feat: add determinant algorithm (#1438)

* feat: add determinant calculating algorithm

* test: add self-tests for determinant algorithm

* chore: add wikipedia info link

* fix: change initialization to zero

* fix: add error throw and general code improvements

* fix: add error try and catch

* fix: seperate the test loops of error cases

* clean up a bit

---------

Co-authored-by: Lars Müller <34514239+appgurueu@users.noreply.github.com>

Maths/Determinant.js

@@ -0,0 +1,78 @@
+/**
+ * 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 }