Informatik für Mathematiker und Physiker Woche 7. David Sommer

Transkript

1 Informatik für Mathematiker und Physiker Woche 7 David Sommer David Sommer 30. Oktober

2 Heute: 1. Repetition Floats 2. References 3. Vectors 4. Characters David Sommer 30. Oktober

3 Übungen Hat alles geklappt? David Sommer 30. Oktober

4 Exercise 5.5: Fixing Functions What are the problems (if any) with the following functions? Fix them and find appropriate pre- and post conditions. // PRE : x is not zero // POST : returns the inverse of x bool is_even ( unsigned int i) { if ( i % 2 == 0) return true ; // POST : returns either the inverse of x, or zero if x is zero double invert ( double x) { double result ; if (x!= 0) result = 1 / x; return result ; David Sommer 30. Oktober

5 Repetition Floats Consider F (β, p, e min, e max ) with β = 2, p = 3, e min = 4, e max = 4. Compute the following expressions as the parentheses suggest. Remember: Use the normalized floating point representation for all intermediate results! ( ) decimal binary ( ) + 10 decimal binary 10????? + 0.5????? =????? + 0.5????? =??????? 0.5????? + 0.5????? =????? + 10????? =??????? David Sommer 30. Oktober

6 Repetition Floats - Solution ( ) ( ) + 10 decimal binary decimal binary = = = = Vorsicht beim Addieren unterschiedlich grosser Fliesskommazahlen. David Sommer 30. Oktober

7 References I Ähnliche Bedeutung wie Referenz oder Alias Kann nur auf ein bereits existierendes objekt zeigen int a = 3; int & b = a; b = 2; std :: cout << a; // 2 David Sommer 30. Oktober

8 References II Wird oft auch als zusätzlichen return value für Funktionen gebraucht Beispiel: int foo ( int i) {... i wird kopiert beim ausführen von foo ( pass by value ) Was wenn die Funktion i verändern sollte? int foo ( int &i) {... Es wird eine Referenz von i übergeben (i wird nicht kopiert) pass by reference David Sommer 30. Oktober

9 References Funktionen - Beispiel // PRE : zwei Punkte p1(x1, y1) und p2(x2,y2) // POST : die Steigung m und Offset q der Geraden durch p1 und p2 // Falls x1 == x2 oder y1 == y2 return -1 // Sonst return 0; int gerade ( int x1, int y1, int x2, int y2, double & m, double & q) { if( x1 == x2 y1 == y2) return -1; m = (y2 - y1) / double (x2 - x1 ); q = y1 - m * x1; return 0; David Sommer 30. Oktober

10 References Funktionen - Vorteile Was für Vorteile hat pass by reference? Mehr return values Input variablen müssen nicht kopiert werden. Beispiel: Ein Eintrag aus einen gigantischen Vektor lesen void read_ i ( Vector & v, unsigned int i); Der Vektor muss nicht kopiert werden! Einige Objekte können nicht kopiert werden: std :: ostream o = std :: cout ; // Error std :: ostream & o = std :: cout ; // This works! David Sommer 30. Oktober

11 References Funktionen - Return Reference Referenzen können auch zur ckgegeben werden!beispiel: int & increment ( int & m) { return ++m; int main () { int n = 3; increment ( increment (n )); std :: cout << n << std :: endl ; // outputs 5 return 0; David Sommer 30. Oktober

12 Exercise 2

13 Exercise 2 (a) What is the output of the program for the following variant of foo? int foo (int& a, int b) { a += b; return a; int main() { int a = 0; int b = 1; for (int i=0; i<5; ++i) { b = foo (a, b); std::cout << b << " "; return 0; (From: Exam Summer 2015, Exercise 9) 15

14 Exercise 2 (a) What is the output of the program for the following variant of foo? int foo (int& a, int b) { a += b; return a; int main() { int a = 0; int b = 1; for (int i=0; i<5; ++i) { b = foo (a, b); std::cout << b << " "; return 0; (From: Exam Summer 2015, Exercise 9) 16

15 Exercise 2 (b) What is the output of the program for the following variant of foo? int foo (int a, int b) { a += b; return a; int main() { int a = 0; int b = 1; for (int i=0; i<5; ++i) { b = foo (a, b); std::cout << b << " "; return 0; (From: Exam Summer 2015, Exercise 9) 17

16 Exercise 2 (b) What is the output of the program for the following variant of foo? int foo (int a, int b) { a += b; return a; int main() { int a = 0; int b = 1; for (int i=0; i<5; ++i) { b = foo (a, b); std::cout << b << " "; return 0; (From: Exam Summer 2015, Exercise 9) 18

17 Exercise 2 (c) What is the output of the program for the following variant of foo? int foo (int a, int& b) { a += b; return a; int main() { int a = 0; int b = 1; for (int i=0; i<5; ++i) { b = foo (a, b); std::cout << b << " "; return 0; (From: Exam Summer 2015, Exercise 9) 19

18 Exercise 2 (c) What is the output of the program for the following variant of foo? int foo (int a, int& b) { a += b; return a; int main() { int a = 0; int b = 1; for (int i=0; i<5; ++i) { b = foo (a, b); std::cout << b << " "; return 0; (From: Exam Summer 2015, Exercise 9) 20

19 Vectors Statische Liste (Arrays) Länge der Liste zur compilezeit bekannt Die Länge kann sich nicht verändern Dynamische Liste (Vektor) Kann vollkommen dynamisch verlängert werded Warum würde jemand überhaupt statische Listen brauchen? Geschwindigkeit David Sommer 30. Oktober

20 Vectors Instanzierung # include <vector > std :: vector < int > vec ; // empty vector with type int std :: vector < int > vec ( 0); // empty vector with type int std :: vector <int > vec (3); // {0, 0, 0 std :: vector <int > vec = {1, 2, 3; // {1, 2, 3 std :: vector <int > vec (5, 2); // {2, 2, 2, 2, 2 David Sommer 30. Oktober

21 Vectors Access and Modify Elements Wichtig: index [0, length) Access: std :: cout << vec.at (0) << std :: endl ; // with range - check std :: cout << vec [0] << std :: endl ; // w/o range - check Modify: vec [0] = 3; vec. push_ back ( 3); // add new element to the back vec. insert ( vec. begin (), 3); // add element to the start vec. insert ( vec. begin () + i, 3); // insert element at i David Sommer 30. Oktober

22 Vectors Loops Wichtig: index [0, length) Normaler Loop for ( int i = 0; i < vec. size (); i ++) std :: cout << vec [i] << std :: endl ; For-each for ( int entry : vec ) std :: cout << entry << std :: endl ; David Sommer 30. Oktober

23 Vectors Loops For-each Achtung: For-each loops können nicht verwendet werden um Einträge zu manipulieren: std :: vector <int > vec (2, 0); for ( int i : vec ) i = 10; // i is copied - > vec is not modified for ( int i : vec ) std :: cout <<i<< std :: endl ; // outputs 0 David Sommer 30. Oktober

24 Vectors: C++ Reference Jetzt auch auf Deutsch! David Sommer 30. Oktober

25 Vectors Exercise Write a program that reads a number n(n <= 10) followed by a sequence of n numbers and outputs the sequence in reverse order. Please put the code that reverses the sequence in a seperate function. Example Input: Example Output: Reversing Vector on expert.ethz.ch David Sommer 30. Oktober

26 Vectors Exercise Solution // POST : swap the values of i and j void swap ( int & i, int & j) { const int tmp = i; i = j; j = tmp ; // PRE : length length of the vector sequence. // POST : Reverses the sequence void reverse (std :: vector <int >& sequence, unsigned int length ) { int front = 0; int back = length -1; while ( front < back ) { swap ( sequence [ front ], sequence [back ]); ++ front ; -- back ; int main () { unsigned int length ; std :: vector <int > sequence (10); // Step 1: Read input. std :: cin >> length ; assert ( length <= 10); for ( unsigned int i = 0; i < length ; ++i) { std :: cin >> sequence [i]; // Step 2: Reverse sequence ; reverse ( sequence, length ); // Step 3: Output for ( unsigned int i = 0; i < length ; ++i) { std :: cout << sequence [i] << " "; std :: cout << std :: endl ; return 0; David Sommer 30. Oktober

27 Characters Wie speichert C++ Charaktere? ASCII ASCII = American Standard Code for Information Interchange Für euch Mathematiker: Injektive Abbildung [0, 255) Chars Wichtig: Unterschied zwischen A und "A"? A ist ein einzelner char (0 x41) "A" ist ein string (Folge von chars) und Nullterminiert (0 x41 0 x00) " ABc " ist 0 x41 0 x42 0 x63 0 x00 Beispiel: A = 65, B = 66,..., a = 97, b = 98,... int a = a ; // 0 x (32 - Bit <-> 4- Byte ) char a = a ; // 0 x61 ( 8- Bit <-> 1- Byte ) ASCII Tabelle: David Sommer 30. Oktober

28 Characters - Convert to UPPERCASE Write a program that reads a sequence of characters delimited by the new-line character and then outputs the sequence with all lower-case letters changed to UPPER-CASE letters. Please put the code that converts the entire sequence to upper-case and a single character to upper-case into separate functions (you should have at least three functions). Hint: variables of type char can be treated as numbers. Example Input: helloworld Example Output: HELLOWORLD1 David Sommer 30. Oktober

29 Characters - Convert to UPPERCASE Solution int main () { // Say to std :: cin not to ignore whitespace. std :: cin >> std :: noskipws ; // POST : Converts the letter to upper case. void char_to_upper ( char & letter ) { if ( a <= letter && letter <= z ) { letter -= a - A ; // a > A // POST : Converts all letters to upper - case. void to_upper (std :: vector <char >& letters ) { for ( unsigned int i = 0; i < letters.size (); ++i) { char_to_upper ( letters [i ]); std :: vector <char > letters ; char ch; // Step 1: Read input. do { std :: cin >> ch; letters. push_back (ch ); while (ch!= \n ); // Step 2: Convert to upper - case. to_upper ( letters ); // Step 3: Output. for ( unsigned int i = 0; i < letters.size (); ++ i) { std :: cout << letters [i]; David Sommer 30. Oktober

30 Fragen? David Sommer 30. Oktober