Sorting Algorithm analysis on a list of 0 and 1 element. I'm trying to understand the difference would it make if following sorting algorithms are given a set of binary inputs i.e. collection of 0 and 1's only.
a) Heapsort
b) Quicksort
c) MergeSort
d) Insertion Sort.
I'm looking for difference in number of comparison required for sorting the list. 
Exact Question: How the restriction of 0's and 1's element may affect the total number of comparison done and give the resulting \theta bound. In my perspective there won't be any change in MergeSort and Insertion sort as they would require the same number of comparison.
However on a very different thought, I'm thinking that if we know about the data (i.e. they are 0 or 1) then in decision tree there won't be n! factorial outputs. As we can reduce it to few less I'm not sure about this decision tree thought. Please provide your thoughts on this.

Best case = data already sorted
Average case= some data sorted, some data unsorted.
Worst case= data totally unsorted
Merge sort: Best = NlogN , AVE=NlogN,  WORST = NlogN
Insertion Sort = Best = N , AVE=N^2,  WORST = N^2
Quicksort = NlogN , AVE=NlogN,  WORST = N^2
