Added matrix multiplication algo in dynamic programming

Author: MishtiGarg250

Dynamic-Programming/MatrixMultiplication.js

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+/*
+Wikipedia -> https://en.wikipedia.org/wiki/Matrix_multiplication
+
+Q. -> Given two matrices `A` and `B`, find the product of both matrices.
+Matrix multiplication is only possible when the number of columns in A equals the number of rows in B.
+
+Formula -> 
+If A is of size (n × m) and B is of size (m × p),
+then the result matrix C will be of size (n × p),
+where each element C[i][j] = Σ (A[i][k] * B[k][j]) for k = 0 to m-1.
+
+Algorithm details ->
+time complexity - O(n * m * p)
+space complexity - O(n * p)
+*/
+
+const matrixMultiplication = (A, B) => {
+  const n = A.length;           // rows in A
+  const m = A[0].length;        // columns in A (and rows in B)
+  const p = B[0].length;        // columns in B
+
+  // Check if multiplication is possible
+  if (m !== B.length) {
+    throw new Error('Matrix multiplication not possible: columns of A must equal rows of B');
+  }
+
+  // Create a result matrix filled with 0s of size (n × p)
+  const result = new Array(n).fill(0).map(() => new Array(p).fill(0));
+
+  /*
+    Perform matrix multiplication:
+    For each row in A and column in B,
+    multiply and sum corresponding elements.
+  */
+  for (let i = 0; i < n; i++) {
+    for (let j = 0; j < p; j++) {
+      let sum = 0;
+      for (let k = 0; k < m; k++) {
+        sum += A[i][k] * B[k][j];
+      }
+      result[i][j] = sum;
+    }
+  }
+
+  return result;
+};
+
+// Example usage
+const A = [
+  [1, 2, 3],
+  [4, 5, 6]
+];
+
+const B = [
+  [7, 8],
+  [9, 10],
+  [11, 12]
+];
+
+console.log(matrixMultiplication(A, B));
+// Output: [ [ 58, 64 ], [ 139, 154 ] ]
+
+export { matrixMultiplication };

Dynamic-Programming/tests/MatrixMultiplication.test.js

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+import { matrixMultiplication } from '../MatrixMultiplication'
+
+test('matrixMultiplication([[1,2,3],[4,5,6]], [[7,8],[9,10],[11,12]]) => [[58,64],[139,154]]', () => {
+  const A = [
+    [1, 2, 3],
+    [4, 5, 6]
+  ]
+  const B = [
+    [7, 8],
+    [9, 10],
+    [11, 12]
+  ]
+  const res = matrixMultiplication(A, B)
+  expect(res).toEqual([
+    [58, 64],
+    [139, 154]
+  ])
+})
+
+test('matrixMultiplication([[2,4],[3,4]], [[1,2],[1,3]]) => [[6,16],[7,18]]', () => {
+  const A = [
+    [2, 4],
+    [3, 4]
+  ]
+  const B = [
+    [1, 2],
+    [1, 3]
+  ]
+  const res = matrixMultiplication(A, B)
+  expect(res).toEqual([
+    [6, 16],
+    [7, 18]
+  ])
+})
+
+test('matrixMultiplication([[1,2],[3,4]], [[5,6],[7,8]]) => [[19,22],[43,50]]', () => {
+  const A = [
+    [1, 2],
+    [3, 4]
+  ]
+  const B = [
+    [5, 6],
+    [7, 8]
+  ]
+  const res = matrixMultiplication(A, B)
+  expect(res).toEqual([
+    [19, 22],
+    [43, 50]
+  ])
+})
+
+test('matrixMultiplication([[1]], [[2]]) => [[2]]', () => {
+  const A = [[1]]
+  const B = [[2]]
+  const res = matrixMultiplication(A, B)
+  expect(res).toEqual([[2]])
+})
+
+test('throws error when matrices cannot be multiplied', () => {
+  const A = [
+    [1, 2, 3],
+    [4, 5, 6]
+  ]
+  const B = [
+    [1, 2],
+    [3, 4]
+  ]
+  expect(() => matrixMultiplication(A, B)).toThrow(
+    'Matrix multiplication not possible: columns of A must equal rows of B'
+  )
+})