“The greatest crimes do not arise from a want of feeling for others but from an over-sensibility for ourselves and an over-indulgence to our own desires.” – Edmund Burke Thought for the Day

Pre- and Postconditions and Assertions Techniques for clarifying what a program is doing –“snapshots” or “checkpoints” Preconditions and postconditions –Beginning and end of methods Assertions –More generally –May be checked at runtime

Automated Documentation Several current programming languages provide automatic system documentation facilities Java: Javadoc –Special comments turned into HTML documentation

System Development MyClass.java MyClass.class javac MyClass.html javadoc

Example /** The approximate square root is found using * the Newton-Raphson method. x The value whose square root is to * be calculated. The approximate square root of x. */ public static double squareRoot (double x) {... } // squareRoot

End of Chapter 1 Advanced programming –Advanced data structures –Advanced algorithms –Program quality (efficiency) General program quality issues Preconditions, postconditions and assertions Automatic documentation

Chapter 2: Advanced Programming Techniques Objectives –Revise the use of recursion in programs –Introduce interfaces in Java

Recursion Many problems are naturally recursive –i.e. the solution is best expressed in terms of the solution! n! = n × (n-1) × (n-2) × … × 3 × 2 × 1 A simple arithmetic example: –factorials

Factorials How is this recursive? n! = n × (n-1) × (n-2) × … × 3 × 2 × 1 = (n-1)! So: n! = n × (n-1)! –The factorial function is defined in terms of itself (i.e. recursively)

Recursive Calculation of Factorials In order for this to work, we need a stop case (the simplest case) Here: 0! = 1 n! = n × (n-1)!

A Recursive Factorial Function in Java int factorial (int n) { if (n == 0) // The stop case return 1; else return n * factorial(n-1); } // factorial A recursive method call

How does this work? int factorial (int n) { if (n == 0) // The stop case return 1; else return n * factorial(n-1); } // factorial int x = factorial(3); factorial(3) factorial(2)factorial(1)factorial(0) 1126

Recursion In general: –We describe the solution to a problem in terms of solving a slightly simpler version of the same problem –We must have a stop case: the simplest case that can be solved on its own

Recursion While recursion can be used to solve many problems it is not always the most efficient solution int factorial (int n) { int fact = 1; for (int k = 1; k <= n; k++) fact = fact * k; return fact; } // factorial