Understanding the Recursion of mergesort

Question

Most of the mergesort implementations I see are similar to this. intro to algorithms book along with online implentations I search for. My recursion chops don\'t go much fur

Answer 1

the mergesort() simply divides the array in two halves until the if condition fails that is low < high. As you are calling mergesort() twice : one with low to pivot and second with pivot+1 to high, this will divide the sub arrays even more further.

Lets take an example :

a[] = {9,7,2,5,6,3,4}
pivot = 0+6/2 (which will be 3)
=> first mergesort will recurse with array {9,7,2} : Left Array
=> second will pass the array {5,6,3,4} : Right Array

It will repeat until you have 1 element in each left as well as right array. In the end you'll have something similar to this :

L : {9} {7} {2} R : {5} {6} {3} {4} (each L and R will have further sub L and R)
=> which on call to merge will become

L(L{7,9} R{2}) : R(L{5,6} R{3,4})
As you can see that each sub array are getting sorted in the merge function.

=> on next call to merge the next L and R sub arrays will get in order
L{2,7,9} : R{3,4,5,6}

Now both L and R sub array are sorted within
On last call to merge they'll be merged in order

Final Array would be sorted => {2,3,4,5,6,7,9}

See the merging steps in answer given by @roliu