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Program Development
At this point you should be able to look at complete C++ functions and tell what they do. But it may not be clear yet how to go about writing them. I am going to suggest one technique that I call incremental development.
The first step is to consider what a distance function should look like in C++. In other words, what are the inputs (parameters) and what is the output (return value). In this case, the two points are the parameters, and it is natural to represent them using four doubles. The return value is the distance, which will have type double. Already we can write an outline of the function: double distance (double x1, double y1, double x2, double y2) {return 0.0; } The return statement is a placekeeper so that the function will compile and return something, even though it is not the right answer. At this stage the function doesn't do anything useful, but it is worthwhile to try compiling it so we can identify any syntax errors before we make it more complicated. In order to test the new function, we have to call it with sample values. Somewhere in main I would add: double dist = distance (1.0, 2.0, 4.0, 6.0);cout << dist << endl; I chose these values so that the horizontal distance is 3 and the vertical distance is 4; that way, the result will be 5 (the hypotenuse of a 345 triangle). When you are testing a function, it is useful to know the right answer. Once we have checked the syntax of the function definition, we can start adding lines of code one at a time. After each incremental change, we recompile and run the program. That way, at any point we know exactly where the error must bein the last line we added. The next step in the computation is to find the differences x_{2}  x_{1} and y_{2}  y_{1}. I will store those values in temporary variables named dx and dy. double distance (double x1, double y1, double x2, double y2) {double dx = x2  x1; double dy = y2  y1; cout << "dx is " << dx << endl; cout << "dy is " << dy << endl; return 0.0; } I added output statements that will let me check the intermediate values before proceeding. As I mentioned, I already know that they should be 3.0 and 4.0. When the function is finished I will remove the output statements. Code like that is called scaffolding, because it is helpful for building the program, but it is not part of the final product. Sometimes it is a good idea to keep the scaffolding around, but comment it out, just in case you need it later. The next step in the development is to square dx and dy. We could use the pow function, but it is simpler and faster to just multiply each term by itself. double distance (double x1, double y1, double x2, double y2) {double dx = x2  x1; double dy = y2  y1; double dsquared = dx*dx + dy*dy; cout << "dsquared is " << dsquared; return 0.0; } Again, I would compile and run the program at this stage and check the intermediate value (which should be 25.0). Finally, we can use the sqrt function to compute and return the result. double distance (double x1, double y1, double x2, double y2) {double dx = x2  x1; double dy = y2  y1; double dsquared = dx*dx + dy*dy; double result = sqrt (dsquared); return result; } Then in main, we should output and check the value of the result. As you gain more experience programming, you might find yourself writing and debugging more than one line at a time. Nevertheless, this incremental development process can save you a lot of debugging time. The key aspects of the process are:


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