Add solution for challenge #53

Author: Mauricio Klein

README.md

@@ -52,3 +52,4 @@
 - [x] [Challenge 50: Create a balanced binary search tree](challenge-50/)
 - [x] [Challenge 51: Subsequences of string](challenge-51/)
 - [x] [Challenge 52: Deepest Node in a Binary Tree](challenge-52/)
+- [x] [Challenge 53: Thousand missing numbers](challenge-53/)

challenge-53/Makefile

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

challenge-53/README.md

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+# Thousand missing numbers
+
+This problem was asked by Two Sigma.
+
+## Description
+
+You are given an unsorted list of 999,000 unique integers, each from 1 and 1,000,000. Find the missing 1000 numbers.
+
+What is the computational and space complexity of your solution?

challenge-53/__init__.py

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+#
+# Time complexity : O(n)       (every elements is swapped at most once)
+# Space complexity: O(1000000) (constant one million, for the extended array)
+#
+def first_thousand_missing(nums):
+  # Extend the array to length 1M, filling with "None"
+  diff = 1000000 - len(nums)
+  nums.extend([None for _ in range(diff)])
+
+  # Put the elements in the right position (i.e. nums[i] = i+1)
+  # If find a "None", skip it)
+  for i in range(len(nums)):
+    while nums[i] != None and nums[i] != i+1:
+      num = nums[i]
+      nums[i], nums[num - 1] = nums[num - 1], nums[i]
+
+  # Iterate over the nums and, when find a "None", means
+  # the element at the position is missing
+  missing = []
+  for i in range(len(nums)):
+    if nums[i] == None:
+      missing.append(i+1)
+
+  return missing

challenge-53/solver.py

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+import unittest, random
+from solver import first_thousand_missing
+
+class TestSolver(unittest.TestCase):
+  def test_first_thousand_missing(self):
+    nums = range(1,1000001)
+    missing = random.sample(nums, 1000)
+
+    # Remove the missing values from the array
+    for num in missing:
+      nums.remove(num)
+
+    # Shuffle the array
+    random.shuffle(nums)
+
+    # Sort the missing values
+    missing.sort()
+
+    self.assertEqual(first_thousand_missing(nums), missing)
+
+if __name__ == "__main__":
+    unittest.main()