Monday, 12/9/02, Slide #1 CS 106 Intro to CS 1 Monday, 12/9/02  QUESTIONS??  On HW #5 (Due 5 pm today)  Today:  Recursive functions  Reading: Chapter.

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Presentation transcript:

Monday, 12/9/02, Slide #1 CS 106 Intro to CS 1 Monday, 12/9/02  QUESTIONS??  On HW #5 (Due 5 pm today)  Today:  Recursive functions  Reading: Chapter 13  Exercises: pp. 328 ff. #4, 10, 15  Wednesday:  Overview and discussion of final exam  Evaluations

Monday, 12/9/02, Slide #2 New topic: Recursion (Chap. 13)  Recursion – means a concept or quantity whose definition refers to itself. An algorithm is called recursive if its implementation contains a call to itself.  Example:  Factorial: n! = 1 * 2 * 3 *... * n. Or we can give the following recursive definition: If n = 1, then n! = 1. If n > 1, then n! = n * (n – 1)!

Monday, 12/9/02, Slide #3 Two basic examples  Factorial(): Design a function definition that implements the recursive definition of Factorial().  Fibonacci(): Design a function that produces the sequence: , in which the first two numbers are 1, and from then on each number is the sum of the two previous ones, i.e., Fibonacci(1) = Fibonacci(2) = 1, and for n > 2, Fibonacci(n) = Fibonacci(n-1) + Fibonacci(n-2).

Monday, 12/9/02, Slide #4 Criteria for (Good) Recursive Functions  Recursive Case: A recursive function must contain at least one statement in which the function calls itself.  Base Case: There must also be at least one case in which the function does not call itself.  Reaching the base: Each recursive call must result in a case that is "closer to" the base case, and the sequence of calls begun by any recursive call must eventually reach the base case. int Fib (int n) { if (n <= 2) { return 1; } else { return Fib (n-1) + Fib (n-2); }

Monday, 12/9/02, Slide #5 Recursive algorithm for binary search  Binary Search Algorithm: To search for key in array A[ ], from index bot to index top,  If bot >= top (empty or 1-item array), check for key in 1 spot, otherwise key has not been found.  If bot 1 items)  Compute index mid = (bot + top) / 2;  If key == A[mid], we’re done!  Else if key > A[mid], do Binary Search from index mid +1 to top  Else (key < A[mid]), do Binary Search from index bot to mid -1