Why does binary search work this way?

[Arnoldjavs3]

Homework Statement

public class BinarySearch {
    public static boolean search(int[] array, int searchedValue) {
        int beginning = 0;
        int end = array.length - 1;

        while (beginning <= end) {
            int middle = (beginning + end) / 2;
            if (array[middle] == searchedValue) {
                return true;
            }
            else if (array[middle] > searchedValue) {
                end = middle - 1;
            }
            else if (array[middle] < searchedValue) {
                beginning = middle + 1;
            }
          
        }
        return false;
    }
}
/*
middle = 3
array[3] > -3
end = 3;
middle = 0 + 3 /2 = 1.5 so 1
array[1]>-3
end = 1
middle = 0 + 1 /2 = 0
array[0] == -3
return true
*/

Homework Equations

The Attempt at a Solution

The following code is meant to search if an array has a searched value(from the user). My question is why do we need to do this:
end = middle - 1
and
beginning = middle + 1

I noticed that when I input some values without the + and - 1 in the algorithm that it still works, to a varying degree. Why is this?

 

[jbriggs444]

I noticed that when I input some values without the + and - 1 in the algorithm that it still works, to a varying degree. Why is this?

Think about what one iteration through the loop will accomplish. Written down in words:

Each iteration will either: 1) Find the searched-for value or 2) Reduce the remaining range to be searched.

Can you think of a way that 2) could fail without the -1 and +1? Hint: integer division.