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Determinant.js

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/**

* 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 }