Understanding the Recursion of mergesort
MERGE SORT:
1) Split the array in half
2) Sort the left half
3) Sort the right half
4) Merge the two halves together
I think the "sort" function name in MergeSort is a bit of a misnomer, it should really be called "divide".
Here is a visualization of the algorithm in process.
Each time the function recurses, it's working on a smaller and smaller subdivision of the input array, starting with the left half of it. Each time the function returns from recursion, it will continue on and either start working on the right half, or recurse up again and work on a larger half.
Like this
[************************]mergesort
[************]mergesort(lo,mid)
[******]mergesort(lo,mid)
[***]mergesort(lo,mid)
[**]mergesort(lo,mid)
[**]mergesort(mid+1,hi)
[***]merge
[***]mergesort(mid+1,hi)
[**]mergesort*(lo,mid)
[**]mergesort(mid+1,hi)
[***]merge
[******]merge
[******]mergesort(mid+1,hi)
[***]mergesort(lo,mid)
[**]mergesort(lo,mid)
[**]mergesort(mid+1,hi)
[***]merge
[***]mergesort(mid+1,hi)
[**]mergesort(lo,mid)
[**]mergesort(mid+1,hi)
[***]merge
[******]merge
[************]merge
[************]mergesort(mid+1,hi)
[******]mergesort(lo,mid)
[***]mergesort(lo,mid)
[**]mergesort(lo,mid)
[**]mergesort(mid+1,hi)
[***]merge
[***]mergesort(mid+1,hi)
[**]mergesort(lo,mid)
[**]mergesort(mid+1,hi)
[***]merge
[******]merge
[******]mergesort(mid+1,hi)
[***]mergesort(lo,mid)
[**]mergesort*(lo,mid)
[**]mergesort(mid+1,hi)
[***]merge
[***]mergesort(mid+1,hi)
[**]mergesort(lo,mid)
[**]mergesort(mid+1,hi)
[***]merge
[******]merge
[************]merge
[************************]merge