Add solution for challenge #62

Author: Mauricio Klein

README.md

@@ -61,3 +61,4 @@
 - [x] [Challenge 59: Sort Colors](challenge-59/)
 - [x] [Challenge 60: Group anagrams](challenge-60/)
 - [x] [Challenge 61: Full Binary Tree](challenge-61/)
+- [x] [Challenge 62: Palindrome with maximum "k" deletions](challenge-62/)

challenge-62/Makefile

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

challenge-62/README.md

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+# Palindrome with maximum "k" deletions
+
+This problem was asked by Google.
+
+## Description
+
+Given a string which we can delete at most k, return whether you can make a palindrome.
+
+## Example
+
+```
+Input:
+  word = "waterrfetawx"
+  k = 2
+
+Output: True # Deleting "f" and "x" gives us a palindrome
+```

challenge-62/__init__.py

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+"""
+  Time  complexity: O(2^min(n,k)) (where n = length of the word)
+  Space complexity: O(2^min(n,k)) (for the call stack)
+"""
+def has_palindrome(word, k):
+  return helper(word, k, 0, len(word)-1)
+
+def helper(word, k, left, right):
+  while left < right:
+    if word[left] != word[right]:
+      """ No more removals left: not a solution """
+      if k == 0:
+        return False
+     
+      """
+      Recurse...
+        - Removing the left most char  (l)
+        - Removing the right most char (r)
+      """
+      l = helper(word, k - 1, left + 1, right    )
+      r = helper(word, k - 1, left    , right - 1)
+
+      return l or r
+
+    left += 1
+    right -= 1
+
+  """ Found a palindrome """
+  return True

challenge-62/solver.py

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+import unittest
+from solver import has_palindrome
+
+class TestSolver(unittest.TestCase):
+  def test_has_palindrome(self):
+    self.assertTrue (has_palindrome("waterrfetawx", 2))
+    self.assertTrue (has_palindrome("waterrfetawx", 3))
+    self.assertFalse(has_palindrome("waterrfetawx", 1))
+    self.assertTrue (has_palindrome("waterretaw"  , 0))
+    self.assertTrue (has_palindrome("yyyyaxxxx"   , 8))
+    self.assertTrue (has_palindrome("yyyyxxxx"    , 8))
+
+if __name__ == "__main__":
+    unittest.main()