computational logic and computational thinking programming

Chihlee University of Technology, Fall 2020Computational Logic & Programming ApplicationsAssociate Professor: Chien-Hua Tsai

2020/10/23

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Computational Logic and Programming Applications

Computational Thinking & Algorithms (II)

Department of Accounting InformationChihlee University of TechnologyChien-Hua Tsai

http://www1.chihlee.edu.tw/teachers/chienhua/

Chien-Hua Tsai 2

Roadmap

> Scheduling> Backtracking> Planning and Optimization> Pipelining

Computational Thinking

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Roadmap



Chien-Hua Tsai


4Chien-Hua Tsai

> Algorithms are at the heart of Computational Thinking and Computer Science, because in Computer Science the solutions to problems are not simply an answer (e.g. ‘75’, or a fact), they are algorithms.

Computational Thinking & Algorithms


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AlgorithmsComputational Thinking

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An algorithm is a sequence of instructions, or set of rules, for performing a task

An algorithm is a sequence of instructions, or set of rules, for performing a task

Chien-Hua Tsai

> A step by step procedure to solve a problem or explain a process.

> A plan of the steps you would have to go through to solve a problem.

Process ManagementComputational Thinking

6Chien-Hua Tsai

> As a process executes, it changes state:— new: The process is being created— ready: The process is waiting to be assigned to run— running: Instructions are being executed— waiting: The process waiting for some event to occur— terminated: The process has finished execution

Multiprocessing vs. MultiprogrammingComputational Thinking

7Chien-Hua Tsai

> Multi-processing: Supports running a program on more than one CPU.

> Multi-programming (or, multi-tasking): Allows more than one program to run concurrently.

> Multi-threading: Allows different parts of a single program to run concurrently.

> Remember Definitions:— Multi-processing Multiple CPUs— Multi-programming Multiple programs— Multi-threading Multiple threads per program

> What does it mean to run two threads “concurrently”?— Threads run in any order and interleaving


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Multiprocessing vs. Multiprogramming

A B C

BA ACB C BMultiprogramming

ABC

Multiprocessing


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Can threads make this easier?Computational Thinking

9Chien-Hua Tsai

> Most of the time, threads are working on separate data, so scheduling doesn’t matter:

Thread A Thread Bx = 1; y = 2;

> However, what about (initially, y = 12):Thread A Thread B

x = 1; y = 2;x = y+1; y = y2;

— What are the possible values of x?

Scheduling AssumptionsComputational Thinking

10Chien-Hua Tsai

> CPU scheduling big area of research in early 70s> Many implicit assumptions for CPU scheduling:

— One program per user— One thread per program— Programs are independent

> The high-level goal: dole out CPU time to optimize some desired parameters of system

> Maximum CPU utilization obtained with multiprogramming

> CPU utilization – keep the CPU as busy as possible> Throughput – # of processes that complete their

execution per time unit

First-Come, First-Served (FCFS) SchedulingComputational Thinking

11Chien-Hua Tsai

Process Burst TimeP1 24P2 3P3 3

> Suppose that the processes arrive in the order: P1, P2, P3The Gantt Chart for the schedule is:

> Waiting time for P1 = 0; P2 = 24; P3 = 27> Average waiting time: (0 + 24 + 27)/3 = 17> Average completion time: (24 + 27 + 30)/3 = 27

P1 P2 P3

24 27 300

First-Come, First-Served (FCFS) SchedulingComputational Thinking

12Chien-Hua Tsai

> Suppose that the processes arrive in the orderP2, P3, P1

> The Gantt chart for the schedule is:

> Waiting time for P1 = 6; P2 = 0; P3 = 3> Average waiting time: (6 + 0 + 3)/3 = 3> Average completion time: (3 + 6 + 30)/3 = 13> Much better than previous case

P1P3P2

63 300


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13Chien-Hua Tsai

Your Turn: FCFS Scheduling

Job Arrival CPU Burst

A 0 10B 1 2C 2 4

What is the Gantt chart for the schedule?What is the average waiting time?

Shortest-Job-First (SJF) SchedulingComputational Thinking

14Chien-Hua Tsai

Process Arrival Time Burst TimeP1 0.0 7P2 2.0 4P3 4.0 1P4 5.0 4


> Average waiting time = (0 + 6 + 3 + 7)/4 = 4> Average completion time = (7 + 10 + 4 + 11)/4 = 8

P1 P3 P2

73 160

P4

8 12

Shortest-Remaining-Time-First (SRTF) Scheduling


15Chien-Hua Tsai

Process Arrival Time Burst TimeP1 0.0 7P2 2.0 4P3 4.0 1P4 5.0 4


> Average waiting time = (9 + 1 + 0 + 2)/4 = 3> Average completion time = (16 + 5 + 1 + 6)/4 = 7

P1 P3P2

42 110

P4

5 7

P2 P1

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Your Turn: SJF & SRTF Scheduling

Job Arrival CPU BurstA 0 8B 1 4C 2 9D 3 5

What are the Gantt charts for SJF and SRTF?What is the average waiting time respectively?


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Priority SchedulingComputational Thinking

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Process Burst Time PriorityP1 10 3P2 1 1P3 2 4P4 1 5P5 5 2


> Average waiting time: (6 + 0 + 16 + 18 + 1)/5 = 8.2> Average completion time: (16 + 1 + 18 + 19 + 6)/5 = 12

P1P5P2

61 190

P3 P4

16 18


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Your Turn: Priority Scheduling

Job Arrival CPU Burst PriorityA 0 4 4B 1 3 3C 2 1 2D 3 5 1E 4 2 1

What are the Gantt charts for he schedule?What is the average waiting time?

Round Robin (RR) Scheduling with Time Quantum = 20


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P1 P2 P3 P4 P1 P3 P4 P1 P3 P3

0 20 37 57 77 97 117 121 134 154 162

Process Burst TimeP1 53P2 17P3 68P4 24


> Waiting time for P1 = (77–20)+(121–97) = 81P2 = (20–0) = 20 P3 = (37–0)+(97–57)+(134–117) = 94P4 = (57–0)+(117–77) = 97

Round Robin (RR) Scheduling with Time Quantum = 20


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P1 P2 P3 P4 P1 P3 P4 P1 P3 P3

0 20 37 57 77 97 117 121 134 154 162

Process Burst TimeP1 53P2 17P3 68P4 24


> Average waiting time = (81+20+94+97)/4=73> Average completion time = (134+37+162+121)/4=113.5


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Your Turn: RR Scheduling with Time Quantum = 1

Job Arrival CPU Burst

A 0 10B 1 2C 2 4

What is the Gantt chart for the schedule?What is the average waiting time?

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Roadmap



Chien-Hua Tsai

BacktrackingComputational Thinking

23Chien-Hua Tsai

> Backtracking is a methodical way of trying out various sequences of decisions, until you find one that “works”

> At each intersection, you have to decide between three or fewer choices:— Go straight— Go left— Go right


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Backtracking Problem: An Example

> You wish to find a goal state

CC DD

AA BB

EE FF

RootRoot

badbad badbad badbadgoodgood

1. Starting at Root, your options are A and B. You choose A.

2. At A, your options are C and D. You choose C.

3. C is bad. Go back to A.

4. At A, you have already tried C, and it failed. Try D.

5. D is bad. Go back to A.

6. At A, you have no options left to try. Go back to Root.

7. At Root, you have already tried A. Try B.

8. At B, your options are E and F. Try E.

9. E is good. Congratulations!


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Your Turn: Backtracking for Finding Permutations of a given string

> Given a set, enumerate all possible permutations.— Input: {1, 2, 3}— Output: { [1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1] }— Permutation describes an arrangement or ordering of items.


26Chien-Hua Tsai

Your Turn: Backtracking for Finding Combinations of a given string

> Given a set, print all its combinations.— Input: {1, 2, 3}— Output: { {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3} }— It involves a set and none of the subsets repeats itself, but just

changing the order.

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Roadmap



Chien-Hua Tsai

Planning and OptimizationComputational Thinking

28Chien-Hua Tsai

> Planning is a search problem that requires to find an efficient sequence of actions that transform a system from a given starting state to the goal state— Planning may require

sophisticated analysis of multiple scenario

> For any given optimization problem, we would like to come up with a (hopefully efficient) algorithm— That ideally finds the global

minimum of the objective function


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Planning & Optimization: An Example

> The shortest path problem is the problem of finding a path between two nodes such that the sum of the weights of its constituent edges is minimized.


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> Kruskal's Algorithm


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> Kruskal's Algorithm


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> Prim's Algorithm


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> Prim's Algorithm


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Your Turn: Planning and Optimization

> Given a graph and a source vertex in the graph, find shortest paths from source to all vertices by Kruskal's and Prim's algorithms respectively.


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Open Shortest-Path First (OSPF) Routing(Dijkstra's Algorithm)

Network is a graph with routers and linksEach unidirectional link has a weightShortest-path routes from sum of link weights

Weights are assigned statically (configuration file)Weights based on capacity, distance, and trafficFlooding of info about weights and IP addresses

u

yx

wv

z2

21

3

1

12

53

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Graph: G = (N,E)N = set of routers = { u, v, w, x, y, z }E = set of links ={ (u,v), (u,x), (v,x), (v,w), (x,w), (x,y), (w,y), (w,z), (y,z) }

link

router


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Building OSPF Routing Table

8

1712

10 20

32

12

14 A

B

E

F D

C

A(0)


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8

1712

10 20

32

12

14 A

B

E

F D

C

A(0)

B(8)

D(20)

C(32)


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8

1712

10 20

32

12

14 A

B

E

F D

C

A(0)

B(8)

D(20)

C(32)

D(25)


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8

1712

10 20

32

12

14 A

B

E

F D

C

A(0)

B(8)

D(20)

C(32)

D(25)

F(32)

C(30)


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A(0)

B(8)

D(20)

C(32)

D(25)

F(32)

C(30)

8

1712

10 20

32

12

14 A

B

E

F D

C

F(42)

E(44)


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A(0)

B(8)

D(20)

C(32)

D(25)

F(32)

C(30)

8

1712

10 20

32

12

14 A

B

E

F D

C

F(42)

E(44)


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A(0)

B(8)

D(20)

C(32)

D(25)

F(32)

C(30)

8

1712

10 20

32

12

14 A

B

E

F D

C

F(42)

E(44)


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8

1712

10 20

32

12

14 A

B

E

F D

C

A(0)

B(8)

D(20)

F(32)

C(30)

E(44)


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Forwarding table

The shortest path treeof router A

A(0)

B(8)

D(20)

F(32)

C(30)

E(44)

Destination Next hop

Shortest path

Total cost

B B A B 8

C D A D C 30

D D A D 20

E D A D C E 44

F D A D F 32


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45Chien-Hua Tsai

Your Turn: Building Routing Table

8

1712

10

32

12

14 A

B

E

F D

C

Check the case!


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Your Turn: Building Routing Table

Forwarding table

The shortest path treeof router A

Destination Next hop

Shortest path

Total cost

B

C

D

E

F

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Roadmap



Chien-Hua Tsai

PipeliningComputational Thinking

48Chien-Hua Tsai

> Pipelining is an implementation technique where multiple instructions are overlapped in execution.

> The pipeline designer's goal is to balance the length of each pipeline stage.


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49Chien-Hua Tsai

Pipelining: An Example

> Ann, Brian, Cathy, Dave each have one load of clothes to wash, dry, and fold— Washer takes 30 minutes— Dryer takes 40 minutes— Folder takes 20 minutes


50Chien-Hua Tsai

Your Turn: Pipelining Arrangement

> Consider a processor having 4 stages and let there be 2 instructions to be executed.

> We can visualize the execution sequence in the space-time diagram at the right.

What does it need a total of cycles for execution in a pipelined processor?

What does it need a total of cycles for execution in a pipelined processor?

Reading AssignmentComputational Thinking

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> Related materials are covered in the lecture slides

Chien-Hua Tsai

Computational Logic and Programming Applications

Computational Thinking & Algorithms (II)

End of the Lecture

computational logic and computational thinking programming

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