Download Lecture 4 Powerpoint

Mathematics for Computing
Lecture 4:
Algorithms and flowcharts
Dr Andrew Purkiss-Trew
Cancer Research UK
[email protected]
Algorithms
An algorithm is a step-by-step set of
instructions for solving a particular problem
We will be using flowcharts to explore
simple algorithms
Flowchart
Graphical representation of an algorithm
Show the ‘layout’ of a program
Form is a series of symbols linked with
arrows
Flowchart symbols 1
Terminator
Data Entry
(or Input/Output)
Process
Flowchart Symbols 2
Decision
Preparation
Connector
1
Flowchart example 1
Find the mean
of two numbers
Start
Read X,Y
Stop
Sum = X+Y
Mean = Sum / 2
Print Mean
Flowchart example 2:1
Solve a quadratic equation ax2+bx+c = 0
Discriminant, D = b2-4ac, tells us how many
real solutions.
D <0 means no real solution,
D=1 means 1 solution: x = -b/2a
D>0 means 2 solns: x = -b ± √(b2 – 4ac)
2a
Flowchart example 2:2
1
2
3
X = -B
2xA
X1 = -B + √D
2xA
X2 = -B - √D
2xA
Start
Print ‘No
real solution
Read A,B,C
Print
‘solution’, X
D = B2-4xAxC
negative Sign of
D?
positive
Stop
zero
1
2
3
Print
X1, X2
Pseudocode
Algorithms can also be represented as
‘English language’ instructions.
These are then converted to the relevant
program code.
Variables and Constants
Variable
Constants
Numerical: Integer or exponential
Non-numerical: Strings
Logical: True or False
Flowchart Symbols
Terminal
Decision
Input / Output
Connector
Process
Preparation