feat: add determinant calculating algorithm

piyushk77 · piyushk77 · commit 13a5d57be02e · 2023-10-05T01:13:34.000+05:30
diff --git a/Maths/Determinant.js b/Maths/Determinant.js
@@ -0,0 +1,77 @@
+/**
+ * Given a square matrix, find its 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
+    } else {
+      subMatrix.push([])
+      for (let y = 0; y < matrixSize; y++) {
+        if (y === j) {
+          continue
+        } else {
+          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])
+  ) {
+    return 'Input is not a valid 2D matrix.'
+  }
+  if (isMatrixSquare(matrix) === false) {
+    return 'Square matrix is required.'
+  }
+  let numCols = matrix[0].length
+  if (numCols === 1) {
+    return matrix[0][0]
+  }
+  let result = null
+  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 }
