Question

Do a trace on the binarySearch method below: variable key holds the value 17, and

variable list is a reference to an array with these values {9, 20, 23, 28, 33, 38, 42, 48, 54, 61,73}.

public static int binarySearch(int[] list, int key) {

    int lowIndex = 0;

    int highIndex = list.length - 1;

    while (highIndex >= lowIndex) {

      int midIndex = (lowIndex + highIndex) / 2;

      if (key < list[midIndex]){

           highIndex = midIndex - 1;

     }

      else if (key > list[midIndex]){

           lowIndex = midIndex + 1;      

     }

      else if (key == list[midIndex]){

           return midIndex;            

     }

    } // end of while loop

    return -1;

} // end of binary search method

Each row in the table below corresponds to one iteration of the while loop in the method above. You can add or remove rows according to the actual number of iterations. The first row’s information corresponds to the first iteration, and its value has been filled. You need to continue for the following rows.

key	lowIndex	highIndex	highIndex>=lowIndex	midIndex	key==list[midIndex]	key<list[midIndex]
17	0	10	true	5	false	true

Given the key value and array content listed above, what is the return value of the binary search method?

Answer 1

The table is:

key	lowIndex	highIndex	highIndex>=lowIndex	midIndex	key==list[midIndex]	key<list[midIndex]
17	0	10	true	5	false	true
17	0	4	true	2	false	true
17	0	1	true	0	false	false
17	1	1	true	1	false	true

The return value of the binary search method is -1 because highIndex == lowIndex value is true and key == list[midIndex] value if false, so it exists the while loop and after it exists the while loop only one value is returned i.e. -1.

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