problem solving is algorithms

• Analysis of Algorithms
• Backtracking
• Dynamic Programming
• Divide and Conquer
• Geometric Algorithms
• Mathematical Algorithms
• Pattern Searching
• Bitwise Algorithms
• Branch & Bound
• Randomized Algorithms

What is Algorithm | Introduction to Algorithms

Definition of algorithm.

The word Algorithm means ” A set of finite rules or instructions to be followed in calculations or other problem-solving operations ” Or ” A procedure for solving a mathematical problem in a finite number of steps that frequently involves recursive operations” .

Therefore Algorithm refers to a sequence of finite steps to solve a particular problem.

Use of the Algorithms:

Algorithms play a crucial role in various fields and have many applications. Some of the key areas where algorithms are used include:

• Computer Science: Algorithms form the basis of computer programming and are used to solve problems ranging from simple sorting and searching to complex tasks such as artificial intelligence and machine learning.
• Mathematics: Algorithms are used to solve mathematical problems, such as finding the optimal solution to a system of linear equations or finding the shortest path in a graph.
• Operations Research : Algorithms are used to optimize and make decisions in fields such as transportation, logistics, and resource allocation.
• Artificial Intelligence: Algorithms are the foundation of artificial intelligence and machine learning, and are used to develop intelligent systems that can perform tasks such as image recognition, natural language processing, and decision-making.
• Data Science: Algorithms are used to analyze, process, and extract insights from large amounts of data in fields such as marketing, finance, and healthcare.

These are just a few examples of the many applications of algorithms. The use of algorithms is continually expanding as new technologies and fields emerge, making it a vital component of modern society.

Algorithms can be simple and complex depending on what you want to achieve.

It can be understood by taking the example of cooking a new recipe. To cook a new recipe, one reads the instructions and steps and executes them one by one, in the given sequence. The result thus obtained is the new dish is cooked perfectly. Every time you use your phone, computer, laptop, or calculator you are using Algorithms. Similarly, algorithms help to do a task in programming to get the expected output.

The Algorithm designed are language-independent, i.e. they are just plain instructions that can be implemented in any language, and yet the output will be the same, as expected.

What is the need for algorithms?

• Algorithms are necessary for solving complex problems efficiently and effectively. 
• They help to automate processes and make them more reliable, faster, and easier to perform.
• Algorithms also enable computers to perform tasks that would be difficult or impossible for humans to do manually.
• They are used in various fields such as mathematics, computer science, engineering, finance, and many others to optimize processes, analyze data, make predictions, and provide solutions to problems.

What are the Characteristics of an Algorithm?

As one would not follow any written instructions to cook the recipe, but only the standard one. Similarly, not all written instructions for programming are an algorithm. For some instructions to be an algorithm, it must have the following characteristics:

• Clear and Unambiguous : The algorithm should be unambiguous. Each of its steps should be clear in all aspects and must lead to only one meaning.
• Well-Defined Inputs : If an algorithm says to take inputs, it should be well-defined inputs. It may or may not take input.
• Well-Defined Outputs: The algorithm must clearly define what output will be yielded and it should be well-defined as well. It should produce at least 1 output.
• Finite-ness: The algorithm must be finite, i.e. it should terminate after a finite time.
• Feasible: The algorithm must be simple, generic, and practical, such that it can be executed with the available resources. It must not contain some future technology or anything.
• Language Independent: The Algorithm designed must be language-independent, i.e. it must be just plain instructions that can be implemented in any language, and yet the output will be the same, as expected.
• Input : An algorithm has zero or more inputs. Each that contains a fundamental operator must accept zero or more inputs.
•   Output : An algorithm produces at least one output. Every instruction that contains a fundamental operator must accept zero or more inputs.
• Definiteness: All instructions in an algorithm must be unambiguous, precise, and easy to interpret. By referring to any of the instructions in an algorithm one can clearly understand what is to be done. Every fundamental operator in instruction must be defined without any ambiguity.
• Finiteness: An algorithm must terminate after a finite number of steps in all test cases. Every instruction which contains a fundamental operator must be terminated within a finite amount of time. Infinite loops or recursive functions without base conditions do not possess finiteness.
• Effectiveness: An algorithm must be developed by using very basic, simple, and feasible operations so that one can trace it out by using just paper and pencil.

Properties of Algorithm:

• It should terminate after a finite time.
• It should produce at least one output.
• It should take zero or more input.
• It should be deterministic means giving the same output for the same input case.
• Every step in the algorithm must be effective i.e. every step should do some work.

Types of Algorithms:

There are several types of algorithms available. Some important algorithms are:

1. Brute Force Algorithm :

It is the simplest approach to a problem. A brute force algorithm is the first approach that comes to finding when we see a problem.

2. Recursive Algorithm :

A recursive algorithm is based on recursion . In this case, a problem is broken into several sub-parts and called the same function again and again.

3. Backtracking Algorithm :

The backtracking algorithm builds the solution by searching among all possible solutions. Using this algorithm, we keep on building the solution following criteria. Whenever a solution fails we trace back to the failure point build on the next solution and continue this process till we find the solution or all possible solutions are looked after.

4. Searching Algorithm :

Searching algorithms are the ones that are used for searching elements or groups of elements from a particular data structure. They can be of different types based on their approach or the data structure in which the element should be found.

5. Sorting Algorithm :

Sorting is arranging a group of data in a particular manner according to the requirement. The algorithms which help in performing this function are called sorting algorithms. Generally sorting algorithms are used to sort groups of data in an increasing or decreasing manner.

6. Hashing Algorithm :

Hashing algorithms work similarly to the searching algorithm. But they contain an index with a key ID. In hashing, a key is assigned to specific data.

7. Divide and Conquer Algorithm :

This algorithm breaks a problem into sub-problems, solves a single sub-problem, and merges the solutions to get the final solution. It consists of the following three steps:

8. Greedy Algorithm :

In this type of algorithm, the solution is built part by part. The solution for the next part is built based on the immediate benefit of the next part. The one solution that gives the most benefit will be chosen as the solution for the next part.

9. Dynamic Programming Algorithm :

This algorithm uses the concept of using the already found solution to avoid repetitive calculation of the same part of the problem. It divides the problem into smaller overlapping subproblems and solves them.

10. Randomized Algorithm :

In the randomized algorithm, we use a random number so it gives immediate benefit. The random number helps in deciding the expected outcome.

To learn more about the types of algorithms refer to the article about “ Types of Algorithms “.

Advantages of Algorithms:

• It is easy to understand.
• An algorithm is a step-wise representation of a solution to a given problem.
• In an Algorithm the problem is broken down into smaller pieces or steps hence, it is easier for the programmer to convert it into an actual program.

Disadvantages of Algorithms :

• Writing an algorithm takes a long time so it is time-consuming.
• Understanding complex logic through algorithms can be very difficult.
• Branching and Looping statements are difficult to show in Algorithms (imp) .

How to Design an Algorithm?

To write an algorithm, the following things are needed as a pre-requisite: 

• The problem that is to be solved by this algorithm i.e. clear problem definition.
• The constraints of the problem must be considered while solving the problem.
• The input to be taken to solve the problem.
• The output is to be expected when the problem is solved.
• The solution to this problem is within the given constraints.

Then the algorithm is written with the help of the above parameters such that it solves the problem.

Example: Consider the example to add three numbers and print the sum.

Step 1: Fulfilling the pre-requisites  

As discussed above, to write an algorithm, its prerequisites must be fulfilled. 

• The problem that is to be solved by this algorithm : Add 3 numbers and print their sum.
• The constraints of the problem that must be considered while solving the problem : The numbers must contain only digits and no other characters.
• The input to be taken to solve the problem: The three numbers to be added.
• The output to be expected when the problem is solved: The sum of the three numbers taken as the input i.e. a single integer value.
• The solution to this problem, in the given constraints: The solution consists of adding the 3 numbers. It can be done with the help of the ‘+’ operator, or bit-wise, or any other method.

Step 2: Designing the algorithm

Now let’s design the algorithm with the help of the above pre-requisites:

Algorithm to add 3 numbers and print their sum:  

• Declare 3 integer variables num1, num2, and num3.
• Take the three numbers, to be added, as inputs in variables num1, num2, and num3 respectively.
• Declare an integer variable sum to store the resultant sum of the 3 numbers.
• Add the 3 numbers and store the result in the variable sum.
• Print the value of the variable sum

Step 3: Testing the algorithm by implementing it.

To test the algorithm, let’s implement it in C language.

Here is the step-by-step algorithm of the code:

• Declare three variables num1, num2, and num3 to store the three numbers to be added.
• Declare a variable sum to store the sum of the three numbers.
• Use the cout statement to prompt the user to enter the first number.
• Use the cin statement to read the first number and store it in num1.
• Use the cout statement to prompt the user to enter the second number.
• Use the cin statement to read the second number and store it in num2.
• Use the cout statement to prompt the user to enter the third number.
• Use the cin statement to read and store the third number in num3.
• Calculate the sum of the three numbers using the + operator and store it in the sum variable.
• Use the cout statement to print the sum of the three numbers.
• The main function returns 0, which indicates the successful execution of the program.

Time complexity: O(1) Auxiliary Space: O(1) 

One problem, many solutions: The solution to an algorithm can be or cannot be more than one. It means that while implementing the algorithm, there can be more than one method to implement it. For example, in the above problem of adding 3 numbers, the sum can be calculated in many ways:

• Bit-wise operators

How to analyze an Algorithm? 

For a standard algorithm to be good, it must be efficient. Hence the efficiency of an algorithm must be checked and maintained. It can be in two stages:

1. Priori Analysis:

“Priori” means “before”. Hence Priori analysis means checking the algorithm before its implementation. In this, the algorithm is checked when it is written in the form of theoretical steps. This Efficiency of an algorithm is measured by assuming that all other factors, for example, processor speed, are constant and have no effect on the implementation. This is done usually by the algorithm designer. This analysis is independent of the type of hardware and language of the compiler. It gives the approximate answers for the complexity of the program.

2. Posterior Analysis:

“Posterior” means “after”. Hence Posterior analysis means checking the algorithm after its implementation. In this, the algorithm is checked by implementing it in any programming language and executing it. This analysis helps to get the actual and real analysis report about correctness(for every possible input/s if it shows/returns correct output or not), space required, time consumed, etc. That is, it is dependent on the language of the compiler and the type of hardware used.

What is Algorithm complexity and how to find it?

An algorithm is defined as complex based on the amount of Space and Time it consumes. Hence the Complexity of an algorithm refers to the measure of the time that it will need to execute and get the expected output, and the Space it will need to store all the data (input, temporary data, and output). Hence these two factors define the efficiency of an algorithm.  The two factors of Algorithm Complexity are:

• Time Factor : Time is measured by counting the number of key operations such as comparisons in the sorting algorithm.
• Space Factor : Space is measured by counting the maximum memory space required by the algorithm to run/execute.

Therefore the complexity of an algorithm can be divided into two types :

1. Space Complexity : The space complexity of an algorithm refers to the amount of memory required by the algorithm to store the variables and get the result. This can be for inputs, temporary operations, or outputs. 

How to calculate Space Complexity? The space complexity of an algorithm is calculated by determining the following 2 components:   

• Fixed Part: This refers to the space that is required by the algorithm. For example, input variables, output variables, program size, etc.
• Variable Part: This refers to the space that can be different based on the implementation of the algorithm. For example, temporary variables, dynamic memory allocation, recursion stack space, etc. Therefore Space complexity S(P) of any algorithm P is S(P) = C + SP(I) , where C is the fixed part and S(I) is the variable part of the algorithm, which depends on instance characteristic I.

Example: Consider the below algorithm for Linear Search

Step 1: START Step 2: Get n elements of the array in arr and the number to be searched in x Step 3: Start from the leftmost element of arr[] and one by one compare x with each element of arr[] Step 4: If x matches with an element, Print True. Step 5: If x doesn’t match with any of the elements, Print False. Step 6: END Here, There are 2 variables arr[], and x, where the arr[] is the variable part of n elements and x is the fixed part. Hence S(P) = 1+n. So, the space complexity depends on n(number of elements). Now, space depends on data types of given variables and constant types and it will be multiplied accordingly.

2. Time Complexity : The time complexity of an algorithm refers to the amount of time required by the algorithm to execute and get the result. This can be for normal operations, conditional if-else statements, loop statements, etc.

How to Calculate , Time Complexity? The time complexity of an algorithm is also calculated by determining the following 2 components: 

• Constant time part: Any instruction that is executed just once comes in this part. For example, input, output, if-else, switch, arithmetic operations, etc.
• Variable Time Part: Any instruction that is executed more than once, say n times, comes in this part. For example, loops, recursion, etc. Therefore Time complexity  [Tex]T(P)                        [/Tex] of any algorithm P is T(P) = C + TP(I) , where C is the constant time part and TP(I) is the variable part of the algorithm, which depends on the instance characteristic I.

Example: In the algorithm of Linear Search above, the time complexity is calculated as follows:

Step 1: –Constant Time Step 2: — Variable Time (Taking n inputs) Step 3: –Variable Time (Till the length of the Array (n) or the index of the found element) Step 4: –Constant Time Step 5: –Constant Time Step 6: –Constant Time Hence, T(P) = 1 + n + n(1 + 1) + 1 = 2 + 3n, which can be said as T(n).

How to express an Algorithm?

• Natural Language:- Here we express the Algorithm in the natural English language. It is too hard to understand the algorithm from it.
• Flowchart :- Here we express the Algorithm by making a graphical/pictorial representation of it. It is easier to understand than Natural Language.
• Pseudo Code :- Here we express the Algorithm in the form of annotations and informative text written in plain English which is very much similar to the real code but as it has no syntax like any of the programming languages, it can’t be compiled or interpreted by the computer. It is the best way to express an algorithm because it can be understood by even a layman with some school-level knowledge.

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• 4. Problem Solving and Algorithms
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Problem Solving and Algorithms

Learn a basic process for developing a solution to a problem. Nothing in this chapter is unique to using a computer to solve a problem. This process can be used to solve a wide variety of problems, including ones that have nothing to do with computers.

Problems, Solutions, and Tools

I have a problem! I need to thank Aunt Kay for the birthday present she sent me. I could send a thank you note through the mail. I could call her on the telephone. I could send her an email message. I could drive to her house and thank her in person. In fact, there are many ways I could thank her, but that's not the point. The point is that I must decide how I want to solve the problem, and use the appropriate tool to implement (carry out) my plan. The postal service, the telephone, the internet, and my automobile are tools that I can use, but none of these actually solves my problem. In a similar way, a computer does not solve problems, it's just a tool that I can use to implement my plan for solving the problem.

Knowing that Aunt Kay appreciates creative and unusual things, I have decided to hire a singing messenger to deliver my thanks. In this context, the messenger is a tool, but one that needs instructions from me. I have to tell the messenger where Aunt Kay lives, what time I would like the message to be delivered, and what lyrics I want sung. A computer program is similar to my instructions to the messenger.

The story of Aunt Kay uses a familiar context to set the stage for a useful point of view concerning computers and computer programs. The following list summarizes the key aspects of this point of view.

A computer is a tool that can be used to implement a plan for solving a problem.

A computer program is a set of instructions for a computer. These instructions describe the steps that the computer must follow to implement a plan.

An algorithm is a plan for solving a problem.

A person must design an algorithm.

A person must translate an algorithm into a computer program.

This point of view sets the stage for a process that we will use to develop solutions to Jeroo problems. The basic process is important because it can be used to solve a wide variety of problems, including ones where the solution will be written in some other programming language.

An Algorithm Development Process

Every problem solution starts with a plan. That plan is called an algorithm.

There are many ways to write an algorithm. Some are very informal, some are quite formal and mathematical in nature, and some are quite graphical. The instructions for connecting a DVD player to a television are an algorithm. A mathematical formula such as πR 2 is a special case of an algorithm. The form is not particularly important as long as it provides a good way to describe and check the logic of the plan.

The development of an algorithm (a plan) is a key step in solving a problem. Once we have an algorithm, we can translate it into a computer program in some programming language. Our algorithm development process consists of five major steps.

Step 1: Obtain a description of the problem.

Step 2: analyze the problem., step 3: develop a high-level algorithm., step 4: refine the algorithm by adding more detail., step 5: review the algorithm..

This step is much more difficult than it appears. In the following discussion, the word client refers to someone who wants to find a solution to a problem, and the word developer refers to someone who finds a way to solve the problem. The developer must create an algorithm that will solve the client's problem.

The client is responsible for creating a description of the problem, but this is often the weakest part of the process. It's quite common for a problem description to suffer from one or more of the following types of defects: (1) the description relies on unstated assumptions, (2) the description is ambiguous, (3) the description is incomplete, or (4) the description has internal contradictions. These defects are seldom due to carelessness by the client. Instead, they are due to the fact that natural languages (English, French, Korean, etc.) are rather imprecise. Part of the developer's responsibility is to identify defects in the description of a problem, and to work with the client to remedy those defects.

The purpose of this step is to determine both the starting and ending points for solving the problem. This process is analogous to a mathematician determining what is given and what must be proven. A good problem description makes it easier to perform this step.

When determining the starting point, we should start by seeking answers to the following questions:

What data are available?

Where is that data?

What formulas pertain to the problem?

What rules exist for working with the data?

What relationships exist among the data values?

When determining the ending point, we need to describe the characteristics of a solution. In other words, how will we know when we're done? Asking the following questions often helps to determine the ending point.

What new facts will we have?

What items will have changed?

What changes will have been made to those items?

What things will no longer exist?

An algorithm is a plan for solving a problem, but plans come in several levels of detail. It's usually better to start with a high-level algorithm that includes the major part of a solution, but leaves the details until later. We can use an everyday example to demonstrate a high-level algorithm.

Problem: I need a send a birthday card to my brother, Mark.

Analysis: I don't have a card. I prefer to buy a card rather than make one myself.

High-level algorithm:

Go to a store that sells greeting cards Select a card Purchase a card Mail the card

This algorithm is satisfactory for daily use, but it lacks details that would have to be added were a computer to carry out the solution. These details include answers to questions such as the following.

"Which store will I visit?"

"How will I get there: walk, drive, ride my bicycle, take the bus?"

"What kind of card does Mark like: humorous, sentimental, risqué?"

These kinds of details are considered in the next step of our process.

A high-level algorithm shows the major steps that need to be followed to solve a problem. Now we need to add details to these steps, but how much detail should we add? Unfortunately, the answer to this question depends on the situation. We have to consider who (or what) is going to implement the algorithm and how much that person (or thing) already knows how to do. If someone is going to purchase Mark's birthday card on my behalf, my instructions have to be adapted to whether or not that person is familiar with the stores in the community and how well the purchaser known my brother's taste in greeting cards.

When our goal is to develop algorithms that will lead to computer programs, we need to consider the capabilities of the computer and provide enough detail so that someone else could use our algorithm to write a computer program that follows the steps in our algorithm. As with the birthday card problem, we need to adjust the level of detail to match the ability of the programmer. When in doubt, or when you are learning, it is better to have too much detail than to have too little.

Most of our examples will move from a high-level to a detailed algorithm in a single step, but this is not always reasonable. For larger, more complex problems, it is common to go through this process several times, developing intermediate level algorithms as we go. Each time, we add more detail to the previous algorithm, stopping when we see no benefit to further refinement. This technique of gradually working from a high-level to a detailed algorithm is often called stepwise refinement .

The final step is to review the algorithm. What are we looking for? First, we need to work through the algorithm step by step to determine whether or not it will solve the original problem. Once we are satisfied that the algorithm does provide a solution to the problem, we start to look for other things. The following questions are typical of ones that should be asked whenever we review an algorithm. Asking these questions and seeking their answers is a good way to develop skills that can be applied to the next problem.

Does this algorithm solve a very specific problem or does it solve a more general problem ? If it solves a very specific problem, should it be generalized?

For example, an algorithm that computes the area of a circle having radius 5.2 meters (formula π*5.2 2 ) solves a very specific problem, but an algorithm that computes the area of any circle (formula π*R 2 ) solves a more general problem.

Can this algorithm be simplified ?

One formula for computing the perimeter of a rectangle is:

length + width + length + width

A simpler formula would be:

2.0 * ( length + width )

Is this solution similar to the solution to another problem? How are they alike? How are they different?

For example, consider the following two formulae:

Rectangle area = length * width Triangle area = 0.5 * base * height

Similarities: Each computes an area. Each multiplies two measurements.

Differences: Different measurements are used. The triangle formula contains 0.5.

Hypothesis: Perhaps every area formula involves multiplying two measurements.

Example 4.1: Pick and Plant

This section contains an extended example that demonstrates the algorithm development process. To complete the algorithm, we need to know that every Jeroo can hop forward, turn left and right, pick a flower from its current location, and plant a flower at its current location.

Problem Statement (Step 1)

A Jeroo starts at (0, 0) facing East with no flowers in its pouch. There is a flower at location (3, 0). Write a program that directs the Jeroo to pick the flower and plant it at location (3, 2). After planting the flower, the Jeroo should hop one space East and stop. There are no other nets, flowers, or Jeroos on the island.

Analysis of the Problem (Step 2)

The flower is exactly three spaces ahead of the jeroo.

The flower is to be planted exactly two spaces South of its current location.

The Jeroo is to finish facing East one space East of the planted flower.

There are no nets to worry about.

High-level Algorithm (Step 3)

Let's name the Jeroo Bobby. Bobby should do the following:

Get the flower Put the flower Hop East

Detailed Algorithm (Step 4)

Get the flower Hop 3 times Pick the flower Put the flower Turn right Hop 2 times Plant a flower Hop East Turn left Hop once

Review the Algorithm (Step 5)

The high-level algorithm partitioned the problem into three rather easy subproblems. This seems like a good technique.

This algorithm solves a very specific problem because the Jeroo and the flower are in very specific locations.

This algorithm is actually a solution to a slightly more general problem in which the Jeroo starts anywhere, and the flower is 3 spaces directly ahead of the Jeroo.

Java Code for "Pick and Plant"

A good programmer doesn't write a program all at once. Instead, the programmer will write and test the program in a series of builds. Each build adds to the previous one. The high-level algorithm will guide us in this process.

FIRST BUILD

To see this solution in action, create a new Greenfoot4Sofia scenario and use the Edit Palettes Jeroo menu command to make the Jeroo classes visible. Right-click on the Island class and create a new subclass with the name of your choice. This subclass will hold your new code.

The recommended first build contains three things:

The main method (here myProgram() in your island subclass).

Declaration and instantiation of every Jeroo that will be used.

The high-level algorithm in the form of comments.

The instantiation at the beginning of myProgram() places bobby at (0, 0), facing East, with no flowers.

Once the first build is working correctly, we can proceed to the others. In this case, each build will correspond to one step in the high-level algorithm. It may seem like a lot of work to use four builds for such a simple program, but doing so helps establish habits that will become invaluable as the programs become more complex.

SECOND BUILD

This build adds the logic to "get the flower", which in the detailed algorithm (step 4 above) consists of hopping 3 times and then picking the flower. The new code is indicated by comments that wouldn't appear in the original (they are just here to call attention to the additions). The blank lines help show the organization of the logic.

By taking a moment to run the work so far, you can confirm whether or not this step in the planned algorithm works as expected.

THIRD BUILD

This build adds the logic to "put the flower". New code is indicated by the comments that are provided here to mark the additions.

FOURTH BUILD (final)

Example 4.2: replace net with flower.

This section contains a second example that demonstrates the algorithm development process.

There are two Jeroos. One Jeroo starts at (0, 0) facing North with one flower in its pouch. The second starts at (0, 2) facing East with one flower in its pouch. There is a net at location (3, 2). Write a program that directs the first Jeroo to give its flower to the second one. After receiving the flower, the second Jeroo must disable the net, and plant a flower in its place. After planting the flower, the Jeroo must turn and face South. There are no other nets, flowers, or Jeroos on the island.

Jeroo_2 is exactly two spaces behind Jeroo_1.

The only net is exactly three spaces ahead of Jeroo_2.

Each Jeroo has exactly one flower.

Jeroo_2 will have two flowers after receiving one from Jeroo_1. One flower must be used to disable the net. The other flower must be planted at the location of the net, i.e. (3, 2).

Jeroo_1 will finish at (0, 1) facing South.

Jeroo_2 is to finish at (3, 2) facing South.

Each Jeroo will finish with 0 flowers in its pouch. One flower was used to disable the net, and the other was planted.

Let's name the first Jeroo Ann and the second one Andy.

Ann should do the following: Find Andy (but don't collide with him) Give a flower to Andy (he will be straight ahead) After receiving the flower, Andy should do the following: Find the net (but don't hop onto it) Disable the net Plant a flower at the location of the net Face South

Ann should do the following: Find Andy Turn around (either left or right twice) Hop (to location (0, 1)) Give a flower to Andy Give ahead Now Andy should do the following: Find the net Hop twice (to location (2, 2)) Disable the net Toss Plant a flower at the location of the net Hop (to location (3, 2)) Plant a flower Face South Turn right

The high-level algorithm helps manage the details.

This algorithm solves a very specific problem, but the specific locations are not important. The only thing that is important is the starting location of the Jeroos relative to one another and the location of the net relative to the second Jeroo's location and direction.

Java Code for "Replace Net with Flower"

As before, the code should be written incrementally as a series of builds. Four builds will be suitable for this problem. As usual, the first build will contain the main method, the declaration and instantiation of the Jeroo objects, and the high-level algorithm in the form of comments. The second build will have Ann give her flower to Andy. The third build will have Andy locate and disable the net. In the final build, Andy will place the flower and turn East.

This build creates the main method, instantiates the Jeroos, and outlines the high-level algorithm. In this example, the main method would be myProgram() contained within a subclass of Island .

This build adds the logic for Ann to locate Andy and give him a flower.

This build adds the logic for Andy to locate and disable the net.

This build adds the logic for Andy to place a flower at (3, 2) and turn South.