Minor code style fixes for bitwise multiplication.

trekhleb · trekhleb · commit de6a24e0d166 · 2018-09-08T23:09:04.000+03:00
diff --git a/src/algorithms/math/bits/README.md b/src/algorithms/math/bits/README.md
@@ -38,12 +38,14 @@ This method is a combination of "Clear Bit" and "Set Bit" methods.
 #### isEven
 
 This method determines if the number provided is even.
+It is based on the fact that odd numbers have their last
+right bit to be set to 1.
 
-```
-Number: 5
+```text
+Number: 5 = 0b0101
 isEven: false
 
-Number: 4
+Number: 4 = 0b0100
 isEven: true
 ```
 
@@ -108,18 +110,19 @@ inverting all of the bits of the number and adding 1 to it.
 #### Multiply Two Signed Numbers
 
 This method multiplies two signed integer numbers using bitwise operators.
-This method is based on the following :
+This method is based on the following facts:
 
 ```text
-a * b can be written in the below formats
+a * b can be written in the below formats:
   0                     if a is zero or b is zero or both a and b are zeroes
   2a * (b/2)            if b is even
   2a * (b - 1)/2 + a    if b is odd and positive
   2a * (b + 1)/2 - a    if b is odd and negative
 ```
 
-The advantage of this approach is that in each recursive step one of the operands reduces to half its original value.
-Hence, the run time complexity is O(log b) where b is the operand that reduces to half on each recursive step.
+The advantage of this approach is that in each recursive step one of the operands
+reduces to half its original value. Hence, the run time complexity is `O(log(b)` where `b` is
+the operand that reduces to half on each recursive step.
 
 > See [multiply.js](multiply.js) for further details.
 
diff --git a/src/algorithms/math/bits/__test__/isEven.test.js b/src/algorithms/math/bits/__test__/isEven.test.js
@@ -7,5 +7,13 @@ describe('isEven', () => {
     expect(isEven(-2)).toBe(true);
     expect(isEven(1)).toBe(false);
     expect(isEven(-1)).toBe(false);
+    expect(isEven(-3)).toBe(false);
+    expect(isEven(3)).toBe(false);
+    expect(isEven(8)).toBe(true);
+    expect(isEven(9)).toBe(false);
+    expect(isEven(121)).toBe(false);
+    expect(isEven(122)).toBe(true);
+    expect(isEven(1201)).toBe(false);
+    expect(isEven(1202)).toBe(true);
   });
 });
diff --git a/src/algorithms/math/bits/__test__/multiply.test.js b/src/algorithms/math/bits/__test__/multiply.test.js
@@ -12,5 +12,7 @@ describe('multiply', () => {
     expect(multiply(4, -2)).toBe(-8);
     expect(multiply(-4, -4)).toBe(16);
     expect(multiply(4, -5)).toBe(-20);
+    expect(multiply(2, 121)).toBe(242);
+    expect(multiply(121, 2)).toBe(242);
   });
 });
diff --git a/src/algorithms/math/bits/isEven.js b/src/algorithms/math/bits/isEven.js
@@ -1,6 +1,6 @@
 /**
  * @param {number} number
- * @return bool
+ * @return {boolean}
  */
 export default function isEven(number) {
   return (number & 1) === 0;
diff --git a/src/algorithms/math/bits/multiply.js b/src/algorithms/math/bits/multiply.js
@@ -1,27 +1,38 @@
+import multiplyByTwo from './multiplyByTwo';
 import divideByTwo from './divideByTwo';
 import isEven from './isEven';
-import multiplyByTwo from './multiplyByTwo';
 
 /**
- * FUNCTION DEFINITION
- * multiply(a, b) = 0 if a is zero or b is zero or if both a and b are zeros
- * multiply(a, b) = multiply(2a, b/2) if b is even
- * multiply(a, b) = multiply(2a, (b-1)/2) + a if b is odd and b is positive
- * multiply(a, b) = multiply(2a, (b+1)/2) - a if b is odd and b is negative
+ * Multiply two signed numbers using bitwise operations.
+ *
+ * If a is zero or b is zero or if both a and b are zeros:
+ * multiply(a, b) = 0
+ *
+ * If b is even:
+ * multiply(a, b) = multiply(2a, b/2)
+ *
+ * If b is odd and b is positive:
+ * multiply(a, b) = multiply(2a, (b-1)/2) + a
+ *
+ * If b is odd and b is negative:
+ * multiply(a, b) = multiply(2a, (b+1)/2) - a
+ *
+ * Time complexity: O(log b)
  *
- * COMPLEXITY
- * O(log b)
  * @param {number} a
  * @param {number} b
- * @return {number} a * b
+ * @return {number}
  */
 export default function multiply(a, b) {
+  // If a is zero or b is zero or if both a and b are zeros then the production is also zero.
   if (b === 0 || a === 0) {
     return 0;
   }
 
+  // Otherwise we will have four different cases that are described above.
   const multiplyByOddPositive = () => multiply(multiplyByTwo(a), divideByTwo(b - 1)) + a;
   const multiplyByOddNegative = () => multiply(multiplyByTwo(a), divideByTwo(b + 1)) - a;
+
   const multiplyByEven = () => multiply(multiplyByTwo(a), divideByTwo(b));
   const multiplyByOdd = () => (b > 0 ? multiplyByOddPositive() : multiplyByOddNegative());
 
