Btukfyl

On solving a kata on codewars I came across a single line solution to the problem of converting a binary number (in the form of a list ) to integer.
I am unable to understand the solution where people have used java stream api reduce function.Please help me understand it.

Eg: [0, 0, 0, 1] is treated as 0001 which is the binary representation of 1.

import java.util.List;



public class BinaryArrayToNumber {



    public static int ConvertBinaryArrayToInt(List<Integer> binary) {

       return binary.stream().reduce((x, y) -> x * 2 + y).get();

 }

}

First of all the math behind it is based on the method described here

The working of the code is best understood with the help of an example. Consider a binary number 1011 (Decimal 11)

• The operation is streamed sequentially . From the way the reduce operation behaves we'll rename x as accumulator and y as ele
  


• 
  

  We can now state the above operation mathematically as

  
  
  

  accumulator = (accumulator*2)+ ele // refer here for why

  
  



• Lets run the formula on 1011



• Streaming begins with the first element i.e the left side and goes sequentially


• start: accumulator = 0


• 1) accumulator = (0 * 2) + 1 //first element, accumulator = 1


• 2) accumulator = (1 * 2) + 0 //second element, accumulator = 2


• 3) accumulator = (2 * 2) + 1 //third element, accumulator = 5


• 4) accumulator = (5 * 2) + 1 //last element, accumulator = 11

You can extend this to n binary digits.

One important thing to note is that although this is okay for coding competitions, this should never be used in a real world appication as the reduce() expects an associative operation and also gives no guarantees of running sequentially

The purpose of the reduce function is to accumulate the elements from the stream into a single result, using the given formula.

This accumulation process is done repeatedly for each element of the stream. Initially, 1st argument("x") takes 0, and the 2nd argument("y") takes first value from the stream. For each subsequent step, the result from the previous calculation will be used as the 1st argument, and the next value from the stream will be used as the 2nd argument.

Using procedural programming, return binary.stream().reduce((x, y) -> x * 2 + y).get(); in your case would be equivalent to the following snippet:

int x = 0;

for(int y : binary) {

    x = x * 2 + y;

}

return x;

reduce essentially enables one to "reduce" (also known as fold, accumulate) the streams elements into a single value.

You don't need to look any further than the reduce method documentation to find out the exact steps taken:

it provides an example saying it's equivalent to:

boolean foundAny = false;

T result = null;

for (T element : this stream) {

     if (!foundAny) {

         foundAny = true;

         result = element;

     }

     else

         result = accumulator.apply(result, element);

}

return foundAny ? Optional.of(result) : Optional.empty();

where accumulator is the function you've supplied i.e. (x, y) -> x * 2 + y