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

Author: kamyu104

Diff for: Python/non-negative-integers-without-consecutive-ones.py

@@ -0,0 +1,41 @@
+# 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