Slide #1.

Algorithms
More slides like this


Slide #2.

Definition of Algorithm An algorithm is an ordered set of unambiguous, executable steps that defines a (ideally) terminating process.
More slides like this


Slide #3.

Algorithm Representation • Requires well-defined primitives • A collection of primitives that the computer can follow constitutes a programming language.
More slides like this


Slide #4.

Folding a bird from a square piece of paper
More slides like this


Slide #5.

Origami primitives
More slides like this


Slide #6.

Pseudocode Primitives • Pseudocode is “sort of” code that a computer can understand, but a higher level to be more easily human understandable – But becomes pretty straightforward to convert to an actual programming language • Assignment name  expression • Conditional selection if condition then action
More slides like this


Slide #7.

Pseudocode Primitives (continued) • Repeated execution while condition do activity • Procedure (aka Method, Subroutine, Function) procedure name list of primitives associated with name
More slides like this


Slide #8.

The procedure Greetings in pseudocode
More slides like this


Slide #9.

Running Example • You are running a marathon (26.2 miles) and would like to know what your finishing time will be if you run a particular pace. Most runners calculate pace in terms of minutes per mile. So for example, let’s say you can run at 7 minutes and 30 seconds per mile. Write a program that calculates the finishing time and outputs the answer in hours, minutes, and seconds. • Input: Distance : 26.2 PaceMinutes: 7 PaceSeconds: 30 • Output: 3 hours, 16 minutes, 30 seconds
More slides like this


Slide #10.

One possible solution • Express pace in terms of seconds per mile by multiplying the minutes by 60 and then add the seconds; call this SecsPerMile • Multiply SecsPerMile * 26.2 to get the total number of seconds to finish. Call this result TotalSeconds. • There are 60 seconds per minute and 60 minutes per hour, for a total of 60*60 = 3600 seconds per hour. If we divide TotalSeconds by 3600 and throw away the remainder, this is how many hours it takes to finish. • The remainder of TotalSeconds / 3600 gives us the number of seconds leftover after the hours have been accounted for. If we divide this value by 60, it gives us the number of minutes. • The remainder of ( the remainder of(TotalSeconds / 3600) / 60) gives us the number of seconds leftover after the hours and minutes are accounted for • Output the values we calculated!
More slides like this


Slide #11.

Pseudocode SecsPerMile  (PaceMinutes * 60) + PaceSeconds TotalSeconds  Distance * SecsPerMile Hours  Floor(TotalSeconds / 3600) LeftoverSeconds  Remainder of (TotalSeconds / 3600) Minutes  Floor(LeftoverSeconds / 60) Seconds  Remainder of (LeftoverSeconds /60) Output Hours, Minutes, Seconds as finishing time
More slides like this


Slide #12.

Polya’s Problem Solving Steps 1. Understand the problem. 2. Devise a plan for solving the problem. 3. Carry out the plan. 4. Evaluate the solution for accuracy and its potential as a tool for solving other problems.
More slides like this


Slide #13.

Getting a Foot in the Door • Try working the problem backwards • Solve an easier related problem – Relax some of the problem constraints – Solve pieces of the problem first (bottom up methodology) • Stepwise refinement: Divide the problem into smaller problems (top-down methodology)
More slides like this


Slide #14.

Ages of Children Problem • Person A is charged with the task of determining the ages of B’s three children. – – – – – – B tells A that the product of the children’s ages is 36. A replies that another clue is required. B tells A the sum of the children’s ages. A replies that another clue is needed. B tells A that the oldest child plays the piano. A tells B the ages of the three children. • How old are the three children?
More slides like this


Slide #15.

Solution
More slides like this


Slide #16.

Iterative Structures • Pretest loop: while (condition) do (loop body) • Posttest loop: repeat (loop body) until(condition)
More slides like this


Slide #17.

The while loop structure
More slides like this


Slide #18.

The repeat loop structure
More slides like this


Slide #19.

Components of repetitive control
More slides like this


Slide #20.

Example: Sequential Search of a List Fred Alex Diana Byron Carol Want to see if Byron is in the list
More slides like this


Slide #21.

The sequential search algorithm in pseudocode procedure Search(List, TargetValue) If (List is empty) Then (Target is not found) Else ( name  first entry in List while (no more names on the List) ( if (name = TargetValue) (Stop, Target Found) else name  next name in List ) (Target is not found) )
More slides like this


Slide #22.

Sorting the list Fred, Alex, Diana, Byron, and Carol alphabetically Insertion Sort: Moving to the right, insert each name in the proper sorted location to its left Fred Alex Diana Byron Carol
More slides like this


Slide #23.

The insertion sort algorithm expressed in pseudocode 1 2 3 4 Fred Alex Diana 5 Byron Carol
More slides like this


Slide #24.

Recursion • The execution of a procedure leads to another execution of the procedure. • Multiple activations of the procedure are formed, all but one of which are waiting for other activations to complete. • Example: Binary Search
More slides like this


Slide #25.

Applying our strategy to search a list for the entry John Alice Bob Carol David Elaine Fred George Harry Irene John Kelly Larry Mary Nancy Oliver
More slides like this


Slide #26.

A first draft of the binary search technique
More slides like this


Slide #27.

The binary search algorithm in pseudocode
More slides like this


Slide #28.

Searching for Bill
More slides like this


Slide #29.

Searching for David
More slides like this


Slide #30.

Algorithm Efficiency • Measured as number of instructions executed • Big theta notation: Used to represent efficiency classes – Example: Insertion sort is in Θ(n2) • Best, worst, and average case analysis
More slides like this


Slide #31.

Applying the insertion sort in a worst-case situation
More slides like this


Slide #32.

Graph of the worst-case analysis of the insertion sort algorithm
More slides like this


Slide #33.

Graph of the worst-case analysis of the binary search algorithm
More slides like this


Slide #34.

Software Verification • Proof of correctness – Assertions • Preconditions • Loop invariants • Testing
More slides like this


Slide #35.

Chain Separating Problem • A traveler has a gold chain of seven links. • He must stay at an isolated hotel for seven nights. • The rent each night consists of one link from the chain. • What is the fewest number of links that must be cut so that the traveler can pay the hotel one link of the chain each morning without paying for lodging in advance?
More slides like this


Slide #36.

Separating the chain using only three cuts
More slides like this


Slide #37.

Solving the problem with only one cut
More slides like this