Bounds Checking

[andersonwq]

I am making a program that tells you how many possible ways there are from the top left to the bottom right. The grid can either be a square/rectangle or an L-shape. The L-grid bounds checking is where I am having problems.

#include <iomanip>
#include <iostream>

using namespace std;

int grid(int low,int left, int right, int bottom)
{
        if(low>bottom)
                return 0;
        if(left>right)
                return 0;
        if(low == 0 || left== 0)
                return 1;
        else
                return grid(low-1,left,right,bottom)+grid(low,left-1,right,bottom);
}



int main()
{
        int startrow,startcol,endrow,endcol,numrow,numcol,topd,rightd,leftd,bottomd;

        startrow=0;
        startcol=0;

        cout<<"Enter the dimentions of your grid starting with the top."<<endl;
        cin>>topd;

        cout<<"Now enter the right dimention(your right must be less then your left)"<<endl;
        cin>>rightd;

        cout<<"Now the left"<<endl;
        cin>>leftd;

        cout<<"Now the bottom(your bottom must be greater then your top)"<<endl;
        cin>>bottomd;
        
        cout<<"You are starting at the top left corner(0,0)"<<endl;
        //cout<<"Enter the ending coordinates(row and colum): "<<endl;

        endrow=bottomd;
        endcol=rightd;

        numrow=endrow-startrow;
        numcol=endcol-startcol;

        if(numrow < 0 || numcol <0)
                cout<<"There are no possible paths "<<endl;
        else
                cout<<"There are "<<grid(numrow,numcol,rightd,bottomd)<<" paths"<<endl;
}

[andersonwq]

Can someone please help?

[Albatross]

What sort of problems are you having?

-Albatross

[andersonwq]

no thickness to them..... the grid we are making, are divided up into little squares each having a dimension of 2X2, so it takes four points. So a grid with 4X4 would have a total of 9 squares in it. So our problem is say if we have a top of 4, a left side of 11, a bottom side of 8, and a right side of 6. In the top right corner of the grid, there would be nothing there, so how would we write bounds checking for that area?

[andersonwq]

it is kinda a hard program to explain. did that help?

[ne555]

Suppose that you move your L, so the sides of the hole corresponds to the axis x and y.
Then a point is inside the hole if both its coordinates are positive.

[andersonwq]

explain more

[ne555]

move the concave vertex to (0,0). Now your problem was simplified.
Instead of looking for a point inside an L shape, you look for a point in any of the 3 valid rectangles (thing that you know how to do it)

Another one:
An L is formed by the subtraction of two rectangles. If a point is inside the minuend then it is not inside the L.