Reading – Chapter 10

Recursion The process of solving a problem by reducing it to smaller versions of itself Example: Sierpinski’s TriangleSierpinski’s Triangle

Recursive algorithm An algorithm is called recursive if it solves a problem by reducing the problem to smaller versions of itself A recursive algorithm can be implemented using a recursive function

Recursive function A function that calls itself What is the danger? we need to avoid infinite recursion A recursive function must have recursive call(s) to the function with a smaller instance of the problem one or more base cases to stop recursion

Finding a recursive solution A recursive solution to a problem must be written carefully The idea is for each successive recursive call to take us one step closer to the base case (a situation in which the problem can easily be solved)

General format for many recursive functions if (some easily-solved condition) // base case solution statement(s); else // general case recursive function call(s);

Example Write a recursive function Fact() to find the factorial of n. What should Fact(4) return? What can be a good base case that represents an easily- solved situation? What can be a good general case that takes us closer to the base case?

Example int Fact (int n) { if (n == 1) // base case return 1; else // general case return n * Fact(n-1); } // this is an example of tail recursion

Example – Trace of calls n = 4 n = 3 n = 2 Call 1: Fact(4) Call 2: Fact(3) n = 1 Call 3: Fact(2) Call 4: Fact(1) n = 1 Returns 1 Returns 2 * Fact(1) = 2 * 1 = 2 Returns 3 * Fact(2) = 3 * 2 = 6 Returns 4 * Fact(3) = 4 * 6 = 24

Iteration or Recursion? Key factors nature of the problem efficiency Every recursive call has its own set of parameters and local variables time and space overhead associated with executing a recursive function Certain problems are inherently recursive and a recursive solution is the most natural one