Non-negative Integers without Consecutive Ones — LeetCode 600 Python Solution

The problem

Given a positive integer n, return the number of the integers in the range [0, n] whose binary representations do not contain consecutive ones.

Example

Input

n = 5

Output

5

Explanation

Here are the non-negative integers <= 5 with their corresponding binary representations:

Python solution

class Solution:
    def findIntegers(self, n: int) -> int:
        @cache
        def dfs(i: int, pre: int, limit: bool) -> int:
            if i < 0:
                return 1
            up = (n >> i & 1) if limit else 1
            ans = 0
            for j in range(up + 1):
                if pre and j:
                    continue
                ans += dfs(i - 1, j, limit and j == up)
            return ans

        return dfs(n.bit_length() - 1, 0, True)

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 600. Non-negative Integers without Consecutive Ones is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

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