CS 112
Lecture 14
Recursion
- Recursive definitions: refer to themselves. Example: definition for
fully parenthesized arithmetic expressions.
- A recursive function is defined in such a way that it refers
to itself within its own definition. A recursive program is an
implementation (in some programming language) of a recursive function.
- Simple examples: factorial, sum of the first n
integers, fibonacci function. More elaborate examples:
Towers of Hanoi, and others to be done next time (sorting).
- Short lab session: everybody implements the factorial
function.
- Extra examples (to look at after class);
Sum, a function
to add all the numbers in an array. If n is 0, it returns the
a[0].
Otherwise, it adds a[n] to the
sum of the first (n-1) elements, computed recursively.
Do you hear the
self-reference in this description?
Here is an implementation in
C++.
- How a recursive function call is evaluated. Trace the stack
during the function call for sum(4) and fib(4).
- Reading: Ch. 5 in textbook.
- More examples later: a recursive function implementing a recursive
definition. A function testing whether a given arithmetic
expression
(given as a string of characters) is in
prefix form (code not available, but we will discuss it in class).
- When to use recursive functions? When you "hear" the
recursive reference in the very description of the function.
- Recursive algorithms: a very powerful technique of algorithm
design. Sometimes it produces very efficient algorithms.
- A few recursive definitions that you might "hear": the
factorial function (product of the the first n numbers); finding
the minimum element of an array; searching in an array; binary search.
Ileana Streinu