1. Mathematics for Computing Lecture 4: Algorithms and flowcharts Dr Andrew Purkiss-Trew Cancer Research UK a.purkiss@mail.cryst.bbk.ac.uk

2. 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

3. Flowchart Graphical representation of an algorithm Show the ‘layout’ of a program Form is a series of symbols linked with arrows

4. Flowchart symbols 1 Terminator Data Entry (or Input/Output) Process

5. Flowchart Symbols 2 Decision Preparation Connector 1

6. Flowchart example 1 Find the mean of two numbers Start Read X,Y Sum = X+Y Mean = Sum / 2 Print Mean Stop

7. 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

8. 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

9. Pseudocode Algorithms can also be represented as ‘English language’ instructions. These are then converted to the relevant program code.

12. Variables and Constants Variable Constants Numerical: Integer or exponential Non-numerical: Strings Logical: True or False

13. Flowchart Symbols Input / Output Process Decision Connector Preparation Terminal