Create integer-replacement.py

Python/integer-replacement.py

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+# Time:  O(logn)
+# Space: O(1)
+
+# Given a positive integer n and you can do operations as follow:
+#
+# If n is even, replace n with n/2.
+# If n is odd, you can replace n with either n + 1 or n - 1.
+# What is the minimum number of replacements needed for n to become 1?
+#
+# Example 1:
+#
+# Input:
+# 8
+#
+# Output:
+# 3
+#
+# Explanation:
+# 8 -> 4 -> 2 -> 1
+# Example 2:
+#
+# Input:
+# 7
+#
+# Output:
+# 4
+#
+# Explanation:
+# 7 -> 8 -> 4 -> 2 -> 1
+# or
+# 7 -> 6 -> 3 -> 2 -> 1
+
+# Iterative solution.
+class Solution(object):
+    def integerReplacement(self, n):
+        """
+        :type n: int
+        :rtype: int
+        """
+        result = 0
+        while n != 1:
+            b = n & 3
+            if n == 3:
+                n -= 1
+            elif b == 3:
+                n += 1
+            elif b == 1:
+                n -= 1
+            else:
+                n /= 2
+            result += 1
+
+        return result
+
+
+# Time:  O(logn)
+# Space: O(logn)
+# Recursive solution.
+class Solution2(object):
+    def integerReplacement(self, n):
+        """
+        :type n: int
+        :rtype: int
+        """
+        if n < 4:
+            return [0, 0, 1, 2][n]
+        if n % 4 in (0, 2):
+            return self.integerReplacement(n / 2) + 1
+        elif n % 4 == 1:
+            return self.integerReplacement((n - 1) / 4) + 3
+        else:
+            return self.integerReplacement((n + 1) / 4) + 3
+