What is the time complexity of Determine Whether Matrix Can Be Obtained By Rotation?

The optimal solution for Determine Whether Matrix Can Be Obtained By Rotation runs in O(n²) time and uses O(1) space. The time complexity remains O(n²) due to the same reasoning as the brute force approach, but we optimize by avoiding unnecessary checks after finding a match.

What is the brute force solution for Determine Whether Matrix Can Be Obtained By Rotation?

The brute force approach for Determine Whether Matrix Can Be Obtained By Rotation is Brute Force, with O(n²) time complexity and O(1) space complexity. We can check if the target matrix can be obtained by rotating the original matrix up to three times (90, 180, and 270 degrees). For each rotation, we compare the resulting matrix with the target matrix. The optimal Optimal Solution approach improves this to O(n²).

What algorithm or data structure is used to solve Determine Whether Matrix Can Be Obtained By Rotation?

Determine Whether Matrix Can Be Obtained By Rotation uses the following concepts: Array, Matrix. The recommended patterns to study are: Matrix Manipulation, Array Rotation.

What are the interview tips for Determine Whether Matrix Can Be Obtained By Rotation?

Always think about edge cases, such as the smallest matrix size. Explain your thought process clearly while coding; it helps the interviewer understand your approach. Practice rotating matrices manually to get comfortable with the concept.

What are common mistakes when solving Determine Whether Matrix Can Be Obtained By Rotation?

Not considering all four rotations of the matrix. Confusing matrix indices when performing rotations.

#1886

Determine Whether Matrix Can Be Obtained By Rotation

Easy

ArrayMatrixMatrix ManipulationArray Rotation

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n²)Space O(1)

Instead of performing rotations, we can directly check if the target matrix can be obtained by comparing the matrices in their rotated forms using a helper function.

⚙️

Algorithm

3 steps

1Step 1: Create a function to check if two matrices are equal.
2Step 2: Create a function to rotate the matrix 90 degrees clockwise.
3Step 3: Check the original matrix and its three rotated forms against the target matrix.

solution.py10 lines

1def rotate(mat):
2    n = len(mat)
3    return [[mat[n - j - 1][i] for j in range(n)] for i in range(n)]
4
5def canBeObtained(mat, target):
6    for _ in range(4):
7        if mat == target:
8            return True
9        mat = rotate(mat)
10    return False

ℹ

Complexity note: The time complexity remains O(n²) due to the same reasoning as the brute force approach, but we optimize by avoiding unnecessary checks after finding a match.

1The problem requires understanding matrix rotations, which can be visualized as rotating a physical object.
2Checking all four orientations of the matrix is essential to determine if the target can be achieved.

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