#### Determinant

N
/**
* Given a square matrix, find its determinant using Laplace Expansion.
* Time Complexity : O(n!)
*
*
* @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 }