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.

Constraints:

• n == matrix.length == matrix[i].length
• 1 <= n <= 20
• -1000 <= matrix[i][j] <= 1000

Examples

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

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],
]

Solution

The problem gives us an n x n matrix, which means it's a square matrix. The approach is to first transpose the matrix along the diagonal. Using example 1, swap 2 with 4, 3 with 7, and 6 with 8 to get the middle matrix shown below. Then reverse each row to get the final result.

1 2 3     Transpose     1 4 7     Reverse Rows     7 4 1
4 5 6  ------------->   2 5 8  ----------------->  8 5 2
7 8 9                   3 6 9                      9 6 3

JavaScript

/**
 * @param {number[][]} matrix
 * @return {void} Do not return anything, modify matrix in-place instead.
 */
var rotate = function (matrix) {
  const n = matrix.length

  for (let i = 0; i < n; i++) {
    for (let j = i; j < n; j++) {
      ;[matrix[i][j], matrix[j][i]] = [matrix[j][i], matrix[i][j]]
    }
  }

  for (let i = 0; i < n; i++) {
    matrix[i].reverse()
  }
}

Rust

pub fn rotate(matrix: &mut Vec<Vec<i32>>) {
    let n = matrix.len();

    for i in 0..n {
        for j in i..n {
            let temp = matrix[i][j];
            matrix[i][j] = matrix[j][i];
            matrix[j][i] = temp;
        }
    }

    for i in 0..n {
        matrix[i].reverse();
    }
}

Complexity Analysis

• Time Complexity: O(n²) - We traverse the entire matrix twice: once for transposing and once for reversing each row.
• Space Complexity: O(1) - We modify the matrix in-place without using any additional space.