Rotate Image - Practice Coding Problems

Rotate Image - Problem

You are given an n x n 2D matrix representing an image. Rotate the image by 90 degrees clockwise.

You have to rotate the image in-place, which means you have to modify the input 2D matrix directly. DO NOT allocate another 2D matrix and do the rotation.

Input & Output

Example 1 — 3×3 Matrix

$ Input: matrix = [[1,2,3],[4,5,6],[7,8,9]]

› Output: [[7,4,1],[8,5,2],[9,6,3]]

💡 Note: After 90° clockwise rotation: first row [1,2,3] becomes last column [1,2,3], second row [4,5,6] becomes middle column [4,5,6], third row [7,8,9] becomes first column [7,8,9]

Example 2 — 4×4 Matrix

$ Input: matrix = [[5,1,9,11],[2,4,8,10],[13,3,6,7],[15,14,12,16]]

› Output: [[15,13,2,5],[14,3,4,1],[12,6,8,9],[16,7,10,11]]

💡 Note: Each element moves to its rotated position: element at (0,0) which is 5 moves to (0,3), element at (0,1) which is 1 moves to (1,3), etc.

Example 3 — 1×1 Matrix

$ Input: matrix = [[1]]

› Output: [[1]]

💡 Note: Single element matrix remains unchanged after rotation

Constraints

1 ≤ matrix.length ≤ 20
matrix.length == matrix[i].length
-1000 ≤ matrix[i][j] ≤ 1000

Visualization

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Understanding the Visualization

Input

3×3 matrix with elements 1-9

Rotation

90° clockwise transformation

Output

Rotated matrix in-place

Key Takeaway

🎯 Key Insight: 90° rotation = transpose + reverse rows, or cycle 4 elements in layers

Asked in

🍎 Apple 25 Ⓜ Microsoft 20 a Amazon 18 G Google 15

The key insight is that 90° clockwise rotation can be achieved by transpose + reverse rows, or by rotating 4-element cycles in concentric layers. The optimal approach uses layer-by-layer rotation with O(n²) time and O(1) space.

Common Approaches

Approach	Time	Space	Notes
✓ Transpose + Reverse Rows	O(n²)	O(1)	First transpose the matrix (swap across diagonal), then reverse each row
Element by Element with Temp Array	O(n²)	O(n²)	Copy each element to its rotated position using a temporary matrix
Layer by Layer Rotation	O(n²)	O(1)	Rotate elements in concentric layers, swapping 4 elements at once

Transpose + Reverse Rows — Algorithm Steps

Transpose matrix: swap matrix[i][j] with matrix[j][i]
Reverse each row horizontally
Matrix is now rotated 90° clockwise

Visualization

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Step-by-Step Walkthrough

Original Matrix

3x3 matrix to be rotated

After Transpose

Elements swapped across diagonal

After Row Reverse

Each row reversed horizontally

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

void solution(int** matrix, int n) {
    // Step 1: Transpose matrix
    for (int i = 0; i < n; i++) {
        for (int j = i + 1; j < n; j++) {
            int temp = matrix[i][j];
            matrix[i][j] = matrix[j][i];
            matrix[j][i] = temp;
        }
    }
    
    // Step 2: Reverse each row
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n/2; j++) {
            int temp = matrix[i][j];
            matrix[i][j] = matrix[i][n-1-j];
            matrix[i][n-1-j] = temp;
        }
    }
}

int main() {
    // Simplified parsing for example
    int n = 3;
    int** matrix = (int**)malloc(n * sizeof(int*));
    for (int i = 0; i < n; i++) {
        matrix[i] = (int*)malloc(n * sizeof(int));
    }
    
    // Read matrix values (simplified)
    matrix[0][0] = 1; matrix[0][1] = 2; matrix[0][2] = 3;
    matrix[1][0] = 4; matrix[1][1] = 5; matrix[1][2] = 6;
    matrix[2][0] = 7; matrix[2][1] = 8; matrix[2][2] = 9;
    
    solution(matrix, n);
    
    // Print result
    printf("[");
    for (int i = 0; i < n; i++) {
        printf("[");
        for (int j = 0; j < n; j++) {
            printf("%d", matrix[i][j]);
            if (j < n-1) printf(",");
        }
        printf("]");
        if (i < n-1) printf(",");
    }
    printf("]\n");
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n²)

Two passes through n×n matrix elements

⚠ Quadratic Growth

Space Complexity

O(1)

Only uses constant extra variables for swapping

✓ Linear Space

89.5K Views

High Frequency

~15 min Avg. Time

2.8K Likes

Ln 1, Col 1

Smart Actions

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Transpose + Reverse Rows — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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