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For this problem, we will be writing a function which takes
two rectangles, determines the region in which they overlap
(which is also a rectangle), and returns that region.
Before proceeding, think about what the corner case(s) [no pun intended!]
in this problem might be.
1. Open the provided file called "rectangle.c"
2. In the "rectangle.c" file, define a struct for rectangles
which has 4 fields: x, y, width, and height. Each of these
fields should be an int. Use typedef so that the typename
"rectangle" refers to your struct.
3. One corner we might have to deal with is if the rectangle's
representation is non-standard: if the width or height are
negative. One way to deal with inputs that come in non-standard
formats is to "canonicalize" them---convert them to the standard
(or "canonical") representation. First, write the function
rectangle canonicalize(rectangle r);
which takes a rectangle, and "fixes" its representation
by ensuring that the width and height are non-negative (and
appropriately adjusting the x and/or y co-ordinate). That is,
if your canonicalize function were passed a rectangle with
x=3, y=2, width=-2, height=4
then it should return a rectangle with
x=1, y=2, width=2, height=4
as these both describe the same rectangle, but the later is
in a canonical representation.
It may be a good idea to stop and test this function
before proceeding. Compile and run your code.
The main function we have provided should be useful,
as it canonicalizes the rectangles it prints.
4. Now, write the function
rectangle intersection(rectangle r1, rectangle r2)
which takes two rectangles (r1, and r2), and returns
the rectangle representing the intersection of the two.
Note that there is a corner case where the correct answer
is "no intersection". We have not learned how to represent
"no such thing" yet, but we will consider a rectangle with
both width and height equal to 0 to mean "no such rectangle".
We will consider a rectangle to have one (but not the other)
of width or height equal to 0 to be an appropriate answer
when rectangles share an edge but do not overlap. For example,
x=0,y=0,width=1, height=1
and
x=-1,y=1,width=3,height=2
Should result in the "rectangle"
x=0,y=1,width=1,height=0
5. We have provided a main function which tests your code,
as well as correct output (rectangle_ans.txt) to diff against.
6. Submit your code
Hint:
Do Step 1 (work an example yourself) four or five times.
Draw a variety of different ways that rectangles can overlap.
Use these to help you think abou the general algorithm for how
to determine their overlapping region.
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