How do you solve Concatenation of Consecutive Binary Numbers on LeetCode?

Concatenation of Consecutive Binary Numbers (LeetCode #1680) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: Understanding bit manipulation can significantly optimize performance for problems involving binary representations.

What is the brute force solution for Concatenation of Consecutive Binary Numbers?

The brute force approach for Concatenation of Consecutive Binary Numbers is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves converting each integer from 1 to n into its binary representation, concatenating these binary strings, and then converting the final binary string back into a decimal number. This method is straightforward but inefficient for larger values of n. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Concatenation of Consecutive Binary Numbers?

Concatenation of Consecutive Binary Numbers uses the following concepts: Math, Bit Manipulation, Simulation. The recommended patterns to study are: Bit Manipulation, Simulation.

What are the interview tips for Concatenation of Consecutive Binary Numbers?

Always discuss your thought process and approach before jumping into coding. Consider edge cases, such as the smallest and largest possible values for n. Practice bit manipulation problems to become more comfortable with shifting and masking operations.

What are common mistakes when solving Concatenation of Consecutive Binary Numbers?

Not considering the impact of large numbers and overflow when concatenating binary strings. Forgetting to apply modulo operation to the final result, which can lead to incorrect outputs.

#1680

Concatenation of Consecutive Binary Numbers

Medium

MathBit ManipulationSimulationBit ManipulationSimulation

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

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Intuition

Time O(n)Space O(1)

The optimal approach leverages bit manipulation to build the result incrementally without creating a large binary string. By keeping track of the current result and the number of bits each integer contributes, we can efficiently compute the final value.

⚙️

Algorithm

4 steps

1Step 1: Initialize result to 0 and a variable to track the total number of bits used.
2Step 2: Loop through each integer from 1 to n.
3Step 3: For each integer, calculate its bit length and shift the result left by that many bits, then add the integer.
4Step 4: After processing all integers, return the result modulo (10^9 + 7).

solution.py7 lines

1def concatenatedBinary(n):
2    result = 0
3    for i in range(1, n + 1):
4        result = (result << i.bit_length()) | i
5    return result % (10**9 + 7)
6
7print(concatenatedBinary(3))

ℹ

Complexity note: The time complexity is O(n) because we iterate through each integer from 1 to n exactly once, and the operations performed inside the loop (bit shifting and bitwise OR) are constant time operations. The space complexity is O(1) since we only use a fixed amount of space for variables.

1Understanding bit manipulation can significantly optimize performance for problems involving binary representations.
2Using modulo operations early can help prevent overflow in languages with fixed integer sizes.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.