Determinant.js

/**
 * Given a square matrix, find its determinant using Laplace Expansion.
 * Time Complexity : O(n!)
 *
 * For more info: https://en.wikipedia.org/wiki/Determinant
 *
 * @param {number[[]]} matrix - Two dimensional array of integers.
 * @returns {number} - An integer equal to the determinant.
 *
 * @example
 * const squareMatrix = [
 * [2,3,4,6],
 * [5,8,9,0],
 * [7,4,3,9],
 * [4,0,2,1]
 * ];
 *
 * const result = determinant(squareMatrix);
 * // The function should return 858 as the resultant determinant.
 */

const subMatrix = (matrix, i, j) => {
 let matrixSize = matrix[0].length
 if (matrixSize === 1) {
 return matrix[0][0]
 }
 let subMatrix = []
 for (let x = 0; x < matrixSize; x++) {
 if (x === i) {
 continue
 }
 subMatrix.push([])
 for (let y = 0; y < matrixSize; y++) {
 if (y === j) {
 continue
 }
 subMatrix[subMatrix.length - 1].push(matrix[x][y])
 }
 }
 return subMatrix
}

const isMatrixSquare = (matrix) => {
 let numRows = matrix.length
 for (let i = 0; i < numRows; i++) {
 if (numRows !== matrix[i].length) {
 return false
 }
 }
 return true
}

const determinant = (matrix) => {
 if (
 !Array.isArray(matrix) ||
 matrix.length === 0 ||
 !Array.isArray(matrix[0])
 ) {
 throw new Error('Input is not a valid 2D matrix.')
 }
 if (!isMatrixSquare(matrix)) {
 throw new Error('Square matrix is required.')
 }
 let numCols = matrix[0].length
 if (numCols === 1) {
 return matrix[0][0]
 }
 let result = 0
 let setIndex = 0
 for (let i = 0; i < numCols; i++) {
 result +=
 Math.pow(-1, i) *
 matrix[setIndex][i] *
 determinant(subMatrix(matrix, setIndex, i))
 }
 return result
}
export { determinant }