{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

L06cs2110fa09-6up

# L06cs2110fa09-6up - RECURSION Lecture 6 CS2110 Fall 2009 2...

This preview shows pages 1–3. Sign up to view the full content.

24/08/2009 1 RECURSION Lecture 6 CS2110 – Fall 2009 2 3 Recursion Overview 4 Recursion is a powerful technique for specifying functions, sets, and programs Example recursively-defined functions and programs factorial factorial combinations exponentiation (raising to an integer power) Example recursively-defined sets grammars expressions data structures (lists, trees, ...) The Factorial Function (n!) 5 Define n! = n·(n 1)·(n 2)···3·2·1 read: “n factorial” E.g., 3! = 3·2·1 = 6 By convention, 0! = 1 The function int int that gives n! on input n is called the factorial function The Factorial Function (n!) 6 n! is the number of permutations of n distinct objects There is just one permutation of one object. 1! = 1 There are two permutations of two objects: 2! = 2 There are two permutations of two objects: 2! = 2 1 2 2 1 There are six permutations of three objects: 3! = 6 1 2 3 1 3 2 2 1 3 2 3 1 3 1 2 3 2 1 If n > 0, n! = n·(n 1)!

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document