Given an integer, write a function to determine if it is a power of two

Author: anantkaushik

231-power-of-two.py

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+"""
+Given an integer, write a function to determine if it is a power of two.
+
+Example 1:
+Input: 1
+Output: true
+
+Example 2:
+Input: 16
+Output: true
+
+Example 3:
+Input: 218
+Output: false
+"""
+class Solution(object):
+    def isPowerOfTwo(self, n):
+        return n > 0 and not(n & n-1)
+
+"""
+Explanation:
+At a power of 2, we only have one bit set to 1 at its respective decimal place (e.g. 1000).
+At the power of 2 minus 1, we have all the bits before the current decimal place set to 1 (e.g. 0111), which means that n & (n - 1) == 0 
+for powers of 2.
+The reason why this happens is because we're in the binary number system and a power of 2 means we're going to the next decimal place 
+(i.e. 0111 + 1 = 1000).
+
+What about when n is not a power of 2? If you look at a list of binary numbers:
+0100
+0101
+0110
+0111
+1000
+
+Remember how the power of 2 is the special case where adding 1 results in us moving to the next decimal place (i.e. 0111 + 1 = 1000)? 
+Since every other case doesn't result in that, there is at least the current power of 2's 1 bit overlapping with whatever the number 
+is (i.e. we're at 0100, 0101 will always share the 0100 bit. The only time the 0100 bit becomes 0 again is if we go to the next power of 2).
+"""