1. Slide 1 Where are we, and where to go? Simple types of variables (variables=objects) 3 program structures (assignment, conditional, iteration) Static objects Dynamic objects Functions on objects Procedural programming, Or structured programming, Or imperative programming (104), modularity (member) variables OOP (104, 151 ) Data structure: Linear: list, stack, queue Nonlinear: tree, graph Algorithms Algorithms+Data Structures = Programs Niklaus Wirth ( 171) (member) functions Array, struct pointer objects Data, variable, object Operation, function, procedure, subprogram, module, method operation class C, Pascal C++, Java ( 152)

2. Slide 2 Programming paradigms * Procedural programming * Object-oriented programming * Generic programming

3. Slide 3 int main() { int x,y,z; int a,b,c; a=f1(x); b=f2(y); c=f3(z); … } int f1() { } int f2() { } int f3() { } main(), is the first function, and is composed of a sequence of ‘procedures’ (or ‘functions’ in C++). Functions communicate by passing parameters. int main() { A a; B b; C c; a.f1(); b.f2(); c.f3(); … } Class A { Int x; Int f1(); } Class B { Int y; Int f2() } Class C { Int z; Int f3(); } procedural programming: Object oriented programming: a sequence of ‘objects’! Objects communicate by sending messages.

4. Slide 4 l Pass by value: formal parameters and arguments are different variables. ideal desirable behavior (but not efficient some times) l Pass by reference: they are the same variables, but different names! should carefully handled! Communication between functions:

5. Slide 5 Reference: X& l int& b a; l b is an alternative name for a void f(int& b) {}; int main() { int a; f(a); } int a=10; int& b = a; int& c = a; b = 100; a ??? int& b; 10 a b c Relationship with pointers (later on)!

6. Slide 6 int f(int x) { cout << “value of x = “ << x << endl; x = 4; } main() { int v = 5; f(v); cout << “value of v = “ << v << endl; } Output: Value of x = Value of v = n When a variable v is passed by value to a function f, its value is copied to the corresponding variable x in f n Any changes to the value of x does NOT affect the value of v n Call by value is the default mechanism for parameter passing in C++ 5 5 Call by Value

7. Slide 7 int f(int& x) { cout << “value of x = “ << x << endl; x = 4; } main() { int v = 5; f(v); cout << “value of v = “ << v << endl; } Output: Value of x = Value of v = n When a variable v is passed by reference to a parameter x of function f, v and the corresponding parameter x refer to the same variable n Any changes to the value of x DOES affect the value of v 5 4 Call by Reference poor style of writing f(int &x)!

8. Slide 8 int f( const int& x ) { cout << “value of x = “ << x << endl; x = 4; // invalid } main() { int v = 5; f(v); cout << “value of v = “ << v << endl; } Passing variable v by constant reference to parameter x of f will NOT allow any change to the value of x. It is appropriate for passing large objects that should not be changed by the called function. Call by Constant Reference

9. Slide 9 * Call by value n for small objects that should not be changed by the function * Call by constant reference n for large objects that should not be changed by the function * Call by reference n is appropriate for all objects that may be changed by the function, n not recommended!!! rare! Parameter Passing Trade-off between the ‘ideal’ and ‘efficiency’!

10. Slide 10 * return by value, n for small objects that should not be changed by the function * return by constant reference, n for large objects that should not be changed by the function * return by reference, n for all objects that may be changed by the function, n not recommended!!! rare! Return Passing

11. Slide 11 Scope of variables The scope of a declaration is the block of code where the identifier is valid for use. n A global declaration is made outside the bodies of all functions and outside the main program. It is normally grouped with the other global declarations and placed at the beginning of the program file. n A local declaration is one that is made inside the body of a function. Locally declared variables cannot be accessed outside of the function they were declared in. Local to a function (the variables in Main are also local, local to ‘main’ function) n It is possible to declare the same identifier name in different parts of the program : local to a block Some code enclosed in braces

12. Slide 12 int main() { int x,y,z; … } void f() { int x; … } void f() { int x; x=1; { int x; x=2; cout << x << endl; } cout << x << endl; } int x; int main() { x=0; cout << x << endl; int x; x=1; { int x; x=2; cout << x << endl; } cout << x << endl; } Local to blocksLocal to functions Global (local to the file)

13. Slide 13 In a for-loop { int i; for (i=1;i<10;i++) cout << A[i]; } for (int i=1;i<10;i++) cout << A[i]; equivalent

14. Slide 14 Global Variables * Undisciplined use of global variables may lead to confusion and debugging difficulties. * Instead of using global variables in functions, try passing local variables by reference. It is forbidden in structured programming!

15. Slide 15 int MIN; void min(int,int); int main() { int x,y; cin >> x >> y >> endl; min(x,y); cout << MIN; } void min(int a, int b) { if (a<b) MIN=a; else MIN=b; } void min(int,int,int&); int main() { int x,y,mini; cin >> x >> y >> endl; min(x,y,mini); cout << mini; } void min(int a, int b, int& m) { if (a<b) m=a; else m=b; } int min(int,int); int main() { int x,y,mini; cin >> x >> y >> endl; mini=min(x,y); cout << mini; } int min(int a, int b) { int m; if (a<b) m=a; else m=b; return (m); } Summary Global variablePass by reference Pass by value Good style!!! Bad style!!!

16. Recursion Important for algorithm design and analysis l an illustrative example l a general problem solving method l technicality l recursion vs. iterations l examples

17. Slide 17 The tower of Hanoi Move a stack of disks of different sizes from one rod to another through a third one: - only one disk is moved each time - always smaller ones on top of bigger ones Check any webpage!

18. Slide 18 // move n disks from A to C via B void tower(int n, char A, char B, char C) { if (n==1) move(1,A,C); else {tower(n-1,A,C,B); move(n,A,C); tower(n-1,B,A,C)}; } void move(int k, char X, char Y) { cout << “move disc ” << k << “ from “ << X << “ to “ Y “ << endl; } More declarative than procedural! what vs. how

19. Slide 19 Trace tower(4,A,B,C)

20. Slide 20 Recursion: problem solving, therefore a programming technique * Recursion is one way to decompose a task into smaller subtasks. * At least one of the subtasks is a smaller example of the same task. * The smallest example of the same task has a non-recursive solution. A complex problem is often easier to solve by dividing it into several smaller parts (by top-down analysis), each of which can be solved by itself. The general top-down programming and problem solving: Example: The factorial function n! = n * (n-1) * (n-2) *... * 1 or n! = n * (n-1)! and 1! = 1

21. Slide 21 void three(…) { … } void two (…) { three(); } void one (…) { two(…); } void main() { one(…); } l Functions are calling (DIFFERENT) functions l One function (three) is the last ‘stopping function’ int fac(int n){ int product; if(n <= 1) product = 1; else product = n * fac(n-1); return product; } void main(){ fac(3); } l … calling the SAME function ( with different parameters) … l The ‘stopping function’ is already included as a ‘condition’ Normal (non-recursive) functions Recursive function

22. Slide 22 Recursive function A recursive function is just a function which is calling one (or more) other functions which happen to be the same!!! l Though the function is the same, ‘parameters’ are always ‘smaller’ l There is always at least one stopping case to terminate It is a kind of ‘loop’, even more powerful, as a general problem-solving technique! --- thinking recursively!

23. Slide 23 Everything is recursive … Linear search Length of a string Min, max of an array Selection sort Binary search: n Compare search element with middle element of the array: If not equal, then apply binary search to half of the array (if not empty) where the search element would be.

24. Slide 24 Recursion vs. Iteration (non-recursive) * A recursive solution may be simpler to write (once you get used to the idea) than a non-recursive solution.  But a recursive solution may not be as efficient as a non- recursive solution of the same problem. To iterate is human, to recurse, divine!

25. Slide 25 Start from the first element While (not yet finished) do do the current element move to the next one toto(n) If 0 or 1 element, just do it elsedecompose into first element and the n-1 remaining elements do the first element toto(n-1) For n elements:

26. Slide 26 Sum of the array Write a recursive function that takes a double array and its size as input and returns the sum of the array: if zero or one element, (trivial) sum( zero element or one element) = … ! else (decompose into 1-element and n-1 elements) sum(n elements) = sum( n-1 elements) + nth element

27. Slide 27 double asum(int a[], int size){ double sum; if(size==0) sum=0; else sum=asum(a,size-1)+a[size-1]; return sum; }

28. Slide 28 Product of an array Write a recursive function that takes a double array and its size as input and returns the product of the array: if zero or one element, (trivial) prod( zero element or one element) = …! else (decompose into 1-element and n-1 elements) prod(n elements) = prod(n-1 elements) * nth element

29. Slide 29 double aprod(int a[], int size) { doulbe prod; if(size==0) prod=1; else prod=aprod(a,size-1)*a[size-1]; return prod; }

30. Slide 30 Input: an array of integers A, and a value Output: the position of the value in the array if one element, check it! else decompose into 1-element and n-1 elements check the 1-element search(n-1) Linear search

31. Slide 31 int search(int A[], int size, int value) { int pos; if (size==1) if(A[size-1]==value) pos=1; else pos=-1; else if(A(size-1]==value) pos=size-1; else pos=search(A,size-1,value); return pos; }

32. Slide 32 Input: a sorted array of integers A, and a value Output: the position of the value in the array if the middle element == value, done! else if the middle element > value do the same in the first half of the array else do the same in the second half of the array } Binary search

33. Slide 33 int bsearch(int data[],lower,upper,value) { int pos; if (lower<=upper) { mid=(lower+upper)/ 2; if (data[mid] == value) pos=mid; else if (data[mid]>value) pos=bsearch(data,lower,mid–1,value); else pos=bsearch(data,mid+1,upper,value); } return pos; } Recursive binary search

34. Slide 34 int bsearch(int data[], int size, int value) { int lower, middle, upper; bool found; lower = 0; upper = size - 1; found=false; position=-1; while ((lower<=upper) && (!found)) { middle = (lower+upper)/2; if (data[middle] == value) { found=true; position=middle; } else { if (data[middle] > value) upper = middle - 1; else lower = middle + 1; } return position; } (iterative) Binary search: int main() { const int size=8; int data[size] = {1,5,6,7,9,10,17,30}; int value; cin >> value; cout << “position of the value is “ << bsearch(data,size,value) << endl; }

35. Slide 35 Take the minimum, then sort the remaining elements … Sorting