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19: More Efficient "Round Robin" Program 21 22 BASIC EXERCISES FOR THE ATARI Conclusion In this chapterwe have covered the rudiments offlowcharting. 7, however, presented a more advanced branching technique that is not required knowledge for the beginning programmer but can be useful when more complex problems are attempted . As we study the exercises in the following chapters, we will be able to perfect our general knowledge of flowcharts and, above all, learn how to construct them . CHAPTER 3 Exercises Using Integers Introduction This chapter will present exercises that demonstrate the use of whole numbers in BASIC.

A main program that carries out the input/output and some conditional tests. 2. a subprogram that searches (on each " iteration" ) for the largest admissible Egyptian fraction and computes the remainder fraction for the following iteration. By dividing the program into two parts we have increased the number of program statements. It does, however, make the program easier to write and follow. 12 includes a variable L, which takes on one of two values: 0 or 1. By assigning L a value of 0 at the beginning of the program, we will avoid printing the plus sign (+) in front of the first fraction that is found.

IFibonacci: Leonardo da Pisa, known by the name of Fibonacc i, was bo rn in Pisa aroun d 11 75 and publi shed this algorithm in 1202 . EXERCISES USING INTEGERS Let us assume that you are given the fraction ~ to decompose. To determine the first fraction of the decomposition we will use the largest Egyptian fraction that has a value lower than ~. We will subtract this fraction from ~ and continue this process until a a remainder is encountered . : A 2 1 --=--=- B 2 326 This gives the desired partition : 2=~+~ 326 The decomposition is not always as simple as in the previous example.

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