Add solution for challenge #33

Author: Mauricio Klein

README.md

@@ -32,3 +32,4 @@
 - [x] [Challenge 30: Merge sort](challenge-30/)
 - [x] [Challenge 31: Find cycle in indirected graph](challenge-31/)
 - [x] [Challenge 32: Shortest path in a indirected acyclic graph](challenge-32/)
+- [x] [Challenge 33: Merge Overlapping Intervals](challenge-33/)

challenge-33/Makefile

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

challenge-33/README.md

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+# Merge Overlapping Intervals
+
+This problem was asked by Microsoft.
+
+## Description
+
+You are given an array of intervals - that is, an array of tuples (start, end). The array may not be sorted, and could contain overlapping intervals. Return another array where the overlapping intervals are merged.
+
+## Example
+
+```
+Input:  [(1, 3), (5, 8) , (4, 10), (20, 25)]
+Output: [(1, 3), (4, 10), (20, 25)]
+Explanation: (5, 8) and (4, 10) can be merged into (4, 10)
+```

challenge-33/__init__.py

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+#
+# Time  complexity: O(n*log(n)) (for the sort)
+# Space complexity: O(n)        (for the result array)
+#
+def merge_overlapping_intervals(intervals):
+  # Sort intervals by start timestamp
+  intervals.sort(key=lambda interval: interval[0])
+
+  merged_intervals = []
+
+  for interval in intervals:
+    if merged_intervals and overlap(merged_intervals[-1], interval):
+      merged_intervals[-1] = merge(merged_intervals[-1], interval)
+    else:
+      merged_intervals.append(interval)
+
+  return merged_intervals
+
+def overlap(prev_i, next_i):
+  start, end = next_i[0], prev_i[1]
+
+  return start <= end
+
+def merge(prev_i, next_i):
+  prev_start, prev_end = prev_i
+  next_start, next_end = next_i
+
+  return (prev_start, max(prev_end, next_end))

challenge-33/solver.py

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+import unittest
+from solver import merge_overlapping_intervals
+
+class TestSolver(unittest.TestCase):
+  def test_partial_overlapping(self):
+    self.assertEqual(merge_overlapping_intervals([(1, 3), (5, 8) , (4, 10), (20, 25)]), [(1, 3), (4, 10), (20, 25)])
+
+  def test_full_overlap(self):
+    self.assertEqual(merge_overlapping_intervals([(1, 3), (5, 8) , (6, 7), (20, 25)]), [(1, 3), (5, 8), (20, 25)])
+
+  def test_multiple_overlaps(self):
+    self.assertEqual(merge_overlapping_intervals([(1, 5), (3, 6) , (4, 9), (20, 25)]), [(1, 9), (20, 25)])
+
+  def test_no_overlaps(self):
+    self.assertEqual(merge_overlapping_intervals([(1, 4), (5, 8), (20, 25)]), [(1, 4), (5, 8), (20, 25)])
+
+  def test_no_intervals(self):
+    self.assertEqual(merge_overlapping_intervals([]), [])
+
+if __name__ == "__main__":
+    unittest.main()