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# Thursday Code Puzzler: Overlapping Rectangles

04.25.2013
| 3733 views |

Thursday is code puzzler day here at DZone. The idea is simple: solve the coding problem as efficiently as you can, in any language or framework that you find suitable.

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Determine if Two Rectangles are Overlapping

Write a function that takes two rectangles and determines if they overlap. The rectangle data structure is x, y, width, height.

Catch up on all our previous puzzlers here.

Tags:

### Frank Dietrich replied on Thu, 2013/04/25 - 2:54pm

Java

```@Test
public void overlapTests() {
Rectangle r1;
Rectangle r2;

r1 = new Rectangle(10, 10, 20, 20);
r2 = new Rectangle(0, 0, 20, 20);
Assert.assertTrue("r1 overlap r2", r1.intersects(r2));

r1 = new Rectangle(10, 10, 5, 5);
r2 = new Rectangle(0, 0, 20, 20);
Assert.assertTrue("r1 overlap r2", r1.intersects(r2));

r1 = new Rectangle(10, 10, 5, 5);
r2 = new Rectangle(20, 20, 20, 20);
Assert.assertFalse("r1 do not overlap r2", r1.intersects(r2));
}```

### Peter Huber replied on Fri, 2013/04/26 - 2:50am

@Frank Dietrich: +1 for knowing the API!

---

You can use a much-simplified Version of SAT (Seperating Axis Theorem) which works for any convex object composed of line segements.

Basically the simplified check is: Check if their projections on X-Axis overlap AND if their projections on Y-Axis overlap.

Assuming the rectangles have not been rotated the projections to the axis are very simple...

Let's say R1 is left of R2, then I have to check if their x-Axis-Segments overlap (I assume there's no negative width/heigth extents) - CX12: R1.x + R1.width > R2.x

Then let's say R1 is below R2 - again check if their y axis overlap - CY12: R1.y + R1.height > R2.y

To complete the check I have to add both checks with changed roles and "and" the both axis-related checks (CX12||CX21) && (CY12||CY21)

### koen handekyn replied on Wed, 2013/05/01 - 2:29pm

in ruby
```class Range # extend Range class
def overlaps(other) !(self.max<other.begin or other.max<self.begin) end
end

Rectangle = Struct.new(:x, :y, :width, :height)
class Rectangle # a Rectangle is a struct with extras
def xr() (x)..(x+width) end
def yr() (y)..(y+height) end
def overlap(other) xr.overlaps(other.xr) && yr.overlaps(other.yr) end
end
```
```# basic test

r1 = Rectangle.new(0,0,20,20)
r2 = Rectangle.new(10,5,20,20)
r3 = Rectangle.new(25,5,20,20)
r4 = Rectangle.new(25,25,20,20)

puts r1.overlap(r2) == true
puts r1.overlap(r3) == false
puts r1.overlap(r4) == false
```

### Wissem Belguidoum replied on Wed, 2013/05/01 - 5:46pm

Java :

```public class OverlappingRectangles {

public static void main(String[] args) {
Rectangle r1 = new Rectangle(15, 15, 15, 15);
Rectangle r2 = new Rectangle(10, 10, 20, 20);
System.out.println(areOverlapping(r1, r2));
}

private static boolean areOverlapping(Rectangle r1, Rectangle r2)  {
List<Rectangle> recs = Arrays.asList(r1,r2);
Collections.sort(recs, new ByXComparator());
boolean condition1 = (recs.get(0).getX() + recs.get(0).getWidth()) > recs.get(1).getX();
Collections.sort(recs, new ByYComparator());
boolean condition2 = (recs.get(0).getY() + recs.get(0).getHeight()) > recs.get(1).getY();
return condition1 && condition2;
}

static class ByXComparator implements Comparator<Rectangle> {
@Override
public int compare(Rectangle o1, Rectangle o2) {
Double x1 = o1.getX();
Double x2 = o2.getX();
return x1.compareTo(x2);
}
}

static class ByYComparator implements Comparator<Rectangle> {
@Override
public int compare(Rectangle o1, Rectangle o2) {
Double y1 = o1.getY();
Double y2 = o2.getY();
return y1.compareTo(y2);
}
}
}
```

### Knut W. Hansson replied on Wed, 2013/05/01 - 4:04pm in response to: Peter Huber

Well explained, Peter, but I think you might have to rethink your final check. In the example below, I beleive both CX12 and CY12 are true and therefore the final check should return true, but obviously the two rectangels don't overlap. What do you say?

### Bob Beechey replied on Wed, 2013/05/01 - 9:40pm

Just the obvious in Python, using my own rect part class:

```class rect:
def __init__(self, xin=0,yin=0,length=10,height=10):
self.x=xin
self.y=yin
self.length = length
self.height = height

def is_overlap(self, other):
xdiff = abs(self.x-other.x)
ydiff = abs(self.y-other.y)
if self.x < other.x:
xlap = xdiff < self.length
else:
xlap = xdiff < other.length
if self.y < other.y:
ylap = ydiff < self.height
else:
ylap = ydiff < other.height
return xlap and ylap

r1 = rect(5,6,20,10)
r2=rect(6,15,20,10)
print(r1.is_overlap(r2))
r2=rect(7,18,20,10)
print(r1.is_overlap(r2))
print(r2.is_overlap(r1))

```

### Andre Rieck replied on Thu, 2013/05/02 - 3:46am

#!/usr/bin/python

import unittest

def rectanglesOverlap(r1,r2) :
""" Tests whether two Rectangles represented by two tuples (x,y,width,height) overlap."""
X=0; Y=1; W=2; H=3;
return r1[X] <= r2[X]+r2[W] and r1[X]+r1[W] >= r2[X] and \
r1[Y] <= r2[Y]+r2[H] and r1[Y]+r1[H] >= r2[Y]

class TestOverlappingRectangles(unittest.TestCase) :

def test_overlapping(self) :
self.assertTrue(rectanglesOverlap((10,10,20,20),(0,0,20,20)))
self.assertTrue(rectanglesOverlap((10,10,5,5),(0,0,20,20)))
self.assertTrue(rectanglesOverlap((0,0,20,20),(10,5,20,20)))

def test_non_overlapping(self) :
self.assertFalse(rectanglesOverlap((10,10,5,5),(20,20,20,20)))
self.assertFalse(rectanglesOverlap((0,0,20,20),(25,5,20,20)))
self.assertFalse(rectanglesOverlap((0,0,20,20),(25,25,20,20)))

if (__name__=='__main__') :
unittest.main()

### Clinton Lee replied on Mon, 2013/05/06 - 8:43am

In F#

```let within (x1, y1, width1, height1) (x2, y2, width2, height2) =
let pointWithin start length point = (point >= start) && (point < (start + length))
let lineWithin p1 l1 p2 l2 = (pointWithin p1 l1 p2) || (pointWithin p2 l2 p1)
(lineWithin x1 width1 x2 width2) && (lineWithin y1 height1 y2 height2);;
```

### Philippe Lhoste replied on Mon, 2013/05/27 - 6:34am in response to: Knut W. Hansson

Knut, I think you missed the last sentence, about changing roles and doing a AND.