CareerCup

Definition:
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The union of two rectangles is the smallest single rectangle that completely covers both of the areas covered by the two given rectangles.

Let,
Co-ordinates of Rectangle 1 be,
left top (x1,y1),
right bottom (x2,y2)
Co-ordinates of Rectangle 2 be,
left top (x3,y3),
right bottom (x4,y4)
And x increases when going right an y increases when going up


Co-ordinate of the new union'ed rectangle,
left top (min(x1,x3),max(y1,y3))
right bottom (max(x2,x4),min(y2,y4))

Input: widths, heights, top-left coordinates.

Position the top-left corners of the rects at the origin(widths and heights already known for both rects so no computation necessary). Then the final rect is (max(w1,w2),max(h1,h2)).

Can you please explain what is max and min?? a little elaboration might be good enough if you can..thanks

Aren't Co-ordinate of the new union'ed rectangle?
left top (max(x1,x3),min(y1,y3))
right bottom (min(x2,x4),max(y2,y4))

max = maximum of two numbers
min = minimum of two numbers

I dont think that definition is correct. there is no guarantee that the union is a rectangle. union means shape that covers both rentangles.

Should it be the area of union? The real union is hard to return if
Two rects do not have any intersection;
Union of two rects is a ploygon; ...
Anyway I don't follow this question

you have an intersection answer in previous interviews.
there is an answer writeen by James. i think its very similar, except that the interior points sould be replaced by exterior points.

There is a big problem in all the above answers, whether finding intersection or union, whatever you want to call it. It'll fail when none of the corners of the rectangles is inside the other.

for example
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or even more difficult

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comments?

I think david's solve will works.

As Eila pointed out, we have intersection of the two rectangles then, Union (A,B) = A + B - Intersection(A,B).
This should solve the problem.

The question Elia talking about.....
careercup.com/question/?q=7a052c02-eacf-4fd0-b029-75c4da495ba6

Are their sides supposed to be parallel?

The fefinition of the "union of rectangles" is accurate in the 1st post:
this is the smallest rectangle which includes both our rectangles within it.

Given:
R1: (x1,y1),(x2,y2);
R2: (x3,y3),(x4,y4);

No assumptions about their orientations and coordinate system is needed (i.e. x1>x2 or vise versa), still we have:

left: min(x1,x2,x3,x4);
right: max(x1,x2,x3,x4);
top: min(y1,y2,y3,y4);
bottom: max(y1,y2,y3,y4).

Union: (left,bottom), (right, top)

.

monte carlo method