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Chapter 10:Recursion

Problem Solving & Program Design in C

Sixth Edition

By Jeri R. Hanly &

Elliot B. Koffman

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Figure 10.1 Splitting a Problem into Smaller Problems

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Figure 10.2 Recursive Function multiply

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Figure 10.3 Thought Process of Recursive Algorithm Developer

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Figure 10.4 Recursive Function to Count a Character in a String

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Figure 10.5 Trace of Function multiply

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Figure 10.6 Function reverse_input_words

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Figure 10.7 Trace of reverse_input_words(3) When the Words Entered are "bits" "and" "bytes"

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Figure 10.8 Sequence of Events for Trace of reverse_input_words(3)

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Figure 10.9 Recursive Function multiply with Print Statements to Create Trace and Output from multiply(8, 3)

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Figure 10.9 Recursive Function multiply with Print Statements to Create Trace and Output from multiply(8, 3) (cont’d)

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Why does recursion make it easier to conceptualize a solution?

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•You can use recursion in place of iteration (looping)

•One or more simple cases of the problem have a straightforward, non-recursive solution

• By applying this redefinition process every time the recursive function is called, eventually the problem is reduced to simple cases, which are relatievely easy to solve.

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The efficiency of recursion

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• As stated at the beginning of the chapter, recursive solutions are less efficient than an iterative solution in terms of computer time due to overhead for the extra function calls.• However, in many instances the use of recursion enables us to specify a very natural, simple solution to a problem that would otherwise be very difficult to solve.• It is a very important and powerful tool in problem solving and programming.

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Simple case vs. terminating condition

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• Simple cases involve simple solutions that can be split up into very small prblems

• A terminating condition may consist of an if statement that evaluates a particular condition, n <= 1. When the terminating condition is true, the function is dealing with one of the problem’s simple cases.

• The most common problem with a recursive function is that it may not terminate properly (in case the terminating condition is not correct or incomplete.

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Figure 10.10 Recursive factorial Function

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Figure 10.11 Trace of fact = factorial(3);

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Figure 10.12 Iterative Function factorial

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Figure 10.13 Recursive Function fibonacci

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Figure 10.14 Program Using Recursive Function gcd

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Figure 10.14 Program Using Recursive Function gcd (cont’d)

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Figure 10.15 Recursive Function to Extract Capital Letters from a String

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Figure 10.16 Trace of Call to Recursive Function find_caps

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Figure 10.17 Sequence of Events for Trace of Call to find_caps from printf Statements

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Figure 10.18 Trace of Selection Sort

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Figure 10.19 Recursive Selection Sort

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Figure 10.19 Recursive Selection Sort (cont’d)

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Figure 10.20 Recursive Set Operations on Sets Represented as Character Strings

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Figure 10.20 Recursive Set Operations on Sets Represented as Character Strings (cont’d)

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Figure 10.20 Recursive Set Operations on Sets Represented as Character Strings (cont’d)

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Figure 10.20 Recursive Set Operations on Sets Represented as Character Strings (cont’d)

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Figure 10.20 Recursive Set Operations on Sets Represented as Character Strings (cont’d)

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Figure 10.20 Recursive Set Operations on Sets Represented as Character Strings (cont’d)

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Figure 10.21 Towers of Hanoi

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Figure 10.22 Towers of Hanoi After Steps 1 and 2

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Figure 10.23 Towers of Hanoi After Steps 1, 2, 3.1, and 3.2

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Figure 10.24 Recursive Function tower

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Figure 10.25 Trace of tower ('A', 'C', 'B', 3);

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Figure 10.26 Output Generated by tower('A', 'C', 'B', 3);

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Figure 10.27 Grid with Three Blobs