Is Non-negative Integers without Consecutive Ones easy or hard?

LeetCode classifies this problem as Hard because it requires recognizing the Fibonacci relationship between valid binary strings and applying a digit DP style scan of n. Once the pattern is understood, the implementation is relatively short but the insight is non-trivial.

Non-negative Integers without Consecutive Ones Python/Java solution

Python and Java implementations typically precompute a DP array for valid binary sequences, then iterate through the bits of n from the most significant bit. When a 1 is encountered, the algorithm adds the number of sequences that start with 0 at that position. Both implementations run in O(log n) time and use constant extra space.

How to solve Non-negative Integers without Consecutive Ones in O(n)?

The problem is typically solved in O(log n) time rather than O(n) because the algorithm operates on the binary digits of n. Build a DP array where dp[i] stores the number of valid binary strings of length i without consecutive ones. Then iterate through the bits of n, accumulating counts whenever a 1 appears while ensuring no consecutive 1s occur.

What is the best approach for Non-negative Integers without Consecutive Ones?

The optimal approach uses dynamic programming based on a Fibonacci-like recurrence. Precompute how many valid binary strings exist for each bit length, then scan the bits of n from most significant to least significant. Each time you encounter a 1, add the count of numbers formed by placing 0 at that position and filling the remaining bits with valid sequences. The algorithm runs in O(log n) time and O(1) space.

Is Non-negative Integers without Consecutive Ones asked at Google/Amazon/Meta?

This problem represents a common interview pattern involving digit DP and binary constraints. Variants appear in interviews at large tech companies such as Google, Amazon, and Meta where candidates must count numbers under specific digit restrictions. It tests dynamic programming, bit manipulation, and reasoning about binary representations.

What data structure is used in Non-negative Integers without Consecutive Ones?

The main structure is a small dynamic programming array that stores Fibonacci-like counts for binary lengths. The algorithm also uses bit operations to inspect each bit of n. In recursive solutions, a memoization map or DP table caches states defined by index, previous bit, and tight prefix constraint.

What is the time complexity of Non-negative Integers without Consecutive Ones?

The optimal solution runs in O(log n) time because it processes each bit of the binary representation of n once. Precomputing the Fibonacci-style DP array also takes O(log n). Space complexity can be O(1) when using a fixed-size array for bit lengths.

Description Solution Video 15:26

600. Non-negative Integers without Consecutive Ones

Hard43.7% acceptance5 companies

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 1:

Input: n = 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.

Example 2: