Minor code style fixes for bitwise multiplication.

This commit is contained in:
Oleksii Trekhleb
2018-09-08 23:09:04 +03:00
parent bc8943dee2
commit de6a24e0d1
5 changed files with 41 additions and 17 deletions

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@@ -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.