Where are we, and where to go?

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

2. Programming paradigms • Imperative programming • Declarative programming • Functional (Lisp) and logical (Prolog) programming • Highly recursive • Object-oriented programming • Generic programming

3. procedural programming: 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(); } 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() { } Object oriented programming: a sequence of ‘objects’! Objects communicate by sending messages.

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

5. Reference: X& int& b a; 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; a 10 b c Relationship with pointers (later on)!

6. Call by Value 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 = • When a variable v is passed by value to a function f, its value is copied to the corresponding variable x in f • Any changes to the value of x does NOT affect the value of v • Call by value is the default mechanism for parameter passing in C++ 5 5

7. Call by Reference 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 = • 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 • Any changes to the value of x DOES affect the value of v 5 4

8. Call by Constant Reference 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.

9. Parameter Passing • Call by value • for small objects that should not be changed by the function • Call by constant reference • for large objects that should not be changed by the function • Call by reference • is appropriate for all objects that may be changed by the function, • not recommended!!! rare!

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

11. Scope of variables The scope of a declaration is the block of code where the identifier is valid for use. • 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. • 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) • 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. Global (local to the file) Local to functions Local to blocks int x; int main() { x=0; cout << x << endl; int x; x=1; { int x; x=2; cout << x << endl; } cout << x << endl; } void f() { int x; x=1; { int x; x=2; cout << x << endl; } cout << x << endl; } int main() { int x,y,z; … } void f() { int x; … }

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. 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. Summary Pass by value Global variable Pass by reference 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; } 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); } 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; } Good style!!!

16. Declarative vs. Procedural What to do vs. how to do Interface vs. actions Separate compilation *.h (declaration) vs *.cc (actions, procedures) … Functional programming A procedure is more a ‘mathematical function’

17. Recursion Important for algorithm design and analysis

18. 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!

19. More declarative than procedural! what vs. how // 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; }

20. Trace tower(4,A,B,C)

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

22. Recursive function A recursive function is just a function which is calling one (or more) other functions which happen to be the same!!! Though the function is the same, ‘parameters’ are always ‘smaller’ 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. 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!

24. Everything is recursive … Linear search Length of a string Min, max of an array Selection sort Bubble sort … Binary search: • 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.

25. For n elements: 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 else decompose into first element and the n-1 remaining elements do the first element toto(n-1)

26. Exponential How to write exp(int x, int y) recursively? int exp(int x, int y) { int power; if(y==0) power = 1; else power = x * exp(x, y-1); return power; }

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

29. Counting the number of zeros • Write a recursive function that counts the number of zero digits in a non-negative integer • zeros(10200) returns 3 int zeros(int n){ int z; if (n<10) if (n==0) z=1; else z=0; else z=zeros(n/10)+zeros(n%10); return z; } n/10  the number n with the last digit removed n%10  the last digit of n

30. Find factors Write a recursive function to determine how many factors m are part of n. For example, if n=48 and m=4, then the result is 2 (48=4*4*3). int factors(int n, int m){ int f; if(n%m != 0) f=0; else f=1+factors(n/m, m); return f; }

31. Binary search int bsearch(int data[],lower,upper,value) { 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; }

32. Sorting Take the minimum, then sort the remaining elements …