How do you solve Circular Permutation in Binary Representation on LeetCode?

Circular Permutation in Binary Representation (LeetCode #1238) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Gray code ensures that only one bit changes between consecutive numbers, which is crucial for the problem.

What is the time complexity of Circular Permutation in Binary Representation?

The optimal solution for Circular Permutation in Binary Representation runs in O(n) time and uses O(n) space. Generating the Gray code sequence takes O(n) time, and rotating the array also takes O(n), leading to an overall complexity of O(n).

What is the brute force solution for Circular Permutation in Binary Representation?

The brute force approach for Circular Permutation in Binary Representation is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach generates all possible permutations of the numbers from 0 to 2^n - 1 and checks each permutation to see if it satisfies the conditions. This method is straightforward but inefficient due to the large number of permutations. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Circular Permutation in Binary Representation?

Circular Permutation in Binary Representation uses the following concepts: Math, Backtracking, Bit Manipulation. The recommended patterns to study are: Bit Manipulation, Backtracking, Gray Code.

What are the interview tips for Circular Permutation in Binary Representation?

Always consider if there's a mathematical or algorithmic property that can simplify the problem. Explain your thought process clearly; if you think of Gray code, explain why it applies. Practice generating sequences and manipulating arrays, as these are common in permutation problems.

What are common mistakes when solving Circular Permutation in Binary Representation?

Students often try to brute-force permutations without realizing the efficiency of Gray code. Failing to check the circular condition (first and last elements) can lead to incorrect solutions.

#1238

Circular Permutation in Binary Representation

Medium

MathBacktrackingBit ManipulationBit ManipulationBacktrackingGray Code

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n)Space O(n)

The optimal solution uses Gray code to generate a sequence where each number differs from the previous one by exactly one bit. This method is efficient and directly constructs the required permutation without generating all possibilities.

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Algorithm

3 steps

1Step 1: Generate the Gray code sequence for n bits using the formula: gray(i) = i ^ (i >> 1).
2Step 2: Rotate the sequence such that it starts with the given 'start' value.
3Step 3: Return the rotated sequence.

solution.py6 lines

1# Full working Python code
2
3def circular_permutation_optimal(n, start):
4    gray_code = [(i ^ (i >> 1)) for i in range(2 ** n)]
5    start_index = gray_code.index(start)
6    return gray_code[start_index:] + gray_code[:start_index]

ℹ

Complexity note: Generating the Gray code sequence takes O(n) time, and rotating the array also takes O(n), leading to an overall complexity of O(n).

1Gray code ensures that only one bit changes between consecutive numbers, which is crucial for the problem.
2The optimal solution leverages mathematical properties to avoid unnecessary permutations.

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