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| 1 | +/** |
| 2 | + * Given a square matrix, find its determinant. |
| 3 | + * |
| 4 | + * @param {number[[]]} matrix - Two dimensional array of integers. |
| 5 | + * @returns {number} - An integer equal to the determinant. |
| 6 | + * |
| 7 | + * @example |
| 8 | + * const squareMatrix = [ |
| 9 | + * [2,3,4,6], |
| 10 | + * [5,8,9,0], |
| 11 | + * [7,4,3,9], |
| 12 | + * [4,0,2,1] |
| 13 | + * ]; |
| 14 | + * |
| 15 | + * const result = determinant(squareMatrix); |
| 16 | + * // The function should return 858 as the resultant determinant. |
| 17 | + */ |
| 18 | + |
| 19 | +const subMatrix = (matrix, i, j) => { |
| 20 | + let matrixSize = matrix[0].length |
| 21 | + if (matrixSize === 1) { |
| 22 | + return matrix[0][0] |
| 23 | + } |
| 24 | + let subMatrix = [] |
| 25 | + for (let x = 0; x < matrixSize; x++) { |
| 26 | + if (x === i) { |
| 27 | + continue |
| 28 | + } else { |
| 29 | + subMatrix.push([]) |
| 30 | + for (let y = 0; y < matrixSize; y++) { |
| 31 | + if (y === j) { |
| 32 | + continue |
| 33 | + } else { |
| 34 | + subMatrix[subMatrix.length - 1].push(matrix[x][y]) |
| 35 | + } |
| 36 | + } |
| 37 | + } |
| 38 | + } |
| 39 | + return subMatrix |
| 40 | +} |
| 41 | + |
| 42 | +const isMatrixSquare = (matrix) => { |
| 43 | + let numRows = matrix.length |
| 44 | + for (let i = 0; i < numRows; i++) { |
| 45 | + if (numRows !== matrix[i].length) { |
| 46 | + return false |
| 47 | + } |
| 48 | + } |
| 49 | + return true |
| 50 | +} |
| 51 | + |
| 52 | +const determinant = (matrix) => { |
| 53 | + if ( |
| 54 | + !Array.isArray(matrix) || |
| 55 | + matrix.length === 0 || |
| 56 | + !Array.isArray(matrix[0]) |
| 57 | + ) { |
| 58 | + return 'Input is not a valid 2D matrix.' |
| 59 | + } |
| 60 | + if (isMatrixSquare(matrix) === false) { |
| 61 | + return 'Square matrix is required.' |
| 62 | + } |
| 63 | + let numCols = matrix[0].length |
| 64 | + if (numCols === 1) { |
| 65 | + return matrix[0][0] |
| 66 | + } |
| 67 | + let result = null |
| 68 | + let setIndex = 0 |
| 69 | + for (let i = 0; i < numCols; i++) { |
| 70 | + result += |
| 71 | + Math.pow(-1, i) * |
| 72 | + matrix[setIndex][i] * |
| 73 | + determinant(subMatrix(matrix, setIndex, i)) |
| 74 | + } |
| 75 | + return result |
| 76 | +} |
| 77 | +export { determinant } |
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