Given two integers, write a function to multiply them without using multiplication operator.
There are many other ways to multiply two numbers (For example, see this). One interesting method is the Russian peasant algorithm. The idea is to double the first number and halve the second number repeatedly till the second number doesn’t become 1. In the process, whenever the second number become odd, we add the first number to result (result is initialized as 0)
The following is simple algorithm.
Let the two given numbers be 'a' and 'b' 1) Initialize result 'res' as 0. 2) Do following while 'b' is greater than 0 a) If 'b' is odd, add 'a' to 'res' b) Double 'a' and halve 'b' 3) Return 'res'.
How does this work?
The value of a*b is same as (a*2)*(b/2) if b is even, otherwise the value is same as ((a*2)*(b/2) + a). In the while loop, we keep multiplying ‘a’ with 2 and keep dividing ‘b’ by 2. If ‘b’ becomes odd in loop, we add ‘a’ to ‘res’. When value of ‘b’ becomes 1, the value of ‘res’ + ‘a’, gives us the result.
Note that when ‘b’ is a power of 2, the ‘res’ would remain 0 and ‘a’ would have the multiplication. See the reference for more information.
This article is compiled by Shalki Agarwal. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
- Multiply two integers without using multiplication, division and bitwise operators, and no loops
- Multiply any Number with 4 using Bitwise Operator
- Bitwise Operators in C/C++
- Bitwise right shift operators in Java
- What are the differences between bitwise and logical AND operators in C/C++?
- Check if a number is divisible by 8 using bitwise operators
- Check if a number is divisible by 17 using bitwise operators
- Toggle case of a string using Bitwise Operators
- Check if a number is multiple of 9 using bitwise operators
- Case conversion (Lower to Upper and Vice Versa) of a string using BitWise operators in C/C++
- Multiply Large Numbers represented as Strings
- Numbers whose bitwise OR and sum with N are equal
- Check whether bitwise OR of N numbers is Even or Odd
- Numbers that are bitwise AND of at least one non-empty sub-array
- Add two numbers without using arithmetic operators