CS1010E Programming Methodology Tutorial 5 Macros and Recursion

1. CS1010E Programming MethodologyTutorial 5Macros and Recursion C14,A15,D11,C08,C11,A02

2. Question 1 • Analysis: • We need to simulate our investment return • Simulation is done by run an experiment 1000 times • An experiment is based on the formula: • is the interest rate at year , it is in

3. Question 1 • Breakdown the problem into small parts: • For single experiment, we need a function to compute the return • double futureValue( double lower, double upper, double initial) • For simulation, we need to run 1000 exps and count how many percent will can earn • double proportionHigher(double lower, double upper, double initial)

4. Question 1 • Main function. • We assume proportionHigher() is already implemented

5. Question 1 • proportionHigher • We assume futureValue is implemented!

6. Question 1 • futureValue • Note the trick of computing random double in range [lower, upper]

7. Question 1 • When writing main function, we assume proportionHigheris written and works correctly • When writing proportionHigher, we assume futureValue is written and works correctly • This kind of thinking method is called wishful thinking • Assume some functions are ready, you can focus more on how to use them to solve problem. • If those function aren’t really implemented, we then implement them!

8. Question 2 • Using SWAP to change two variables: • Standard code for changing (x, y): • t=x; x=y; y=t; • Macro Version: • #define SWAP(x,y) intt=x;x=y;y=t; • Not correct, due to int t How to swap two variable without using temp variables ?

9. Question 2 • Function Version: • Will it work by calling: ? • x = 10; y = 20; swap(x, y); • Notice the Pass-By-Value nature of functions!!

10. Question 2(b) • Find maximum value of 3 numbers: • #define MAX(A,B) ((A) > (B) ? (A) : (B)) • max=MAX(MAX(a, b), c) • Note that parenthesis are important !! • Macros vs. Functions? • Macros has no local variables, easily mess up • Program size increases • Normally only 1 line • No wishful thinking can be used, has to know implementation before calling • Why do we use Macro?

11. Recursion • When function calls itself, it is called recursion • Problem solving with recursion • Needs to identify that if a similar problem with smaller input value is solvable ? • If it so, can we use that to solve our problem? • It is essentially a special case of wishful thinking • Recursive Program: • A baseline (stopping condition) • A recursive formula • How to solve bigger problem using similar small problems

12. Question 3 (a) • Find exponent • Given x, and non-negative integer k, find • Loop version:

13. Question 3 (b) • Recursive version: • Analyze: • If we know , we know how to compute • Computing and are similar problem • Recursive formula: • Baseline ?

14. Question 3 (c) • Analyze: • There could be multiple recursive formula: • We can alternative compute by considering parity • Example • So we can use the formula: • Baseline:

15. Question 3 • Now let’s look at efficiency: • Efficiency is determined by number of operations performed in computing • Here we count number of multiplications used forand

16. Thank you See you next week!!