Add solution for challenge #41

Author: Mauricio Klein

README.md

@@ -40,3 +40,4 @@
 - [x] [Challenge 38: Remove k-th Last Element From Linked List](challenge-38/)
 - [x] [Challenge 39: Remove Consecutive Nodes that Sum to 0](challenge-39/)
 - [x] [Challenge 40: Queue Using Two Stacks](challenge-40/)
+- [x] [Challenge 41: Maximum sequence of consecutive numbers](challenge-41/)

challenge-41/Makefile

@@ -0,0 +1,4 @@
+test:
+	python test_*.py
+
+.PHONY: test

challenge-41/README.md

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+# Maximum sequence of consecutive numbers
+
+This problem was asked by Facebook.
+
+## Description
+
+Given a list of integers L, find the maximum length of a sequence of consecutive numbers that can be formed using elements from L.
+
+## Example
+```
+Input: [5, 2, 99, 3, 4, 1, 100]
+Output: 5 # [1, 2, 3, 4, 5]
+```

challenge-41/__init__.py

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+#
+# Time  complexity: O(n*log(n)) (for the sorting)
+# Space complexity: O(1)
+#
+def max_sequence_length(nums):
+  nums.sort()
+
+  max_seq, cur_seq = 0, 0
+  prev_num = None
+
+  for num in nums:
+    if prev_num == None or prev_num + 1 == num:
+      cur_seq += 1
+    else:
+      max_seq = max(max_seq, cur_seq)
+      cur_seq = 1
+
+    prev_num = num
+
+  # Remaining
+  max_seq = max(max_seq, cur_seq)
+  
+  return max_seq

challenge-41/solver.py

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+import unittest
+import random
+from solver import max_sequence_length
+
+class TestSolver(unittest.TestCase):
+  def test_max_sequence_length(self):
+    nums = [1,2,3,4,5,99,100]
+    random.shuffle(nums)
+    self.assertEqual(max_sequence_length(nums), 5) # [1, 2, 3, 4, 5]
+
+    nums = [1,2,5,6,7,15,16]
+    random.shuffle(nums)
+    self.assertEqual(max_sequence_length(nums), 3) # [5, 6, 7]
+
+    nums = [1,3,5,7,9]
+    random.shuffle(nums)
+    self.assertEqual(max_sequence_length(nums), 1)
+
+    nums = [-2,-1,0,1,2,5,6]
+    random.shuffle(nums)
+    self.assertEqual(max_sequence_length(nums), 5) # [-2, -1, 0, 1, 2]
+
+    nums = [1,2,5,6,7,8,9]
+    random.shuffle(nums)
+    self.assertEqual(max_sequence_length(nums), 5) # [5,6,7,8,9]
+    
+    nums = []
+    random.shuffle(nums)
+    self.assertEqual(max_sequence_length(nums), 0)
+
+if __name__ == "__main__":
+    unittest.main()