#
# Axis‑aligned rectangles are simply rectangles whose edges are parallel to the
# coordinate axes — meaning their sides are horizontal and vertical.
# That single assumption makes the overlap test dramatically simpler and faster.
#
#
# Rectangle overlap detection (axis-aligned)
#
# Each rectangle is defined by:
# - x, y : coordinates of its top-left corner
# - w, h : width and height
#
# Two rectangles DO NOT overlap if any separating condition is true:
# - One is completely to the left of the other
# - One is completely to the right of the other
# - One is completely above the other
# - One is completely below the other
#
# Otherwise, they overlap.
#
# This is the standard O(1) test for axis-aligned rectangles.
#
class Rect
attr_accessor :x, :y, :w, :h # top-left X, top-left Y, width, height
def initialize(x, y, w, h)
@x = x
@y = y
@w = w
@h = h
end
end
#
# Returns true if rectangles A and B overlap.
#
def rectangles_overlap(a, b)
# Compute edges of A
a_left = a.x
a_right = a.x + a.w
a_top = a.y
a_bottom = a.y + a.h
# Compute edges of B
b_left = b.x
b_right = b.x + b.w
b_top = b.y
b_bottom = b.y + b.h
# Separating conditions:
return false if a_right <= b_left # A is left of B
return false if b_right <= a_left # B is left of A
return false if a_bottom <= b_top # A is above B
return false if b_bottom <= a_top # B is above A
true # Otherwise, they overlap
end
# Example rectangles
a = Rect.new(10, 10, 30, 20) # Example rectangle A
b = Rect.new(25, 15, 40, 25) # Overlaps A
c = Rect.new(100, 100, 10, 10) # Does not overlap A
puts "A vs B overlap? #{rectangles_overlap(a, b) ? 'YES' : 'NO'}"
puts "A vs C overlap? #{rectangles_overlap(a, c) ? 'YES' : 'NO'}"
#
# run:
#
# A vs B overlap? YES
# A vs C overlap? NO
#
