Binary Search -- A Fundamental Algorithm

	Binary search is a clever though common sense way to search an ordered set of items.  Queries are made, called probes, asking whether the desired item is smaller or larger. If the probe is chosen in the middle of the sequence, 1/2 of the possibilities must be eliminated with any answer.  Now the details...

Reminder … Algorithm vs Program

	The process just described on the title slide -- suitably embellished -- is the binary search algorithm … the idea given abstractly
	A program for binary search -- your goal -- will encode the algorithm for a specific situation, in a specific language, with specific assumptions

Algorithm Analysis

	Understanding the problem …
			Inputs:  The end points, (lo, hi), of an ordered sequence
			Answers to an series of questions
			Outputs: A selected item
			How the inputs are transformed to the outputs:
			A series of questions is posed of the form
			“Is the desired item after item x?”
			so that the xth item is chosen to be midway in the interval
			If the reply is yes, the new interval  (next after x, hi)
			If the reply is no, the new interval is (lo, x)
			The output is the item when the interval contains only a single item

Analyzing Properties Of Solution

	End points … inclusive
	Before/after questions … stay with one form
	Probing odd-length and even-length intervals (\)
	New interval’s endpoints … one is kept, one changes
	Termination … when is it over?

Guessing Days In A Sign

	A complication in searching for a birthday in a given sign is that the signs span parts of two months
	Not to worry … logically extend the starting month

Transforming Probe To A Date

	The size of the interval is: (52 - 21) = 31
	The midpoint of the interval is: 31 \ 2     = 15
	The probe, low end + midpoint: 21 + 15   = 36
	What day is June 36?

Guess?  What?

	What information is needed by the guess procedure?

Using Binary Search In Day Finder

	Inherit the initial configuration from Zodiac
	The guess Procedure asks one
	probe at a time ...
	When is Guess called?

Overall Data Flow ...

	Where do the initial values come from?
		After the Zodiac computation, loEnd and hiEnd can be set
	When are these values used?
		In the guess procedure to compute the midPt for the guess
	How are these values updated?
		In the yes and no button event handlers
		In the case of “yes,” which end moves?
			loEnd = midPt + 1
		In the case of “no”, which end moves?
			hiEnd = midPt
		Why are the two setting not “opposite” one another?
	When the does the questioning terminate?
		When the end points are equal

Structure Of Solution