Boolean Algebra Boolean Algebra

Transcription

1 What is the result and type of the following expressions? Int x=2, y=15; float u=2.0, v=15.0; -x x+y x-y x*v y / x x/y y%x x%y u*v u/v v/u u%v x * u (x+y)*u u / (x-x) x++ u++ u = --x u = x -- u *= ++x v /= x; Are these constants legal? Types 0x5E 0.5E3 0.5E E a % Ab Ab are these variable names legal? MyTotal My_Total MyTotal My Total What does this mean? int mytotal=0; int yourtotal(1); What would be stored in myvar? int myvar; myvar=2.56; What would be stored in yourvar? double yourvar; yourvar=5/2; Logical expressions, IF Logical expressions have the one of two values - true or false A rectangle has three sides. The instructor has a pleasant smile The branch of mathematics that deals with this type of logic is called Boolean algebra Developed by the British mathematician George Boole in the 19th century C++ makes extensive use of Boolean algebra in the form of logical expressions; what is an expression again? Three key logical operators in C++: && - logical and - logical or! - logical not Truth tables Lists all combinations of operand values and the result of the operation for each combination truth table for && (logical and ) P Q P && Q False False False False True False True False False True True True Truth table for (logical or ) P Q P Q False False False False True True True False True True True True

2 Truth table for! (logical not ) P! P False True True False Can create complex logical expressions by combining simple logical expressions Example! (P&& Q) A truth table can be used to determine when a logical expression is true P Q P && Q! (P && Q) False False False True False True False True True False False True True True True False A Boolean Type A Boolean Type C++ contains a type named bool Type bool has two symbolic constants true false Warning! & and are also operators Warning! Older versions of g++ compiler don t have type bool - logical arithmetic can be done on integers Example logical expressions bool P = true; bool Q = false; bool R = true; bool S = P && Q; bool T = P &&!Q bool U =!Q R; bool V = P!Q!R; bool W = P && Q &&!R; bool X = Q (P && R); bool Y =!(R &&!Q); bool Z =!(P && Q && R); Relational Operators Relational Operators Equality operators ==!= Examples int i = 32; int k = 45; bool q = i == k; bool r = i!= k; Ordering operators < > >= (?) <= (?) Examples int i = 5; int k = 12; bool p = i < 10; bool q = k > i; bool r = i >= k; bool s = k <= 12;

3 Operator Precedence Revisited Precedence of operators (from highest to lowest) () Unary + - * / % + - > < >= >=!= == && = Examples of Logical Expressions int a = 5; int b = 10 int c = 20; bool d = a < b; bool e = a > b; bool f = (a > b) (b < c ); bool g = (a > b) && (b < c ); bool h =!(a < b); bool i =!(a==b); bool j = 2*a == b; bool k = (a+b) >= c; bool l =!((a+b)!= c); bool m = (a+b) == (c-a); bool n = (a+b) >= (c-a); int o=a; int p=o=b; What is the outcome of this operation? bool q=true; q = d = false; Operator Precedence Revisited Conditional Constructs Same or different? (a*b)+c a*b + c a*(b+c) a*b + c (a+b) > c a + b > c a+(b>c) a + b > c (a > b) == (b > c) a > b == b > c (a == b) > (b == c) a == b > b == c (a!= b) && (c <= d) a!= b && c <= d (a > b) && (c d) a > b && c d (a = b) && c a = b && c Provide Ability to control whether a statement list is executed Two constructs If statement If If-else If-else-if Switch statement The Basic If Statement Syntax if (Expression) If the Expression is true then execute is either a single statement or a group of statements within braces Example 1: if ( Value > 0) Value =0; Example 2: if (Value < 0) { Value = -Value; i++; Expression true false Sorting Two Numbers cout << "Enter two integers: "; int Value1; int Value2; cin >> Value1 >> Value2; if (Value1 > Value2) { int RememberValue1 = Value1; Value1 = Value2; Value2 = RememberValue1; cout << "The input in sorted order: " << Value1 << " " << Value2 << endl;

4 The If-Else Statement Selection Syntax if (Expression) 1 else 2 If Expression is true then execute 1 otherwise execute 2 if (v == 0) { cout << "v is 0"; else { cout << "v is not 0"; true Expression false 1 2 It is often the case that depending upon the value of an expression we want to perform a particular action Two major ways of accomplishing of this choice If-else-If statement If-else statements glued together Switch statement An advanced construct Multiway If-Else-If Statement Switch Statement Example if ((ch == 'a') (ch == 'A )) else if ((ch == 'e') (ch == 'E")) cout << " ch << " is a vowel" << endl; else if ((ch == 'i') (ch == 'I")) else if ((ch == 'o') (ch == 'O")) else if ((ch == 'u') (ch == 'U")) else cout << ch << " is not a vowel" << endl; switch (ch) { case 'a': case 'A": case 'e': case 'E": case 'i': case 'I": case 'o': case 'O": case 'u': case 'U": break; default: cout << ch << " is not a vowel" << endl; cout << "Enter simple expression: "; int Left; int Right; char Operator; cin >> Left >> Operator >> Right; cout << Left << " " << Operator << " " << Right << " = "; switch (Operator) { case '+' : cout << Left + Right << endl; break; case '-' : cout << Left - Right << endl; break; case '*' : cout << Left * Right << endl; break; case '/' : cout << Left / Right << endl; break; default: cout << "Illegal operation" << endl; Conditional assignment an abbreviated form of branching construct (or expanded assignment?) - conditional assignment variable = expression? true-expression : false-expression; variable is assigned the value of true-expression if expression evaluates to true and the value of false-expression otherwise What branching construct is this assignment equivalent to? example: int I = j >0? j : -j; program that calculates the largest number ( of two) int main() { int n1, n2; cin >> n1 >> n2; int max = n1 > n2? n1 : n2; cout << maximum is << max << endl;

5 Naming constants Using number constants can be tedious: 9.8 does not give a hint of its significance as tax rate. Number constants are hard to modify if spread all over the program named constant provides a name to a constant: const int WINDOW_COUNT = 5; const double TAX_RATE = 9.8; constants are usually declared at the beginning of the program. Capital letters are usually used to give a programmer a hint that this is a constant when he encounters it in the program note to C programmers: #define is totally replaced by const in C++ Blocks and local variables Anything enclosed in curved brackets is called a block block may be placed anywhere a statement can be placed (note the placement of brackets: if ((sale_type == W (sale_type == w )) { total = price * number; a variable can be declared and used within block, such variable is local to the block and does not exist outside of it else if ((sale_type == R (sale_type == R )){ double subtotal; subtotal = price * number; total = subtotal + subtotal * TAX_RATE; pitfall: a local variable is accessed outside of the block