mathematics for computing lecture 4: algorithms and flowcharts dr andrew purkiss-trew cancer...
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Mathematics for Computing
Lecture 4:Algorithms and flowcharts
Dr Andrew Purkiss-TrewCancer Research UK
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 meanof two numbers
Start
Read X,Y
Sum = X+Y
Mean = Sum / 2
Print Mean
Stop
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/2aD>0 means 2 solns: x = -b ± √(b2 – 4ac) 2a
Flowchart example 2:2
Start
Read A,B,C
D = B2-4xAxC
Sign ofD?
1 2 3
negative positive
zero
1 2 3
Print ‘Noreal solution
X = -B 2xA
Print ‘solution’, X
Stop
X1 = -B + √D 2xA
X2 = -B - √D 2xA
PrintX1, X2
Pseudocode
Algorithms can also be represented as ‘English language’ instructions.
These are then converted to the relevant program code.
Variables and Constants
Variable
ConstantsNumerical: Integer or exponentialNon-numerical: StringsLogical: True or False
Flowchart Symbols
Input / Output
Process
Decision
Connector
Preparation
Terminal