Add karatsubaMultiplication

src/algorithms/math/bits/README.md

@@ -91,6 +91,19 @@ inverting all of the bits of the number and adding 1 to it.
 
 > See `switchSign` function for further details.
 
+#### Karatsuba Multiplication
+
+Given two numbers in binary representation, karatsuba algorithm find the multiplication
+in O(n^1.59) T.C.
+
+This uses the fact that
+
+``
+AB = 22ceil(num / 2) A_1B_1 + 2ceil(num / 2) * [(A_1 + A_r)(B_1 + B_r) - A_1B_1 - A_rB_r] + A_rB_r
+``
+
+> See `karasubaMultiplication` function for further details.
+
 #### Multiply Two Numbers
 
 This method multiplies two integer numbers using bitwise operators.
@@ -143,6 +156,7 @@ Count of Bits to be Flipped: 1
 
 > See `bitsDiff` function for further details.
 
+
 ## References
 
 - [Bit Manipulation on YouTube](https://www.youtube.com/watch?v=NLKQEOgBAnw&t=0s&index=28&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)

src/algorithms/math/bits/__test__/karatsubaMultiplication.test.js

@@ -0,0 +1,9 @@
+import karatsubaMultiplication from '../karatsubaMultiplication';
+
+describe('karatsubaMultiplication', () => {
+  it('should multiply two numbers using karatsuba multiplication', () => {
+    const A = 1234;
+    const B = 5678;
+    expect(karatsubaMultiplication(A, B)).toBe(12225730);
+  });
+});

src/algorithms/math/bits/karatsubaMultiplication.js

@@ -0,0 +1,32 @@
+/**
+ * @param {number} number
+ * @return bool
+ */
+export default function karatsubaMultiplication(A, B) {
+  const base = 10;
+
+  if ((A < base) || (B < base)) {
+    return A * B;
+  }
+
+  const tempA = A.toString();
+  const tempB = B.toString();
+
+  const num = (tempA.length > tempB.length) ? tempB.length : tempA.length;
+  const multiplier = Math.round(num >> 1);
+
+  const highBits1 = parseInt(tempA.substring(0, tempA.length - multiplier), base);
+  const lowBits1 = parseInt(tempA.substring(tempA.length - multiplier, tempA.length), base);
+
+  const highBits2 = parseInt(tempB.substring(0, tempB.length - multiplier), base);
+  const lowBits2 = parseInt(tempB.substring(tempB.length - multiplier, tempB.length), base);
+
+
+  const res0 = karatsubaMultiplication(lowBits1, lowBits2);
+  const res1 = karatsubaMultiplication(lowBits1 + highBits1, lowBits2 + highBits2);
+  const res2 = karatsubaMultiplication(highBits1, highBits2);
+
+  const res = (res2 ** (10, multiplier << 1)) + ((res1 - res2 - res0) ** (10, multiplier)) + res0;
+
+  return res;
+}