Add solution for challenge #43

Author: Mauricio Klein

README.md

@@ -42,3 +42,4 @@
 - [x] [Challenge 40: Queue Using Two Stacks](challenge-40/)
 - [x] [Challenge 41: Maximum sequence of consecutive numbers](challenge-41/)
 - [x] [Challenge 42: Depth of a stringified binary tree](challenge-42/)
+- [x] [Challenge 43: Contiguous Subarray with Maximum Sum](challenge-43/)

challenge-43/Makefile

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

challenge-43/README.md

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+# Contiguous Subarray with Maximum Sum
+
+This problem was asked by Twitter.
+
+## Description
+
+You are given an array of integers. Find the maximum sum of all possible contiguous subarrays of the array.
+
+*Your solution should run in linear time.*
+
+## Example
+```
+Input: [34, -50, 42, 14, -5, 86]
+Output: 137 ([42, 14, -5, 86])
+```

challenge-43/__init__.py

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+#
+# Time  complexity: O(n)
+# Space complexity: O(1)
+#
+def max_subarray(nums):
+  # Kadane's algorithm
+  current_sum, max_sum = 0, 0
+
+  for num in nums:
+    current_sum = max(0, current_sum + num)
+    max_sum     = max(max_sum, current_sum)
+
+  return max_sum

challenge-43/solver.py

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+import unittest
+from solver import max_subarray
+
+class TestSolver(unittest.TestCase):
+  def test_max_subarray(self):
+    self.assertEqual(max_subarray([34, -50, 42, 14, -5, 86]), 137) # Max sum is given by "[42, 14, -5, 86]"
+    self.assertEqual(max_subarray([-1, -2, -3             ]),   0) # Max sum is given by "[]"
+    self.assertEqual(max_subarray([-1, 1, 1, 1, -1, 4, -1 ]),   6) # Max sum is given by "[1, 1, 1, -1, 4]"
+    self.assertEqual(max_subarray([                       ]),   0) # Max sum is given by "[]"
+
+if __name__ == "__main__":
+    unittest.main()