Apr 19, 2023

Algorithms

2.2

Overview

In this presentation we will discuss: What is an algorithm? 5 steps in developing an algorithm A Jeroo example

An algorithm is...

A plan for solving a problem

5 steps in algorithm development1. Describe the problem clearly

2. Analyze the problem

3. Develop a high-level algorithm

4. Refine the algorithm by adding detail

5. Review the algorithm

Step 1: describe the problem

Not as easy as it seems. Common defects:

Description relies on unstated assumptions Description is ambiguous Description is incomplete Description has contradictions

Natural spoken languages are not very precise. It’s the developer’s job to spot any of these problems

BEFORE any problem solving happens.

Step 2 : Analyze the problem

Similar to a mathematician determining what factors and given and what must be proven in a complex set of equations.

Ask: What data is available? What formulas are needed? What rules apply? What relationships exist among the data values? What determines a complete solution? (When am I done?)

Step 3: Develop a high-level algorithm

An overview. Not detailed. For example: Step 1 : the problem

I need to send a birthday card to my brother, Mark. Step 2: Analyze

I don’t have a card. I prefer to buy a card rather than make one myself.

Step 3: High Level Algorithm Go to a store that sells cards Select and purchase a card Mail the card

High-level algorithms Go to a store that sells cards Select and purchase a card Mail the card

Lacks enough detail for a computer or robot to understand

•Which store?

•How will you get to the store? (bike, car, bus?)

•What kind of card does Mark like? (funny, risqué, outdoorsy?)

Step 4: Refine the algorithm by adding detail

Stepwise refinement= Keep adding levels of detail. To know what level of detail is needed

You need to know how it will ultimately be implemented

Birthday card example

Who is going?

Me? Very little detail needed

Another family member? Minimal detail

Someone unfamiliar with the area? Lots of detail about directions

A robot? Minute detail.

Stepwise refinement

The more complex the problem, the more steps it takes to refine it to sufficient detail.

High Level detailed level For very large problems you go

through the process many times, developing intermediate level algorithms as you go.

Step 5: Review

First: Work through the algorithm step by step and determine whether or not it actually solves the problem.

Then ask: Does it solve a particular problem or a general one? Should it be generalized? A program to find the area of a circle with radius = 5.2 could

easily be generalized to find the area of any circle with the addition of a single variable.

Can it be simplified? Is this solution similar to something already done?

A Jeroo example

Step 1: the problem clearly defined. A Jeroo starts at (0,0) facing East with no flowers in its

pouch. There is a flower at location (0,3). The Jeroo should pick the flower and plant it at location (2,3) and then hop one square to the East. There are no other nets, flowers or Jeroos on the island.

Analysis of the problem (step 2)

The flower is 3 spaces ahead of the Jeroo The flower should be planted 2 spaces south of its

current location The Jeroo should end up at location (2,4) facing east There are no obstacles to worry about

NORTH

Jeroo

flowerStart positions

High-Level Algorithm (step 3)

Create a Jeroo named Bob

Bob should:Get the flower

Plant the flower

Hop East

Start positions End positions

Detailed Algorithm (step 4)

Create a Jeroo named Bob Bob should:

Get the flower Hop 3 times Pick the flower

Plant the flower Turn right Hop 2 times Plant a flower

Hop East Turn left Hop once

Review (step 5)

The high-level algorithm created 3 distinct, easy sub-problems. This seems like a good technique.

This solves a very specific problem. It actually works for any setup where the Jeroo starts

anywhere and the flower is 3 spaces directly ahead of it.

Good programming practices

Detailed Algorithm: Create a Jeroo named Bob Bob should:

Get the flower Hop 3 times Pick the flower

Plant the flower Turn right Hop 2 times Plant a flower

Hop East Turn left Hop once

method main()

{

Jeroo bob = new Jeroo();

// ---- Get the flower ---

// --- Plant the flower ---

// --- Hop east ---

}

Comments clearly mirror the high-level algorithm

Then add detail

Detailed Algorithm: Create a Jeroo named Bob Bob should:

Get the flower Hop 3 times Pick the flower

Plant the flower Turn right Hop 2 times Plant a flower

Hop East Turn left Hop once

method main()

{

Jeroo bob = new Jeroo();

// ---- Get the flower ---

bob.hop(3);

bob.pick();

// --- Plant the flower ---

bob.turn(RIGHT);

bob.hop(2);

bob.plant();

// --- Hop east ---

//Etc.

}

The End