Decrease and Conquer

• This technique (and that in the next chapter) work by solving part of the problem, then solve the part that remains.
• In this chapter, the problem is decreased by a set amount.
• It is an incremental approach
• And comes in three flavors.
  • Decrease by a constant
  • Decrease by a constant factor
  • Decrease by a variable amount.
• We have seen this in some sort with sequential search, selection sort and bubble sort (which is the variable amount decrease)

Insertion sort

• Another, sort, add it to your test bed.
• Big Idea: the left side of the array is ordered, the right side is unordered.
  • Select the next item.
  • Move it to the place in the ordered array where it belongs.

  • INSERTION_SORT(A)
    
     for i ← 1 to n-1 do
        v ← A[i]
        j ← i-1
        while j ≥ 0 and A[j] > v do
            A[j+1] ← A[j]
            j ← j-1
        A[j+1] ← v
    
    	 

  • Try this with 89, 45, 68, 90, 29, 34, 17
  • Does it terminate?
  • Does it work?
  • Performance?
  • Is there a general class of input when this has very good performance?