Check if 2 rectangles fit in another one, given their length and height

I was very intrigued with the manner to solve this problem. The program needs to know if 2 rectangles fit in another one, considering the lines of the 2 rectangles are always parallel to the other one's.

I know I could just put everything in a single if, but is that more readable? I want to know a good approach for this situation, using only conditions.

NOTE: x and y represent the first rectangle's width and height (the one that will fit the other 2) and l1, h1, l2, and h2 represent the other 2 rectangles' width and height.

```
#include

int main(void)
{
int x, y, l1, h1, l2, h2;

scanf("%d %d %d %d %d %d", &x, &y, &l1, &h1, &l2, &h2);

if ((l1 + l2 <= x && h1 <= y && h2 <= y) ||
(h1 + h2 <= x && l1 <= y && l2 <= y))
{
puts("They fit.");
}
else if ((l1 <= x && h2 <= x && h1 + l2 <= y) ||
(h1 <= x && l2 <= x && l1 + h2 <= y))
{
puts("They fit.");
}

Any two rectangles can fit into a third rectangle (without overlapping with each other) only under 2 cases:

As mentioned in the question, consider:

• x,y -> length and height of first rectangle into which below two rectangles must fit.

• l1,h1 -> length/width and height of second rectangle.

• l2,h2 -> length and height of third rectangle.

Note: You could use structures or 2-dimensional arrays for better readability.

Case 1:

-
When x is greater than or equal to l1+l2

-
Here the height y must be greater than or equal to maximum of h1 and h2 for the rectangles to fit in, else it doesn't fit in.

Note: x >= l1+12 can be written as ((x >= l1) && (x-l1 >= l2)). This is to avoid the overflow while adding integers.

Case 2:

-
When y is greater than or equal to h1+h2

-
Here the length x must be greater than or equal to maximum of l1 and l2 for the rectangles to fit in, else it doesn't fit in.

Note: similarly, even here y >= h1+h2 can be written as (y >= h1) && (y-h1 >= h2). This is to avoid the overflow while adding integers.

Now, keeping the above 2 cases in mind, a simple function can be constructed this way:

int fit( int x, int y, int l1, int h1, int l2, int h2)
{
    //return 1 for fit and 0 if does not fit

    //case 1 or case 2
    if( ( ((x >= l1) && (x-l1 >= l2)) && y >= max(h1,h2)) || 
        ( ((y >= h1) && (y-h1 >= h2)) && x >= max(l1,l2)) )
    {
            return 1;
    }

    return 0;
}

Note: here max() is a function which returns the larger value among the two sent arguments.

int max(int a, int b)
{
    if(a>b)
    {
        return a;
    }
    return b;
}

Now, the 2 rectangles can be sent in 4 different ways to check if they can fit in the rectangle of dimensions x and y:

//sending as entered by the user
fit( x, y, l1, h1, l2, h2)

//interchanging length and height of anyone rectangle
fit( x, y, h1, l1, l2, h2)

//interchanging length and height of other rectangle
fit( x, y, l1, h1, h2, l2)

//interchanging lengths and heights of both rectangles
fit( x, y, h1, l1, h2, l2)

• Now, you can easily know whether the rectangles fit or does not fit by checking for the return value of fit() function.

• If return value of anyone of the above four function calls is 1 then the rectangles fit in!

-
You could use the main() function as:

int main(void)
{
    int x, y, l1, h1, l2, h2;

    scanf("%d %d %d %d %d %d", &x, &y, &l1, &h1, &l2, &h2);

    //tests for fit
    if(fit( x, y, l1, h1, l2, h2) || 
       fit( x, y, h1, l1, l2, h2) || 
       fit( x, y, l1, h1, h2, l2) || 
       fit( x, y, h1, l1, h2, l2))
    {
        printf("fits");
    }
    else
    {
        printf("doesn't fit");
    }

}

-
The above if block functions similarly as an else-if ladder because, || stops evaluation on the first true (i.e, function returns 1).

• So, if any of the function returns a 1, then then "fits" gets printed out and program terminates

• In case, if none of the function calls return 1 the "doesn't fit" gets printed out and program terminates

Altogether your code would be:

#include 

int max(int a, int b)
{
    if(a>b)
    {
        return a;
    }
    return b;
}

int fit( int x, int y, int l1, int h1, int l2, int h2)
{
    //return 1 for fit and 0 if does not fit

    //case 1 or case 2
    if( ( ((x >= l1) && (x-l1 >= l2)) && y >= max(h1,h2)) || 
        ( ((y >= h1) && (y-h1 >= h2)) && x >= max(l1,l2)) )
    {
            return 1;
    }

    return 0;
}

int main(void)
{
    int x, y, l1, h1, l2, h2;

    scanf("%d %d %d %d %d %d", &x, &y, &l1, &h1, &l2, &h2);

    //tests for fit
    if( fit( x, y, l1, h1, l2, h2) || 
        fit( x, y, h1, l1, l2, h2) || 
        fit( x, y, l1, h1, h2, l2) || 
        fit( x, y, h1, l1, h2, l2))
    {
        printf("fits");
    }
    else
    {
        printf("doesn't fit");
    }

}

StackExchange Code Review Q#133118, answer score: 11