SORTING ALGORITHM

INSERTION SORT

•  Stable
• O(1) extra space
• O(n2) comparisons and swaps
• Adaptive: O(n) time when nearly sorted
• Very low overhead 

MERGE SORT

•  Stable
• Θ(n) extra space for arrays (as shown)
• Θ(lg(n)) extra space for linked lists
• Θ(n·lg(n)) time
• Not adaptive
• Does not require random access to data 

QUICK SORT

•  Not stable
• O(lg(n)) extra space (see discussion)
• O(n2) time, but typically O(n·lg(n)) time
• Not adaptive 

public void quicksort(int[] list, int low, int high) 
{
    if (low < high) {
        int mid = partition(list,low,high);
        quicksort(list,low,mid-1);
        quicksort(list,mid+1,high);
    }
}

HEAP SORT

•  Not stable
• O(1) extra space (see discussion)
• O(n·lg(n)) time
• Not really adaptive