What is the optimal time complexity of solving Count Binary Strings?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Count Binary Strings?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Count Binary Strings?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Count Binary Strings?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Competitive ProgrammingEasy

Count Binary Strings

Learn how to solve the 'Count Binary Strings' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function count_binary_strings(n) that returns the number of binary strings of length n that do not contain any consecutive 1s.

Constraints

•1 <= n <= 45

Examples

Example 1

Input

count_binary_strings(2)

Output

Explanation

The valid strings of length 2 are '00', '01', and '10'.

Example 2

Input

count_binary_strings(3)

Output

Explanation

The valid strings of length 3 are '000', '001', '010', '100', and '101'.

Need a Hint?

Define subproblem states, establish the recurrence relation, and use memoization (top-down) or tabulation (bottom-up).

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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