Determine overlapping rectangles

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【Determine overlapping rectangles】
On-Site Question 3 - SOLUTION ProblemGiven two rectangles, determine if they overlap. The rectangles are defined as a Dictionary, for example:
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r1 = {# x and y coordinates of the bottom-left corner of the rectangle ‘x‘: 2 , ‘y‘: 4,# Width and Height of rectangle ‘w‘:5,‘h‘:12}

If the rectangles do overlap, return the dictionary which describes the overlapping section
RequirementsMake sure the dictionary you output is in the same form as the input.
Feel free to use an IDE for the code, but make sure you use paper/pencil or whiteboard to draw out your plan and logic
SolutionThis is a problem where it helps a lot to draw out your thinking. There are a few things we will need to think about:

How can we determine an intersection?
What if a rectangle is fully inside another rectangle?
What if there is no intersection, but the rectangles share an edge?

The key to solving this problem is to break it up in to sub-problems. We can split up the problem into an x-axis problem and a y-axis problem.
We will create a function that can detect overlap in 1 dimension. Then we will split the rectangles into x and width, and y and height components. We can then determine that if there is overlap on both dimensions, then the rectangles themselves intersect!
In order to understand the calc_overlap function, draw out two flat lines and follow along with the function and notice how it detects an overlap!
Let‘s begin by creating a general function to detect overlap in a single dimension:

def calc_overlap(coor1,dim1,coor2,dim2): """ Takes in 2 coordinates and their length in that dimension """# Find greater of the two coordinates # (this is either the point to the most right #or the higher point, depending on the dimension)# The greater point would be the start of the overlap greater = max(coor1,coor2)# The lower point is the end of the overlap lower = min(coor1+dim1,coor2+dim2)# Return a tuple of Nones if there is no overlapif greater > = lower: return (None,None)# Otherwise, get the overlap length overlap = lower-greaterreturn (greater,overlap)

Now let‘s use this function to detect if the rectangles overlap!

def calc_rect_overlap(r1,r2):x_overlap, w_overlap = calc_overlap(r1[‘x‘],r1[‘w‘],r2[‘x‘],r2[‘w‘])y_overlap, h_overlap = calc_overlap(r1[‘y‘],r1[‘h‘],r2[‘y‘],r2[‘h‘])# If either returned None tuples, then there is no overlap! if not w_overlap or not h_overlap: print ‘There was no overlap!‘ return None# Otherwise return the dictionary format of the overlapping rectangle return { ‘x‘:x_overlap,‘y‘: y_overlap,‘w‘:w_overlap,‘h‘:h_overlap}

Our solution is O(1) for both time and space! Let‘s see it in action:
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