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. Show
Problems, Solutions, and ToolsI 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.
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 ProcessEvery problem solution starts with a plan. That plan is called an algorithm. An algorithm is a plan for solving a problem. 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 πR2 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. Step 1: Obtain a description of the problem.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. Step 2: Analyze the problem.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:
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.
Step 3: Develop a high-level algorithm.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.
These kinds of details are considered in the next step of our process. Step 4: Refine the algorithm by adding more detail.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. Stepwise refinement is a process for developing a detailed algorithm by gradually adding detail to a high-level algorithm. 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.
Example 4.1: Pick and PlantThis 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)
High-level Algorithm (Step 3)Let's name the Jeroo Bobby. Bobby should do the following: Get the flower Put the flower Detailed Algorithm (Step 4)Let's name the Jeroo Bobby. Bobby should do the following: Get the flower Review the Algorithm (Step 5)
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. A good programmer works incrementally, add small pieces one at a time and constantly re-checking the work so far. 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 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 BUILDThis 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. public void myProgram() { Jeroo bobby = new Jeroo(); this.add(bobby); // --- Get the flower --- bobby.hop(3); // <-->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 BUILDThis build adds the logic to "put the flower". New code is indicated by the comments that are provided here to mark the additions. public void myProgram() { Jeroo bobby = new Jeroo(); this.add(bobby); // --- Get the flower --- bobby.hop(3); bobby.pick(); // --- Put the flower --- bobby.turn(RIGHT); // <-->This build adds the logic to "hop East". public void myProgram() { Jeroo bobby = new Jeroo(); this.add(bobby); // --- Get the flower --- bobby.hop(3); bobby.pick(); // --- Put the flower --- bobby.turn(RIGHT); bobby.hop(2); bobby.plant(); // --- Hop East --- bobby.turn(LEFT); // <-->Example 4.2: Replace Net with FlowerThis section contains a second example that demonstrates the algorithm development process. Problem Statement (Step 1)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.
Analysis of the Problem (Step 2)
High-level Algorithm (Step 3)Let's name the first Jeroo Ann and the second one Andy. Ann should do the following: Detailed Algorithm (Step 4)Let's name the first Jeroo Ann and the second one Andy. Ann should do the following: Review the Algorithm (Step 5)
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. FIRST BUILDThis 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. public void myProgram() { Jeroo ann = new Jeroo(0, 0, NORTH, 1); this.add(ann); Jeroo andy = new Jeroo(0, 2 , 1); // default EAST this.add(andy); // --- Ann, find Andy --- // --- Ann, give Andy a flower --- // --- Andy, find and disable the net --- // --- Andy, place a flower at (3, 2) --- // --- Andy, face South --- } // ===== end of method myProgram() =====SECOND BUILDThis build adds the logic for Ann to locate Andy and give him a flower. public void myProgram() { Jeroo ann = new Jeroo(0, 0, NORTH, 1); this.add(ann); Jeroo andy = new Jeroo(0, 2 , 1); // default EAST this.add(andy); // --- Ann, find Andy --- ann.turn(LEFT); ann.turn(LEFT); ann.hop(); // Now, Ann is at (0, 1) facing South, and Andy is directly ahead // --- Ann, give Andy a flower --- ann.give(AHEAD); // Ann now has 0 flowers, Andy has 2 // --- Andy, find and disable the net --- // --- Andy, place a flower at (3, 2) --- // --- Andy, face South --- } // ===== end of method myProgram() =====THIRD BUILDThis build adds the logic for Andy to locate and disable the net. public void myProgram() { Jeroo ann = new Jeroo(0, 0, NORTH, 1); this.add(ann); Jeroo andy = new Jeroo(0, 2 , 1); // default EAST this.add(andy); // --- Ann, find Andy --- ann.turn(LEFT); ann.turn(LEFT); ann.hop(); // Now, Ann is at (0, 1) facing South, and Andy is directly ahead // --- Ann, give Andy a flower --- ann.give(AHEAD); // Ann now has 0 flowers, Andy has 2 // --- Andy, find and disable the net --- andy.hop(2); // Andy is at (2, 2) facing the net andy.toss(); // --- Andy, place a flower at (3, 2) --- // --- Andy, face South --- } // ===== end of method myProgram() =====FOURTH BUILD (final)This build adds the logic for Andy to place a flower at (3, 2) and turn South. public void myProgram() { Jeroo ann = new Jeroo(0, 0, NORTH, 1); this.add(ann); Jeroo andy = new Jeroo(0, 2 , 1); // default EAST this.add(andy); // --- Ann, find Andy --- ann.turn(LEFT); ann.turn(LEFT); ann.hop(); // Now, Ann is at (0, 1) facing South, and Andy is directly ahead // --- Ann, give Andy a flower --- ann.give(AHEAD); // Ann now has 0 flowers, Andy has 2 // --- Andy, find and disable the net --- andy.hop(2); // Andy is at (2, 2) facing the net andy.toss(); // --- Andy, place a flower at (3, 2) --- andy.hop(); andy.plant(); // --- Andy, face South --- andy.turn(RIGHT); } // ===== end of method myProgram() =====© 2012 Stephen Edwards, Brian Dorn, and Dean Sanders |