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5.21 The ancient Greeks classified numbers geometrically. For example, a number was called triangular if that number of T1 = 1 T2 = 3 T3 = 6 T4 = 10 pebbles could be arranged in a symmetric triangle. The first ten triangular numbers are 0, 1, 3, 6, 10, 15, 21, 28, 36, and 45. Write and test the boolean function:
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This function returns 1 if the given integer n is a triangular number, and 0 otherwise. 5.22 Write and test the following isSquare() function that determines whether the given integer is a square number:
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The first ten square numbers are 0, 1, 4, 9, 16, 25, 36, 49, 64, and 81. 5.23 Write and test the following isPentagonal() function that determines whether the given integer is a pentagonal number:
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The first ten pentagonal numbers are 0, 1, 5, 12, 22, 35, 51, 70, 92, and 117. 5.24 Write and test the following computeCircle() function that returns the area a and the circumference c of a circle with given radius r: 5.25
void computeCircle(float& a, float& c, float r). Write and test the following computeTriangle() function that returns the area a and the perimeter p of a triangle with given side lengths a, b, and c: void computeTriangle(float& a, float& p, float a, float b, float c) Write and test the following computeSphere() function that returns the volume v and the surface area s of a sphere with given radius r: void computeSphere(float& v, float& s, float r).
Answers to Review Questions
5.1 A separately compiled function can be regarded as an independent black box which performs a specific task. Once the function has been thoroughly tested, the programmer need not be concerned about how it works. This frees the programmer to concentrate on the development of the main program. Moreover, if a better way of implementing the function is found later, it can replace the previous version without affecting the main program. A function s declaration (also called its prototype) is essentially only the function s header. A function s definition is the complete function: header and body block. The declaration provides only the information needed to call the function: its name, its parameter types, and its return type; it is the interface between the function and its caller. The definition gives all the information about the function, including the details of how it works; it is the function s implementation. A function may be declared anywhere as long as its declaration is above all references to the function. So the declaration must come before any calls to it, and if its definition is separate then it too must come after its declaration. An include directive is used to include other files. Typically, function declarations and/or definitions are listed in a separate header file (with.h file extension). If only the declarations are in the header file, then the definitions would be compiled separately in other files. The advantage of putting a function s definition in a separate header file is that it doesn t have to be brought into the editor when changes are made to the functions that call it. The advantage of compiling a function separately is that it does not need to be recompiled when the functions that call it are recompiled.
5.5 5.6
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5.7 5.8 5.9 5.10
A parameter passed by value is duplicated by its corresponding argument. A parameter passed by reference is simply renamed by its corresponding argument. A parameter passed by constant reference cannot be changed by the function to which it is passed. A parameter that is passed by value cannot be changed (rewritten). The function has a default value for a parameter (b) that precedes a parameter (c) that has no default value. This violates the requirement that all default parameters be listed after all the other parameters in the function s parameter list.
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