What is the optimal time complexity of solving N bit binary numbers?

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 N bit binary numbers?

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 N bit binary numbers?

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 N bit binary numbers?

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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Python BasicsEasy

N bit binary numbers

Learn how to solve the 'N bit binary numbers' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function n_bit_binary(n) that generates all n-bit binary numbers (as strings) such that in every prefix of the binary string, the number of 1s is greater than or equal to the number of 0s. Return the result as a sorted list of strings in lexicographic order.

Constraints

•1 <= n <= 15

Examples

Example 1

Input

n = 3

Output

['110', '111']

Explanation

For '110': prefixes '1'(1>=0✓), '11'(2>=0✓), '110'(2>=1✓). For '111': all prefixes have more 1s. '100','101','010' etc. fail the prefix condition.

Example 2

Input

n = 2

Output

['10', '11']

Explanation

'10': prefix '1' has 1>=0✓, '10' has 1>=1✓. '11': both prefixes valid. '00','01' fail.

Example 3

Input

n = 1

Output

['1']

Explanation

Only '1' satisfies the condition. '0' has prefix '0' with 0 ones and 1 zero.

Need a Hint?

Use simple arithmetic operators (like modulo `%`, division `//`), conditional checks, or loops to inspect number properties.

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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