Mathematics for Computing Lecture 4: Algorithms and flowcharts Dr Andrew Purkiss-Trew Cancer 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 mean of two numbers Start Read X,Y Sum = X+Y Mean = Sum / 2 Print Mean Stop

Flowchart example 2:1 Solve a quadratic equation ax 2 +bx+c = 0 Discriminant, D = b 2 -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 ± √(b 2 – 4ac) 2a

Flowchart example 2:2 Start Read A,B,C D = B 2 -4xAxC Sign of D? 123 negative positive zero 123 Print ‘No real solution X = -B 2xA Print ‘solution’, X Stop X1 = -B + √D 2xA X2 = -B - √D 2xA 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 Input / Output Process Decision Connector Preparation Terminal