Algorithms. Gregory D. Weber. April 11, 2016

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1 Algorithms Gregory D. Weber April 11, 2016

2 Learning Objectives Define algorithm, function, variable Interpret algorithms Design algorithms Distinguish algorithms, pseudocode, flowcharts, code (programs).

3 Introduction Putting instructions together: Sequence Repeat until Repeat N times If If/Else

4 Algorithms Algorithms are programs for human computers.

5 Defining algorithm An algorithm is a complete, step-by-step procedure for solving a specific problem. Berman and Paul, Fundamentals of Sequential and Parallel Algorithms (1997).

6 Defining algorithm An algorithm is a complete, step-by-step procedure for solving a specific problem. Berman and Paul, Fundamentals of Sequential and Parallel Algorithms (1997). a precise rule (or set of rules) specifying how to solve some problem WordNet

7 Defining algorithm An algorithm is a complete, step-by-step procedure for solving a specific problem. Berman and Paul, Fundamentals of Sequential and Parallel Algorithms (1997). a precise rule (or set of rules) specifying how to solve some problem WordNet A detailed sequence of actions to perform to accomplish some task. The Free On-line Dictionary of Computing

8 Defining algorithm An algorithm is a complete, step-by-step procedure for solving a specific problem. Berman and Paul, Fundamentals of Sequential and Parallel Algorithms (1997). a precise rule (or set of rules) specifying how to solve some problem WordNet A detailed sequence of actions to perform to accomplish some task. The Free On-line Dictionary of Computing An algorithm is a precise, systematic method for producing a specified result. Snyder, Fluency with Information Technology

9 Defining algorithm An algorithm is a complete, step-by-step procedure for solving a specific problem. Berman and Paul, Fundamentals of Sequential and Parallel Algorithms (1997). a precise rule (or set of rules) specifying how to solve some problem WordNet A detailed sequence of actions to perform to accomplish some task. The Free On-line Dictionary of Computing An algorithm is a precise, systematic method for producing a specified result. Snyder, Fluency with Information Technology Key idea: a procedure that achieves a result or solves a problem.

10 Five Properties of Algoriothms 1. Input specified 2. Output specified 3. Definiteness 4. Effectiveness 5. Finiteness Donald Knuth, The Art of Computer Programming (1968, 1973), via Snyder.

11 Input and Output Desktop computer input devices: Keyboard, mouse Disk drives Network interface Desktop computer output devices: Display Printer Speakers Disk drives, network An algorithm to name the U.S. president...

12 Beyond the Desktop Agents with sensors and actions Sensors provide inputs Actions are outputs

13 Bird and Zombie Actions

14 Angry Bird s Sensors

15 Zombie s Sensors

16 Sensors and Actions Summary Angry bird: Sensor: pig here? Actions: forward, turn left right Zombie: Sensor: sunflower here? path ahead left right? Actions: forward, turn left right Sensors (input), actions (output)

17 Empty Input and Output Can an algorithm have no input? Can an algorithm produce no output?

18 Definiteness Each step of an algorithm must be precisely defined; the actions to be carried out must be rigorously and unambiguously specified for each case. (Knuth) Algorithm (?) to go to the Post Office: 1. Go east through the woods until you come to the most beautiful tree. 2. Turn left 90 degrees, and go forward a stone s throw. 3. If water is flowing from the fountain, then turn right a little and move forward 120 paces. Problems?

19 Effectiveness All of the operations to be performed in the algorithm must be sufficiently basic that they can in principle be done exactly and in a finite length of time by a man using paper and pencil. (Knuth) Limited: text I/O Mechanical : no imagination or creativity required Algorithm (?) to find the square root of x: 1. The square root of x is the number which, multiplied by itself, makes x. Problems?

20 Definiteness and Effectiveness The names are unimportant. Algorithms should be clear and unambiguous. Algorithms should be mechanically and uncreatively executable.

21 Finiteness An algorithm must (usually) be finite Finitely many instructions Finite time to execute Algorithm (?) to go to the pig: repeat u n t i l p i g i s h e r e do t u r n l e f t Exceptions

22 Algorithms and Their Expressions Algorithms are ideas Can be expressed variously For humans: Pseudocode Flowcharts For machines: Programs, code

23 Pseudocode To walk in a square: Do this 4 times: Take 10 steps forward. Turn right 90 degrees. Vary wording Translate to Spanish, etc.

24 Flowchart Figure 1: Move in a Square Flowchart

25 Blocks Language Code

26 JavaScript Code f o r ( v a r count = 0 ; count < 4 ; count++) { f o r w a r d ( 1 0 ) ; t u r n _ r i g h t ( 9 0 ) ; }

27 Python Code f o r count i n range ( 4 ) : f o r w a r d (10) t u r n _ r i g h t (90)

28 Programming Languages Are Strict Slight errors... Because computing machines are dumb

29 Review Algorithms as ideas Expressed for humans Expressed for machines

30 Functions Spreadsheets Square root, sum, average, financial, etc. Name and arguments(s), result A function is an operation that the agent already knows how to perform (Snyder). Some functions do I/O: Angry bird functions Zombie functions Effective algorithms only use operations the agent knows how to perform Not all agents have same functions Effective for one agent may be ineffective for another

31 Memories, Or Variables Some agents need to remember things Shopping errand Angry bird and zombie did not A variable is a named memory for storing information Store Update Retrieve Algorithms using memories must be explicit in their instructions for using the memories

32 Examples of Algorithms Think about: Sensors (inputs) Actions (outputs) Memories (variables) Procedures (instructions)

33 1 Thermostat Algorithm Problem: Design an algorithm for a thermostat to control room temperature (heating only)

34 1 Thermostat Algorithm Problem: Design an algorithm for a thermostat to control room temperature (heating only) 1. Inputs/sensors

35 1 Thermostat Algorithm Problem: Design an algorithm for a thermostat to control room temperature (heating only) 1. Inputs/sensors Measure the actual temperature.

36 1 Thermostat Algorithm Problem: Design an algorithm for a thermostat to control room temperature (heating only) 1. Inputs/sensors Measure the actual temperature. 2. Outputs/actions

37 1 Thermostat Algorithm Problem: Design an algorithm for a thermostat to control room temperature (heating only) 1. Inputs/sensors Measure the actual temperature. 2. Outputs/actions Turn heat on

38 1 Thermostat Algorithm Problem: Design an algorithm for a thermostat to control room temperature (heating only) 1. Inputs/sensors Measure the actual temperature. 2. Outputs/actions Turn heat on Turn heat off

39 1 Thermostat Algorithm Problem: Design an algorithm for a thermostat to control room temperature (heating only) 1. Inputs/sensors Measure the actual temperature. 2. Outputs/actions Turn heat on Turn heat off 3. Memories

40 1 Thermostat Algorithm Problem: Design an algorithm for a thermostat to control room temperature (heating only) 1. Inputs/sensors Measure the actual temperature. 2. Outputs/actions Turn heat on Turn heat off 3. Memories Desired room temperature

41 1 Thermostat Algorithm Problem: Design an algorithm for a thermostat to control room temperature (heating only) 1. Inputs/sensors Measure the actual temperature. 2. Outputs/actions Turn heat on Turn heat off 3. Memories Desired room temperature Built in, or set by user?

42 Thermostat Algorithm 1 repeat f o r e v e r do i f a c t u a l t e m p e r a t u r e < d e s i r e d t e m p e r a t u r e do t u r n heat on e l s e t u r n heat o f f How well would this work?

43 Thermostat Algorithm 2 repeat do f o r e v e r i f a c t u a l temp < d e s i r e d temp 1/2 do t u r n heat on e l s e i f a c t u a l temp > d e s i r e d temp + 1/2 do t u r n heat o f f e l s e do n o t h i n g

44 Comments Sometimes two algorithms are correct, but one is better repeat forever Not finite repeat until False

45 2 Elevator Control Problem: Design a control algorithm for an elevator to pick up passengers and deliver them to their destination floors.

46 2 Elevator Control Problem: Design a control algorithm for an elevator to pick up passengers and deliver them to their destination floors. Sensors: buttons to call the elevator (up, down) on each floor, buttons in the elevator to choose destinations, passenger moving through door, current location

47 2 Elevator Control Problem: Design a control algorithm for an elevator to pick up passengers and deliver them to their destination floors. Sensors: buttons to call the elevator (up, down) on each floor, buttons in the elevator to choose destinations, passenger moving through door, current location Actions: move up, move down, open door, close door, ring bell

48 2 Elevator Control Problem: Design a control algorithm for an elevator to pick up passengers and deliver them to their destination floors. Sensors: buttons to call the elevator (up, down) on each floor, buttons in the elevator to choose destinations, passenger moving through door, current location Actions: move up, move down, open door, close door, ring bell Memories (?): current intended direction (up/down), current floor

49 Elevator Algorithm 0 i f p e o p l e want to get on or o f f h e r e do l e t them get on and o f f i f p e o p l e want to get on or o f f above and we a r e going up do go up to next f l o o r i f p e o p l e want to get on or o f f below and we a r e going down do go down to next f l o o r

50 Elevator Algorithm 1 Intention means the direction the elevator will move, if it moves. s t a r t on bottom f l o o r, i n t e n t i o n = up repeat f o r e v e r do i f a p a s s e n g e r i s c a l l i n g from c u r r e n t f l o o r or a p a s s e n g e r i s going to the c u r r e n t f l o o r do r i n g b e l l open door w a i t 5 s e c o n d s w a i t u n t i l door i s not i n use c l o s e door (continued)

51 Elevator Algorithm, Continued (still in repeat forever) i f ( i n t e n t i o n = up and a p a s s e n g e r i s c a l l i n g from or going to any f l o o r above where we a r e ) do go up 1 f l o o r i f newly a r r i v e d f l o o r = top f l o o r do change i n t e n t i o n to down e l s e i f ( i n t e n t i o n = down and a p a s s e n g e r i s c a l l i n g from or going to any f l o o r below where we a r e ) do go down 1 f l o o r i f newly a r r i v e d f l o o r = bottom f l o o r do change i n t e n t i o n to up e l s e do n o t h i n g

52 Reflections The elevator s sensors and actions Memories: intention (planned direction), floor? Functions: Passenger calling from current floor? Passenger going to current floor? Passenger calling from above? Passenger going to above? Passenger calling from below? Passenger going to below? Who provides these? When? Solving complex problems.

CISC 4090 Theory of Computation

CISC 4090 Theory of Computation 9/2/28 Stereotypical computer CISC 49 Theory of Computation Finite state machines & Regular languages Professor Daniel Leeds dleeds@fordham.edu JMH 332 Central processing unit (CPU) performs all the instructions