JavaScript Program for Rotate a Matrix by 180 degrees

To rotate a matrix by 180 degrees, we can achieve this using various approaches. In this article, we'll explore three different methods with step-by-step explanations and complete examples.

A 180-degree rotation of a matrix means that the first row becomes the last row in reverse order, the second row becomes the second-to-last row in reverse order, and so on. Essentially, we're flipping the matrix both horizontally and vertically.

Example

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

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

Visual Representation

Approaches to Rotate a Matrix by 180 Degrees

Here are three different approaches we'll explore:

• Using Naive Approach
• Using Reverse and Swap
• Using Transpose and Reverse

Using Naive Approach

The naive approach creates a new rotated matrix by traversing the original matrix from the last row to the first row, and within each row, from the last column to the first column.

• Start from the bottom-right corner of the matrix
• Traverse each row from right to left, starting from the bottom row
• Build the rotated matrix row by row

Example

let mat = [[1, 2, 3, 4],
           [5, 6, 7, 8],
           [9, 10, 11, 12],
           [13, 14, 15, 16]];

function rotateMatrix(matrix) {
    let n = matrix.length;
    let rotated = [];
    
    for (let i = n - 1; i >= 0; i--) {
        let row = [];
        for (let j = n - 1; j >= 0; j--) {
            row.push(matrix[i][j]);
        }
        rotated.push(row);
    }
    
    return rotated;
}

console.log("Original Matrix:");
console.log(mat);
console.log("Matrix after 180° rotation:");
console.log(rotateMatrix(mat));

Original Matrix:
[
  [ 1, 2, 3, 4 ],
  [ 5, 6, 7, 8 ],
  [ 9, 10, 11, 12 ],
  [ 13, 14, 15, 16 ]
]
Matrix after 180° rotation:
[
  [ 16, 15, 14, 13 ],
  [ 12, 11, 10, 9 ],
  [ 8, 7, 6, 5 ],
  [ 4, 3, 2, 1 ]
]

Using Reverse and Swap

This approach modifies the matrix in-place by first reversing each row, then swapping rows symmetrically around the center.

• Reverse each row of the matrix individually
• Swap the first row with the last row, second with second-to-last, and so on
• Continue until reaching the middle of the matrix

Step-by-Step Process

<strong>Input:</strong>
[[1, 2, 3],
 [4, 5, 6],
 [7, 8, 9]]

Step 1: Reverse each row
[[3, 2, 1],
 [6, 5, 4],
 [9, 8, 7]]

Step 2: Swap rows (row 0 with row 2)
[[9, 8, 7],
 [6, 5, 4],
 [3, 2, 1]]

<strong>Output:</strong>
[[9, 8, 7],
 [6, 5, 4],
 [3, 2, 1]]

Example

let mat = [[1, 2, 3, 4],
           [5, 6, 7, 8],
           [9, 10, 11, 12],
           [13, 14, 15, 16]];

function rotateMatrix(matrix) {
    let n = matrix.length;
    
    // Step 1: Reverse each row
    for (let i = 0; i < n; i++) {
        matrix[i].reverse();
    }
    
    // Step 2: Swap rows
    for (let i = 0; i < n / 2; i++) {
        [matrix[i], matrix[n - 1 - i]] = [matrix[n - 1 - i], matrix[i]];
    }
    
    return matrix;
}

console.log("Original Matrix:");
let originalMat = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]];
console.log(originalMat);

console.log("Matrix after 180° rotation:");
console.log(rotateMatrix(mat));

Original Matrix:
[ [ 1, 2, 3, 4 ], [ 5, 6, 7, 8 ], [ 9, 10, 11, 12 ], [ 13, 14, 15, 16 ] ]
Matrix after 180° rotation:
[
  [ 16, 15, 14, 13 ],
  [ 12, 11, 10, 9 ],
  [ 8, 7, 6, 5 ],
  [ 4, 3, 2, 1 ]
]

Using Transpose and Reverse

This approach uses the mathematical property that a 180-degree rotation equals two 90-degree rotations. A 90-degree clockwise rotation can be achieved by transposing the matrix and then reversing each row.

• Transpose the matrix (swap rows and columns)
• Reverse each row
• Repeat both steps once more to complete the 180-degree rotation

Step-by-Step Process

<strong>Input:</strong>
[[1, 2, 3],
 [4, 5, 6],
 [7, 8, 9]]

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

Step 2: Reverse rows
[[7, 4, 1],
 [8, 5, 2],
 [9, 6, 3]]

Step 3: Transpose again
[[7, 8, 9],
 [4, 5, 6],
 [1, 2, 3]]

Step 4: Reverse rows again
[[9, 8, 7],
 [6, 5, 4],
 [3, 2, 1]]

<strong>Output:</strong>
[[9, 8, 7],
 [6, 5, 4],
 [3, 2, 1]]

Example

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

function transpose(matrix) {
    let n = matrix.length;
    for (let i = 0; i < n; i++) {
        for (let j = i + 1; j < n; j++) {
            [matrix[i][j], matrix[j][i]] = [matrix[j][i], matrix[i][j]];
        }
    }
}

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

function rotate180(matrix) {
    // First 90-degree rotation
    transpose(matrix);
    reverseRows(matrix);
    
    // Second 90-degree rotation
    transpose(matrix);
    reverseRows(matrix);
    
    return matrix;
}

console.log("Original Matrix:");
let originalMatrix = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]];
console.log(originalMatrix);

console.log("Matrix after 180° rotation:");
console.log(rotate180(matrix));

Original Matrix:
[ [ 1, 2, 3, 4 ], [ 5, 6, 7, 8 ], [ 9, 10, 11, 12 ], [ 13, 14, 15, 16 ] ]
Matrix after 180° rotation:
[
  [ 16, 15, 14, 13 ],
  [ 12, 11, 10, 9 ],
  [ 8, 7, 6, 5 ],
  [ 4, 3, 2, 1 ]
]

Comparison