Searching

















What's Searching?


	int search(list, item);

	return the index of item in list
	return -1 if item is not found

















Linear Search


How does a Linear or Sequential Search work?

    for each i from 0 to size-1
      if item equals list[i]
	return i
    return not found


What's the Big-Oh bound on a Linear Search?


DEMO	(running time of linear search)

















Binary Search


How does a Binary Search work?

    low = index of first item in list
    high = index of last item in list
    while low is less than or equal to high
      mid = index halfway between low and high
      if item is less than list[mid]
	high = mid - 1
      else if item is greater than list[mid]
	low = mid + 1
      else
	return mid
    end while
    return not found


What must be true about the List for a Binary Search to work?

















Show the steps of a binary search for 36 in the List.
What are the values for low, high, and mid at each step?
What part of the List is the algorithm still searching at each step?


	16 18 24 32 36 48 55 64 72 75 77 83 90 96 99
	 0  1  2  3  4  5  6  7  8  9 10 11 12 13 14

















Classwork
You may work with a partner.

Show the steps of a binary search for 80 in the List.
What are the values for low, high, and mid at each step?
What part of the List is the algorithm still searching at each step?


	16 18 24 32 36 48 55 64 72 75 77 83 90 96 99
	 0  1  2  3  4  5  6  7  8  9 10 11 12 13 14

















What's the Big-Oh bound on a Binary Search?


DEMO	(running time of binary search)