Recursion

1. Recursion 2014 Spring CS32 Discussion JungseockJoo

2. Abstract Class • A class with one or more pure virtual functions: • Person = {Male | Female} • You can’t directly create an object: • Person person; -> error • Male male; -> ok • Female female; -> ok • When Male & Female classes have the implementations of print_info()

3. Inheritance Review • Virtual destructors of base classes • “delete pPer” invokes only the destructor of “Person” if not virtual. • Resources of the derived part in Employee class not destroyed • Memory leak

4. Inheritance Review • Order of construction of derived classes • A derived object : base part + derived part

5. Inheritance Review • Order of construction of derived classes • A derived object : base part + derived part 1. Construct the base part • Calls the constructor of the base class • Member initialization list 2. Construct the data members of derived part • Member initialization list 3. Execute the body of the constructor of the derived class

6. Inheritance Review • Destruction : Backward 1. Execute the body of the destructor of the derived class 2. Destroy the data members of derived part 3. Destroy the base part

7. Recursion

8. Recursive Function • Calls itself in the function body • Ex. Fibonacci number

9. Recursion vs. Iteration

10. Recursion • “Divide-and-conquer” • Solve sub-problems and merge the sub-solutions • “Mathematical Induction” • Base case (terminating case) • Eg, if (n < 1) return 1; • Otherwise, infinite loop. • Inductive case • At kth step, we assume 1, … ,k-1th steps are all correct. • “Recursive leap of faith”

11. Recursion • Recursive programming is NOT for optimizing performance. • But it helps: • Organize the code better. • Design the algorithms for complex problems.

12. Problem Partitioning • Define the unit steps of the whole problem. • Your recursive function deals with “one” step. • Once evaluated, the sub-solution for one step must remain valid through the whole procedure.

13. Problem Partitioning • Define the unit steps of the whole problem. • Your recursive function deals with “one” step. • Once evaluated, the sub-solution for one step must remain valid through the whole procedure. • How do you split the whole (or current) problem into sub-problems? • “the First” and “the Rest”, or • Even split (eg, left and right), or • …

14. First & Rest • Write a function to determine if the given array contains the given integer.

15. First & Rest • Write a function to determine if the given array contains the given integer. • Given an array, we check the first element.

16. First & Rest • Write a function to determine if the given array contains the given integer. • Given an array, we check the first element. • And we check the rest elements a[1 ~ n-1]. • But that is another array: (a+1) • So we can use the same function.

17. First & Rest • Write a function to determine if the given array contains the given integer. • We don’t need to worry about “the rest” • They will be taken care of by recursive function calls.

18. Even Split • Merge-sort

19. Even Split • Merge-sort

20. Even Split • Merge-sort Commonly used by many sorting algorithms How do you merge?

21. HW3