Add solution for challenge #45

Author: Mauricio Klein

README.md

@@ -44,3 +44,4 @@
 - [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/)
+- [x] [Challenge 45: Occurrences of a number in a sorted array](challenge-45/)

challenge-45/Makefile

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

challenge-45/README.md

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+# Occurrences of a number in a sorted array
+
+## Description
+
+Given a sorted array, write a function that returns the number of occurences of a number in this array.
+
+**Can you do it in logarithmic time (O(logn))?**
+
+## Example
+```
+Input:  
+  arr = [1,2,2,2,5,7,9]
+  k = 2
+
+Output: 3
+```

challenge-45/__init__.py

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+#
+# Time  complexity: O(logn)
+# Space complexity: O(1)
+#
+def occurrences(nums, k):
+  left  = binsearch(nums, k, search_min=True )
+  right = binsearch(nums, k, search_min=False)
+
+  # "k" not found on the array
+  if left == -1 or right == -1:
+    return 0
+
+  return right - left + 1
+
+def binsearch(nums, k, search_min):
+  def inbounds(x):
+    return 0 <= x < len(nums)
+
+  left, right = 0, len(nums)
+
+  while left <= right:
+    middle = (left + right) // 2
+
+    if k < nums[middle]:
+      right = middle - 1
+    elif k > nums[middle]:
+      left = middle + 1
+    else:
+      if search_min:
+        if inbounds(middle - 1) and nums[middle - 1] == k:
+          # Proceed looking for the min on the left side
+          right = middle - 1
+        else:
+          return middle
+      else:
+        if inbounds(middle + 1) and nums[middle + 1] == k:
+          # Proceed looking for the max on the right side
+          left = middle + 1
+        else:
+          return middle
+
+  return -1

challenge-45/solver.py

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+import unittest
+from solver import occurrences
+
+class TestSolver(unittest.TestCase):
+  def test_occurrences(self):
+    self.assertEqual(occurrences([1, 2, 2, 2, 5, 7, 9], k=2), 3)
+    self.assertEqual(occurrences([1, 2, 5, 7, 8, 9, 9], k=9), 2)
+    self.assertEqual(occurrences([1, 1, 2, 5, 7, 8, 9], k=1), 2)
+    self.assertEqual(occurrences([1, 2, 3, 5, 7, 8, 9], k=0), 0)
+
+if __name__ == "__main__":
+    unittest.main()