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Rotate Matrix, Advanced

Explore how to rotate a square matrix 90 degrees clockwise directly within the original array, using an in-place algorithm. Understand the step-by-step layering approach and swapping logic, and analyze the time and space complexities. This lesson develops skills in spatial reasoning and efficient data manipulation for JavaScript interviews.

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Rotate Square Matrix in Place

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⬇️

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Instructions

Write a function that takes a square matrix as input. A square matrix has the same number of rows and columns, e.g. 3 x 3, 4 x 4, 5 x 5. It should return the same matrix rotated 90 degrees clockwise. The rotation should happen in place, meaning you may not create any extra matrixes or arrays in your function.

Input: Array of arrays of numbers

Output: Array of arrays of numbers

Example

An input of:

[[1, 2, 3],
 [4, 5, 6],
 [7, 8, 9]]

yields an output of:

[[7, 4, 1],
 [8, 5, 2],
 [9, 6, 3]]

Hints

  1. Start at the border and work your way in.
  2. We’ll need some placeholder variables.
Node.js
function rotateClockwise(mat) {
    // Your code here
}

Solution

Node.js
function rotateClockwise(mat) {
  const totalLayers = Math.floor(mat.length / 2);
  
  for(let layer = 0; layer < totalLayers; layer++) {
    const lastIndex = mat.length - 1 - layer;
    for(let forwardIterator = layer + 1; forwardIterator < mat.length - layer; forwardIterator++) {
      const reverseIterator = lastIndex - forwardIterator + layer;
      let temp1 = mat[forwardIterator][lastIndex];
      mat[forwardIterator][lastIndex] = mat[layer][forwardIterator];
      let temp2 = mat[lastIndex][reverseIterator];
      mat[lastIndex][reverseIterator] = temp1;
      temp1 = mat[reverseIterator][layer];
      mat[reverseIterator][layer] = temp2;
      mat[layer][forwardIterator] = temp1;
    }
  }
  return mat;
}

The Strategy

We’ll treat the input matrix as a series of nested layers. We’ll start from the outermost layer and work our way towards the center. Here’s what that means, in terms of a 5x5 matrix. ...