1. Introduction to Computer Systems
Lecturer: Steve Maybank
Department of Computer Science and Information Systems
Spring 2017
Week 1b: Algorithms
10 January 2017
Birkbeck College, U. London

2. Birkbeck College, U. London
Informal Algorithms
Directions to go from one place to another.
Cooking recipes.
How to use a device (TV, microwave, etc.)
How to assemble flat pack furniture
A list of instructions for Tom
10 January 2017
Birkbeck College, U. London

3. Example of a Cooking Algorithm
Obtain a basket of unshelled pea pods and an empty bowl.
As long as there are unshelled pea pods in the basket
Take a pea pod from the basket
Break open the pea pod
Dump the peas from the pod into the bowl
Discard the pod
10 January 2017
Brookshear Section 5.1

4. Birkbeck College, U. London
Commentary
Input: basket of unshelled pea pods and an empty bowl
Output: bowl of peas and the pea pods
Variable: the number of pea pods in the basket
The instructions are carried out in a strict order, one after the other
Instruction 2 affects the order in which the other instructions are carried out.
10 January 2017
Birkbeck College, U. London

5. Effect of Removing Instruction 2
Obtain a basket of unshelled pea pods and an empty bowl
Do nothing
Take a pea pod from the basket
Break open the pea pod
Dump the peas from the pod into the bowl
Discard the pod
10 January 2017
Birkbeck College, U. London

6. Birkbeck College, U. London
Flow Chart
is there a
pea pod in the
basket? no
halt
yes
carry out
3, 4, 5, 6
10 January 2017
Birkbeck College, U. London

7. Reduced Version of the Cooking Algorithm
Store a non-negative integer in a memory location called basket
As long as the value stored in basket is strictly greater than 0
Subtract 1 from the value stored in basket
10 January 2017
Birkbeck College, U. London

8. Birkbeck College, U. London
Variables 1
A variable is a named memory location
e.g. the variable q.
q=5 # store the value 5 in the memory location specified by q
q=5 # assign the value 5 to the variable q
The exact memory location specified by q is chosen when the program runs
10 January 2017
Birkbeck College, U. London

9. Birkbeck College, U. London
Variables 2
q=5+2 # evaluate the right hand side. Assign the resulting value to q.
q=q+2 # evaluate the right hand side. Assign the resulting value to q.
5=q # error
10 January 2017
Birkbeck College, U. London

10. Definition of an Algorithm
An algorithm is an ordered set of unambiguous executable steps that defines a terminating process.
It is implicit that something (e.g. a machine) carries out the steps.
10 January 2017
BB Section 5.1

11. Birkbeck College, U. London
Commentary
Terminating process: print all the integers in the range 1 to 10
Non-terminating process: print all the integers
Executable step: assign to x the value 1
Non executable step: attempt to assign to x a value larger than any that can be stored.
10 January 2017
Birkbeck College, U. London

12. Algorithms and Computers
An algorithms is converted into a list of instructions (program) for a particular computer.
The details of the instructions vary from one computer to another
If an algorithm is programmable on one computer, then in principle it is programmable on any computer.
10 January 2017
Birkbeck College, U. London

13. First Example of an Algorithm
Input: integers 12, 5
Output: quotient q and remainder r on dividing 12 by 5
Algorithm
q = 0; r = 12
Subtract 5 from r; Increase q by 1
Output q, r
Halt
10 January 2017
Birkbeck College, U. London

14. Second Example of an Algorithm
Input: strictly positive integers m, n
Output: quotient q and remainder r on dividing m by n
Algorithm
q = 0
r = m
If r < n, Output q, r; Halt
r = r-n
q = q+1
go to 3
10 January 2017
Birkbeck College, U. London

15. Third Example of an Algorithm
Input: strictly positive integers m, n
Output: quotient q and remainder r on dividing m by n
Algorithm
q = 0
r = m
While r >= n,
r = r-n
q = q+1
EndWhile
Output q, r
Halt
10 January 2017
Birkbeck College, U. London

16. Building a New Algorithm
Give the third algorithm a name:
division(m, n)
Show how division(m, n) can be used in a new algorithm to print out all the exact divisors of m, i.e. those integers n ≥1 for which m/n is an integer.
10 January 2017
Birkbeck College, U. London

17. Birkbeck College, U. London
Exercise
Sketch an algorithm that takes as input a strictly positive integer n and outputs an integer k such that
10 January 2017
Birkbeck College, U. London