Create counting-bits.py

Author: kamyu104

Python/counting-bits.py

@@ -0,0 +1,37 @@
+# Time:  O(n)
+# Space: O(1)
+
+# Given a non negative integer number num. For every numbers i
+# in the range 0 <= i <= num calculate the number 
+# of 1's in their binary representation and return them as an array.
+#
+# Example:
+# For num = 5 you should return [0,1,1,2,1,2].
+#
+# Follow up:
+#
+# It is very easy to come up with a solution with run 
+# time O(n*sizeof(integer)). But can you do it in 
+# linear time O(n) /possibly in a single pass?
+# Space complexity should be O(n).
+# Can you do it like a boss? Do it without using
+# any builtin function like __builtin_popcount in c++ or
+# in any other language.
+# Hint:
+#
+# 1. You should make use of what you have produced already.
+# 2. Divide the numbers in ranges like [2-3], [4-7], [8-15]
+#    and so on. And try to generate new range from previous.
+# 3. Or does the odd/even status of the number help you in
+#    calculating the number of 1s?
+
+class Solution(object):
+    def countBits(self, num):
+        """
+        :type num: int
+        :rtype: List[int]
+        """
+        res = [0]
+        for i in xrange(1, num + 1):
+            res.append(res[i >> 1] + (i & 1))
+        return res