Add solution for challenge #44

Author: Mauricio Klein

README.md

@@ -43,3 +43,4 @@
 - [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/)
+- [x] [Challenge 44: Find the k-th Largest Element in a List](challenge-44/)

challenge-44/Makefile

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

challenge-44/README.md

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+# Find the k-th Largest Element in a List
+
+This problem was asked by Facebook.
+
+## Description
+
+Given a list, find the k-th largest element in the list.
+
+## Example
+```
+Input:  
+  list = [3, 5, 2, 4, 6, 8]
+  k = 3
+
+Output: 5
+```

challenge-44/__init__.py

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+import random
+
+def k_largest(nums, k):
+  N = len(nums)
+
+  k_index = N - k
+  quick_select(nums, k_index, 0, N-1)
+
+  return nums[k_index]
+
+def quick_select(nums, k, left, right):
+  if left == right:
+    return
+
+  wall, pivot = left, ((right + left) // 2)
+
+  # Move pivot to the end of the list
+  swap(nums, right, pivot)
+  pivot = right
+
+  for i in range(left, right):
+    if nums[i] < nums[pivot]:
+      swap(nums, i, wall)
+      wall += 1
+
+  # Put pivot in the right place
+  swap(nums, wall, pivot)
+  pivot = wall
+
+  if k < pivot:
+    quick_select(nums, k, left, pivot - 1)
+  elif k > pivot:
+    quick_select(nums, k, pivot + 1, right)
+
+def swap(arr, i, j):
+  arr[i], arr[j] = arr[j], arr[i]

challenge-44/solver.py

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+import unittest
+import random
+from solver import k_largest
+
+class TestSolver(unittest.TestCase):
+  def test_k_largest(self):
+    self.assertEqual(k_largest([3, 5, 2, 4, 6, 8], k=3), 5)
+    self.assertEqual(k_largest([3, 5, 2, 4, 6, 8], k=1), 8)
+    self.assertEqual(k_largest([3               ], k=1), 3)
+
+if __name__ == "__main__":
+    unittest.main()