non-negative-integers-without-consecutive-ones.py

# Time:  O(1)
# Space: O(1)

# Given a positive integer n, find the number of non-negative integers less than
# or equal to n, whose binary representations do NOT contain consecutive ones.
#
# Example 1:
# Input: 5
# Output: 5
# Explanation: 
# Here are the non-negative integers <= 5 with their corresponding binary representations:
# 0 : 0
# 1 : 1
# 2 : 10
# 3 : 11
# 4 : 100
# 5 : 101
# Among them, only integer 3 disobeys the rule (two consecutive ones) and the other 5 satisfy the rule. 
# Note: 1 <= n <= 10^9

class Solution(object):
    def findIntegers(self, num):
        """
        :type num: int
        :rtype: int
        """
        dp = [0] * 32
        dp[0], dp[1] = 1, 2
        for i in xrange(2, len(dp)):
            dp[i] = dp[i-1] + dp[i-2]
        result, prev_bit = 0, 0
        for i in reversed(xrange(31)):
            if (num & (1 << i)) != 0:
                result += dp[i]
                if prev_bit == 1:
                    result -= 1
                    break
                prev_bit = 1
            else:
                prev_bit = 0
        return result + 1