#136 Medium Time O(n²) Space O(1) Animated

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Rotate an n×n matrix 90 degrees clockwise in-place.

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2 Trace
3 Explain
4 Implement

Pattern Direct simulation with preserved structure

Name the mathematical relationship first, then apply it consistently to every position or digit.

Approach: Reverse & Transpose (In-place)

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Core Insight

Name the mathematical relationship first, then apply it consistently to every position or digit.

Common Pitfall

Write down index and boundary conditions before mutating an in-place structure.

Description

Rotate an n×n matrix 90 degrees clockwise in-place.

Constraints

Time Complexity: O(n²)
Space Complexity: O(1)

Solution — Reverse & Transpose (In-place)

TimeO(n²) SpaceO(1)

Implementation Plan

Translate the invariant into these small, testable moves.

Identify the formula or transformation.
Set boundary conditions.
Process each required position.
Return the transformed result.

def rotate(matrix):
    l, r = 0, len(matrix) - 1
    
    while l < r:
        for i in range(r - l):
            top, bottom = l, r
            
            # save the topleft
            topLeft = matrix[top][l + i]
            
            # move bottom left into top left
            matrix[top][l + i] = matrix[bottom - i][l]
            
            # move bottom right into bottom left
            matrix[bottom - i][l] = matrix[bottom][r - i]
            
            # move top right into bottom right
            matrix[bottom][r - i] = matrix[top + i][r]
            
            # move top left into top right
            matrix[top + i][r] = topLeft
            
        r -= 1
        l += 1

Spiral Matrix

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Steps

Description

Constraints

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Solution — Reverse & Transpose (In-place)