Merge sort implementation using divide-and-conquer

Question

I was told in an interview to write a program for implementing merge sort on the concept of divide-and-conquer.

var myGlobalArray = undefined;

myGlobalArray = [8,4,17,2,1,32];
example01(myGlobalArray);

myGlobalArray = [48,14,17,2,11,132];
example01(myGlobalArray);

myGlobalArray = [45,14,5,2,1,12];
example01(myGlobalArray);

myGlobalArray = [45,-14,-5,2,1,-12];
example01(myGlobalArray);

myGlobalArray = [38,27,43,3,9,82,10];
example01(myGlobalArray);

myGlobalArray = [34,45,1,23,19,12,10];
example01(myGlobalArray);


function example01(myArray){
   var mainArray = [];

   // Divide
   createSubArray(myArray,0);

   // Conquer      
   mainArray = mergeArrays(mainArray);

   console.log(myArray+" => "+mainArray[0]);

   // creates an array which contains n arrays for n numbers present in myarray
   // i.e. if array = [ 34, 1, 27, 3 ] that the below method will return
   // [ [34], [1], [27], [3] ]
   function createSubArray(subArray,index){
        var localArray = [];

        if(subArray[index] !== undefined){
            localArray.push(subArray[index]);
            mainArray.push(localArray);
            createSubArray(subArray,++index); // dividing recursively   
        }       
   }//createSubArray


   // merge the arrays present i.e. 
   // if gblArray = [ [2,5], [1,7] ] 
   // then the below method will return
   // an merged array [ [1, 2, 5, 7] ]
   function mergeArrays(gblArray){
        var mergedArrays = [],
            main_array = gblArray,
            arr = [], 
            left_array = undefined, 
            right_array = undefined, 
            counter = 0, 
            nextCounter = 0;

        do{

            while(counter < main_array.length){
                nextCounter = counter + 1;

                if(main_array[nextCounter] !== undefined){

                    left_array = main_array[counter];
                    right_array = main_array[nextCounter];

                    // merge left and right arrays and sort it                      
                    arr = mergeAndSort(left_array,right_array);     

                    mergedArrays.push(arr);
                }else{
                    mergedArrays.push(main_array[counter]);
                }
                counter = nextCounter + 1;
            }

            main_array = mergedArrays;              
            mergedArrays = [];  
            counter = 0;
            nextCounter = 0;

        }while(main_array.length > 1);

        return main_array;
   }//mergeArrays


   // merges two array and sorts i.e.
   // if array1 = [1,23] and array2 = [4,12] than
   // the below method returns [1,4,12,23]
   function mergeAndSort(array1,array2){
        var array2Counter = 0, 
            array1Counter = 0, 
            mergedArray = [];

        while(array2Counter < array2.length && array1Counter < array1.length){

            if(array2[array2Counter] < array1[array1Counter]){
                mergedArray.push(array2[array2Counter]);
                array2Counter++;
            }else{
                mergedArray.push(array1[array1Counter]);
                array1Counter++;
            }
        }

        while(array1Counter < array1.length){
            mergedArray.push(array1[array1Counter]);
            array1Counter++;
        }

        while(array2Counter < array2.length){
            mergedArray.push(array2[array2Counter]);
            array2Counter++;
        }

        return mergedArray;
   } //mergeAndSort



}//example01

The output is:

8,4,17,2,1,32 => 1,2,4,8,17,32
48,14,17,2,11,132 => 2,11,14,17,48,132
45,14,5,2,1,12 => 1,2,5,12,14,45
45,-14,-5,2,1,-12 => -14,-12,-5,1,2,45
38,27,43,3,9,82,10 => 3,9,10,27,38,43,82
34,45,1,23,19,12,10 => 1,10,12,19,23,34,45

But by looking at my implemented merge-sort program, the inteviewer said that it doesn't follow the divide-and-conquer concept.

I tried to convince him that method mergeArrays and mergeAndSort do the divide-and-conquer, but he didn't agreed. Where am I going wrong?

Answer 1

To expand on CiaPan's answer. Your solution might look like:

result = mergeAndSort([8,4,17,2,1,32]);

You would write code that would do:

let a = mergeAndSort([8,4,17]);
let b = mergeAndSort([2,1,32]);
return merge(a, b);

This would be recursive, so mergeAndSort([8,4,17]) would do:

let a = mergeAndSort([8,4]);
let b = mergeAndSort([17]);
return merge(a, b);

Now mergeAndSort would be called with [8,4] which would be:

let a = mergeAndSort([8]);
let b = mergeAndSort([4]);
return merge(a, b);

Now lastly you have mergeAndSort([8]) which is trivially implemented as

return [8]

Or alternatively, in pseudocode:

function mergeAndSort(array) {
  if (array.length <= 1)
    return array;
  let a = mergeAndSort( leftHalfOfArray(array)  );
  let b = mergeAndSort( rightHalfOfArray(array) );
  return merge(a,b); 
}

Answer 2

The divide and conquer paradigm is based on recurring into subproblems: take a problem, divide it into a few (typically: two) smaller subproblems, solve each of them recursively, then join/merge results.

What you do is: split the problem recursively into a large amount of elementary, trivial problems, then iteratively pick them by pair, join and push back for further joining. It doesn't quite fit the template of 'divide – solve recursively – join solutions'.