Recursion II HampK Chapter 10 Instructor Gokcen Cilingir Cpt S 121 July 25 2011 Washington State University Recall recursive functions A function that calls itself is said to be recursive Here are examples of famous recursively defined functions in math factorial and ID: 761980
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Recursion (II)H&K Chapter 10 Instructor – Gokcen CilingirCpt S 121 (July 25, 2011)Washington State University
Recall: recursive functionsA function that calls itself is said to be recursive. Here are examples of “famous” recursively defined functions in math: factorial and fibonacci Base case/step Recursive case/step The ability to invoke itself enables a recursive function to be repeated with different parameter values
C. Hundhausen, A. O’Fallon3Recall: recursion Problems that may be solved using recursion have these attributes:One or more simple cases have a straightforward, non-recursive solutionThe other cases may be defined in terms of problems that are closer to the simple casesThrough a series of calls to the recursive function, the problem eventually is stated in terms of the simple casesi mage source: H&K, figure 10.1
Example 1Write a function that performs multiplication through addition with the prototype: int multiply(int m, int n); Let’s recursively define multiply: base case: multiply (m,1) is m recursive case: multiply (m, n) is n + multiply (m, n-1)
Example 1 (cont’d)Here is the recursive C implementation of mult: int multiply (int m, int n){ int ans; if (n == 1) ans = m; // base case else ans = m + multiply (m, n – 1); // recursive case return ans ; }
Tracing a recursive function image source: H&K, figure 10.5
Alternative tracing: execute the following codeint multiply ( int m, int n){ int ans; printf("Function called with m: %d, n: %d\n", m, n); if (n == 1) //base case { ans = m; } else // recursive case { ans = m + multiply (m, n - 1); } printf (" ans is: %d\n", ans ); return ans ; }
Case study 1Problem statement: A palindrome consists of a word or deblanked, unpunctuated phrase that is spelled exactly the same when the letters are reversed. Write a recursive function (in C) that returns a value of 1 if its string argument is a palindrome. Notice that in palindromes such as madam i'm adam (madamimadam), level, deed, and sees, the first letter matches the last, the second matches the next-to-last, and so on.
Case study 2Problem statement: Implement the recursive version of binary search algorithm.
10ReferencesJ.R. Hanly & E.B. Koffman, Problem Solving and Program Design in C (6th Ed.), Addison-Wesley, 2010P.J. Deitel & H.M. Deitel, C How to Program (5th Ed.), Pearson Education , Inc., 2007.