Add solution for challenge #35

Author: Mauricio Klein

README.md

@@ -34,3 +34,4 @@
 - [x] [Challenge 32: Shortest path in a indirected acyclic graph](challenge-32/)
 - [x] [Challenge 33: Merge Overlapping Intervals](challenge-33/)
 - [x] [Challenge 34: Subset sum problem](challenge-34/)
+- [x] [Challenge 35: Count rectangles](challenge-35/)

challenge-35/Makefile

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+test:
+	python test_*.py
+
+.PHONY: test

challenge-35/README.md

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+# Count rectangles
+
+## Description
+
+Given a list of carthesian pairs (x, y), return the number of rectangles formed by these pairs.
+
+## Example
+
+```
+Input:[ (1,3), (1,4), (2,3), (2,4), (3,3), (3,4), (4,3), (4,4) ]
+Output: 4
+```

challenge-35/__init__.py

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+#
+# Time complexity: O(n^2)
+# Space complexity: O(n/2) (worst case, where we've distinct vertical lines)
+#
+def count_rectangles(points):
+  vertical_lines = {}
+
+  for p1 in points:
+    for p2 in points:
+      # Same points don't make a line
+      if p1 == p2:
+        continue
+
+      if stacked(p1, p2):
+        point = make_point(p1, p2)
+        vertical_lines[point] = vertical_lines.get(point, 0) + 1
+
+  acc = 0
+  for count in vertical_lines.values():
+    # We need at least two vertical lines to make a rectangle
+    if count < 2:
+      continue
+
+    acc += 1 if count == 2 else count
+
+  return acc
+
+def make_point(p1, p2):
+  p1_y, p2_y = p1[1], p2[1]
+
+  return (
+    min(p1_y, p2_y), 
+    max(p1_y, p2_y)
+  )
+
+
+def stacked(p1, p2):
+  p1_x, p1_y = p1
+  p2_x, p2_y = p2
+
+  if p1_x != p2_x:
+    return False
+
+  return p1_y < p2_y

challenge-35/solver.py

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+import unittest
+from solver import count_rectangles
+
+class TestSolver(unittest.TestCase):
+  def test_count_rectangles(self):
+    points = [
+      (1,3), (1,4), (2,3), (2,4)
+    ]
+
+    self.assertEqual(count_rectangles(points), 1)
+
+  def test_count_multiple_rectangles(self):
+    points = [
+      (1,3), (1,4), (2,3), (2,4),
+      (2,1), (2,2), (3,1), (3,2)
+    ]
+    
+    self.assertEqual(count_rectangles(points), 2)
+
+  def test_count_multiple_paralel_rectangles(self):
+    points = [
+      (1,3), (1,4), (2,3), (2,4), (3,3), (3,4), (4,3), (4,4)
+    ]
+    
+    self.assertEqual(count_rectangles(points), 4)
+
+if __name__ == "__main__":
+    unittest.main()