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float f(a, b, ch) int a, b; char ch; {
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Notice that in classic form, more than one parameter can be in a list after the type name This isn t allowed in the modern form In general, to convert the old-style form into the modern (C++ style) form, simply move the parameter declarations inside the function s parentheses Remember, each parameter must be declared separately, each with its own type specifier
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Recursion
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A recursive function is a function that calls itself
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The last topic that we will examine in this chapter is recursion Sometimes called circular definition, recursion is the process of defining something in terms of itself As it relates to programming, recursion is the process of a function calling itself A function that calls itself is said to be recursive
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C++ from the Ground Up
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The classic example of recursion is the function factr( ), which computes the factorial of an integer The factorial of a number N is the product of all the whole numbers between 1 and N For example, 3 factorial is 1 2 3, or 6 Both factr( ) and its iterative equivalent are shown here:
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#include <iostream> using namespace std; int factr(int n); int fact(int n); int main() { // use recursive version cout << "4 factorial is " << factr(4); cout << '\n'; // use iterative version cout << "4 factorial is " << fact(4); cout << '\n'; return 0; } // Recursive version int factr(int n) { int answer; if(n==1) return(1); answer = factr(n-1)*n; return(answer); } // Iterative version int fact(int n) { int t, answer; answer = 1; for(t=1; t<=n; t++) answer = answer*(t); return(answer); }
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The operation of the nonrecursive version of fact( ) should be clear It uses a loop starting at 1 and progressively multiplies each number by the moving product The operation of the recursive factr( ) is a little more complex When factr( ) is called with an argument of 1, the function returns 1; otherwise it returns the product of factr(n 1)*n To evaluate this expression, factr( ) is called with n 1 This happens until n equals 1 and the calls to the function begin returning For example, when the factorial of 2 is calculated, the first call to factr( ) will cause a second call to be made
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Functions, Part One: The Fundamentals
with the argument of 1 This call will return 1, which is then multiplied by 2 (the original n value) The answer is then 2 You might find it interesting to insert cout statements into factr( ) that will show at what level each call is, and what the intermediate answers are When a function calls itself, new local variables and parameters are allocated storage on the stack, and the function code is executed with these new variables from the start A recursive call does not make a new copy of the function; only the values are new As each recursive call returns, the old local variables and parameters are removed from the stack, and execution resumes at the point of the function call inside the function Recursive functions could be said to "telescope" out and back Keep in mind that most recursive routines do not significantly reduce code size Also, the recursive versions of most routines may execute a bit more slowly than their iterative equivalents, due to the added overhead of the additional function calls Too many recursive calls to a function may cause a stack overrun Because storage for function parameters and local variables is on the stack, and each new call creates a new copy of these variables, it is possible that the stack will be exhausted If this occurs, other data may be destroyed as well However, you probably will not have to worry about any of this unless a recursive function runs wild The main advantage of recursive functions is that they can be used to create clearer and simpler versions of several algorithms than those produced with their iterative relatives For example, the Quicksort sorting algorithm is quite difficult to implement in an iterative way Also, some problems, especially those related to artificial intelligence, seem to lend themselves to recursive solutions Finally, some people find it easier to think recursively rather than iteratively When writing a recursive function, you must include a conditional statement, such as an if, to force the function to return without execution of the recursive call If you don t provide the conditional statement, then once you call the function, it will never return This is a very common error When developing programs with recursive functions, use cout statements liberally so that you can watch what is going on, and abort execution if you see that you have made a mistake Here is another example of a recursive function, called reverse( ) It prints its string argument backwards on the screen
// Print a string backwards using recursion #include <iostream> using namespace std; void reverse(char *s); int main() { char str[] = "this is a test"; reverse(str); return 0; }
// Print string backwards void reverse(char *s) { if(*s) reverse(s+1); else return; cout << *s; }
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