-x2)+(x1*y2-x2*y1);
return ret;
}
bool sameSign(int x, int y)
{
if(x==0||y==0)
return true;
return (x >= 0) ^ (y < 0);
}
int main()
{
int t,i,j,k,n;
int x,y,r,x1,y1,len;
int xmax,ymax,xmin,ymin;
int D1,D2,D3;
int ax,ay,bx,by,cx,cy;
char shape,dump;
scanf("%d",&t);
while(t--)
{
myset.clear();
scanf("%d",&n);
for(i=0;i<n;i++)
{
scanf("%c",&dump);
scanf("%c",&shape);
if(shape=='C')
{
scanf("%d %d %d",&x,&y,&r);
for(j=x;j<=x+r;j++)
{
for(k=y;k<=y+r;k++)
{
point p(j,k);
myset.insert(p);
}
}
for(j=x-r;j<x;j++)
{
for(k=y-r;k<y;k++)
{
point p(j,k);
myset.insert(p);
}
}
}
else if(shape=='S')
{
scanf("%d %d %d",&x1,&y1,&len);
for(j=x1;j<=x1+len;j++)
{
for(k=y1;k<=y1+len;k++)
{
point p(j,k);
myset.insert(p);
}
}
}
else
{
//printf("heren");
scanf("%d %d %d %d %d %d",&ax,&ay,&bx,&by,&cx,&cy);
/*a1=ax;a2=ay;
b1=bx;b2=by;
c1=cx;c2=cy;*/
xmax = max(ax,max(bx,cx));
ymax = max(ay,max(by,cy));
xmin = min(ax,min(bx,cx));
ymin = min(ay,min(by,cy));
/*for each point P check if sum(the determinants PAB,PAC and PBC have the same signs)*/
for(j=xmin;j<=xmax;j++)
{
for(k=ymin;k<=ymax;k++)
{
D1 = findDeter(ax,ay,bx,by,j,k);
//printf("D1 : %dn",D1);
D2 = findDeter(bx,by,cx,cy,j,k);
//printf("D2 : %dn",D2);
D3 = findDeter(cx,cy,ax,ay,j,k);
//printf("D3 : %dn",D3);
if(sameSign(D1,D2)&&sameSign(D2,D3)&&sameSign(D1,D3))
{
//printf("heren");
point p(j,k);
myset.insert(p);
}
}
}
}
}
printf("%dn",myset.size());
}
return 0;
}
After refactoring your code heavily so that it was clearer to me what is going on - I'd say the error is in the circle code. I've included the complete refactored code below but the troublesome section amount s to this:
struct Circle
{
int x;
int y;
int r;
void add_covered_points( set<points> & pts ) const
{
for(int j=x;j<=x+r;j++)
{
for(int k=y;k<=y+r;k++)
{
pts.insert(point(j,k));
}
}
for(int j=x-r;j<x;j++)
{
for(int k=y-r;k<y;k++)
{
pts.insert(point(j,k));
}
}
}
};
This seems to add points from two rectangular sections, one above and the other below the center of the circle. I'd expect the code to look more like this:
void add_covered_points( set<points> & pts ) const
{
for(int j=-r;j<=+r;j++)
{
for(int k=-r;k<=+r;k++)
{
if (j*j + k*k < r*r )
{
pts.insert(point(x+j,x+k));
}
}
}
}
Heres the complete refactored case for your reference
typedef pair<int,int> point;
int findDeter(int x1,int y1,int x2,int y2,int x0,int y0)
{
int ret = x1*(y2-y0)-y1*(x2-x0)+(x2*y0-x0*y2)
-x2*(y1-y0)+y2*(x1-x0)-(x1*y0-x0*y1)
+x0*(y1-y2)-y0*(x1-x2)+(x1*y2-x2*y1);
return ret;
}
bool sameSign(int x, int y)
{
if(x==0||y==0)
return true;
return (x >= 0) ^ (y < 0);
}
struct Circle
{
int x;
int y;
int r;
void add_covered_points( set<points> & pts ) const
{
for(int j=x;j<=x+r;j++)
{
for(int k=y;k<=y+r;k++)
{
pts.insert(point(j,k));
}
}
for(int j=x-r;j<x;j++)
{
for(int k=y-r;k<y;k++)
{
pts.insert(point(j,k));
}
}
}
};
struct Square
{
int x1,y1,len;
void add_covered_points( set<points> & pts ) const
{
for(int j=x1;j<=x1+len;j++)
{
for(int k=y1;k<=y1+len;k++)
{
myset.insert(point(j,k));
}
}
}
};
struct Triangle
{
int ax,ay,bx,by,cx,cy;
void add_covered_points( set<points> & pts ) const
{
int xmax = max(ax,max(bx,cx));
int ymax = max(ay,max(by,cy));
int xmin = min(ax,min(bx,cx));
int ymin = min(ay,min(by,cy));
/*for each point P check if sum(the determinants PAB,PAC and PBC have the same signs)*/
for(int j=xmin;j<=xmax;j++)
{
for(int k=ymin;k<=ymax;k++)
{
int D1 = findDeter(ax,ay,bx,by,j,k);
int D2 = findDeter(bx,by,cx,cy,j,k);
int D3 = findDeter(cx,cy,ax,ay,j,k);
if(sameSign(D1,D2)&&sameSign(D2,D3)&&sameSign(D1,D3))
{
pts.insert(point(j,k));
}
}
}
}
};
int main()
{
set<point>myset;
int t;
scanf("%d",&t);
while(t--)
{
myset.clear();
int n;
scanf("%d",&n);
for(int i=0;i<n;i++)
{
char dump;
char shape;
scanf("%c",&dump);
scanf("%c",&shape);
if(shape=='C')
{
Circle c;
scanf("%d %d %d",&c.x,&c.y,&c.r);
c.add_covered_points( myset );
}
else if(shape=='S')
{
Square s;
scanf("%d %d %d",&s.x1,&s.y1,&s.len);
s.add_covered_points( myset );
}
else
{
Triangle t;
int ax,ay,bx,by,cx,cy;
scanf("%d %d %d %d %d %d",&t.ax,&t.ay,&t.bx,&t.by,&t.cx,&t.cy);
t.add_covered_points( myset );
}
}
}
return 0;
}
Pick's theorem is suitable for counting integer points in the interior of simple polygons with integer vertices.
Here we can see solution for circles.
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