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Recursion
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After a lecture on cosmology and the structure of the solar system, William James was accosted by a little old lady Your theory that the sun is the center of the solar system, and the earth is a ball which rotates around it has a very convincing ring to it, Mr James, but it s wrong I ve got a better theory, said the little old lady And what is that, madam inquired James politely That we live on a crust of earth which is on the back of a giant turtle Not wishing to demolish this absurd little theory by bringing to bear the masses of scienti c evidence he had at his command, James decided to gently dissuade his opponent by making her see some of the inadequacies of her position If your theory is correct, madam, he asked, what does this turtle stand on You re a very clever man, Mr James, and that s a very good question replied the little old lady, but I have an answer to it And it is this: the rst turtle stands on the back of a second, far larger, turtle, who stands directly under him But what does this second turtle stand on persisted James patiently To this the little old lady crowed triumphantly It s no use, Mr James it s turtles all the way down
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INTRODUCTION
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A function de nition that includes a call to itself is said to be recursive Like most modern programming languages, C++ allows functions to be recursive If used with a little care, recursion can be a useful programming technique This chapter introduces the basic techniques needed for de ning successful recursive functions There is nothing in this chapter that is truly unique to C++ If you are already familiar with recursion you can safely skip this chapter This chapter only uses material from s 1 to 5 Sections 131 and 132 do not use any material from 5, so you can cover recursion any time after 4 If you have not read 11, you may nd it helpful to review the section of 1 on namespaces
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I remembered too that night which is at the middle of the Thousand and One Nights when Scheherazade (through a magical oversight of the copyist) begins to relate word for word the story of the Thousand and One Nights, establishing the risk of coming once again to the night when she must repeat it, and thus to in nity
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When you are writing a function to solve a task, one basic design technique is to break the task into subtasks Sometimes it turns out that at least one of the subtasks is a smaller example of the same task For example, if the task is to search a list for a particular value, you might divide this into the subtask of searching the rst half of the list and the subtask of searching the second half of the list The subtasks of searching the halves of the list are smaller versions of the original task Whenever one subtask is a smaller version of the original task to be accomplished, you can solve the original task using a recursive function We begin with a simple example to illustrate this technique
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RECURSION
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In C++ a function definition may contain a call to the function being defined In such cases the function is said to be recursive
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Example
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Display 131 contains a demonstration program for a recursive function named writeVertical that takes one (nonnegative) int argument and writes that int to the screen, with the digits going down the screen one per line For example, the invocation
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writeVertical(1234);
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