Boolean Logic. Boolean Expressions. What and means. And, Or, Not, True, False. What not means. What or means. Truths and Falsehoods

Transcription

1 Boolean Logic Boolean Expressions Truths and Falsehoods Boolean logic (algebra) is named after George Boole He wrote the book Investigation of the Laws of Thought in 1854 Also called propositional logic And, Or, Not, True, False Boolean logic is all about true and false expressions The logical connective words and, or, not In C++, type bool has two possible values: true and false bool p; bool q; What and means bool result = (p and q); p has the value true, or it has the value false q has the value true, or it has the value false result is true just if both p and q are true; otherwise result is false What or means What not means p has the value true, or it has the value false bool p; bool q; bool result = (p or q); q has the value true, or it has the value false bool p; bool result = not p; p has the value true, or it has the value false result is true just if either p or q (or both) is true; otherwise result is false result is true just if p or q is false; otherwise result is true not flips the value of a bool expression

2 Boolean Logic That's it! If you understand what's on the previous slides, you know boolean logic Let's look at some examples... All About and (true and true) is true (true and false) is false (false and true) is false (false and false) is false All About or (true or true) is true (true or false) is true (false or true) is true (false or false) is false All About not (not true) is false (not false) is true What Gets Printed? if (true) { cout << "True!"; else { cout << "False!"; True! This is an if-else statement if (true) { cout << "True!"; else { cout << "False!"; Only one of the code blocks can be executed in an if-else statement, depending on whether the condition is true or false This is the condition of the if statement; the condition is always a boolean expression When the condition is true, this code block is executed When the condition is false, this code block is executed

3 What Gets Printed? if (false) { cout << "True!"; else { cout << "False!"; False! What Gets Printed? bool all_done = true; if (all_done) { cout << "All done!"; else { cout << "More to do!"; All done! What Gets Printed? bool all_done = false; if (all_done) { cout << "All done!"; else { cout << "More to do!" More to do! What Gets Printed? bool red_cursor = true; bool blinking_cursor = false; if (red_cursor and blinking_cursor) { cout << "Red and blinking! "; cout << "Done."; Done. This statement does the same as this one: bool red_cursor(true); What Gets Printed? bool red_cursor = true; bool blinking_cursor = false; if (red_cursor and blinking_cursor) { cout << "Red and blinking! "; cout << "Done."; This statement will always be executed because it s outside the if-statement s code block This is just an if-statement, with no else part bool red_cursor = true; bool blinking_cursor = true; if (red_cursor and blinking_cursor) { cout << "Red and blinking! "; cout << "Done."; Red and blinking! Done.

4 Example Example char ch; cout << "Please enter y for yes, n for no: "; cin >> ch; if (ch == y or ch == Y ) { cout << "\nyes!"; else { cout << "\nno!"; If the user enters any other character, then No! is printed If the user enters y or Y, then Yes! is printed char ch; cout << "Please enter y for yes, n for no: "; cin >> ch; if (ch == y or ch == Y ) { cout << "\nyes!"; else { cout << "\nno!"; Note that you can put any C++ statements at all inside these code blocks, not just cout statements! Equality and Inequality == means the same as C++ let's you test if two expressions have the same or different values We use these tests all the time in boolean expressions... cout << "Please enter two numbers: "; double num1; double num2; cin << num1 << num2; if (num1 == num2) { cout << num1 << " and " << num2 << "are the same!\n"; else { cout << num1 << " and " << num2 << "are different!\n"; Be careful: don t confuse this with the assignment operator, which is =!= means different than Self-test Questions cout << "Please enter two numbers: "; double num1; double num2; cin << num1 << num2; if (num1!= num2) { cout << num1 << " and " << num2 << "are different!\n"; else { cout << num1 << " and " << num2 << "are the same!\n"; Pretend C++ didn't have!=, and show how to simulate!= using only == and not Pretend C++ didn't have ==, and show how to simulate == using only!= and not (Harder!) Pretend C++ didn't have and. Show how to simulate and using only not and or

5 == verus = name = "Mai"; if (name == "Mai") { C++ Danger: Don t Do This! if (name = "Mai") { This is an assignment. A single = means "put a copy of the value of the right-hand side into the variable on the left-hand side This is a comparison. == returns true if both name and "Mai" have the same value; otherwise, it returns false Using an assignment in an if-statement condition like this is almost always a mistake. However, C++ will let you do this! It turns out that assignments return the value being assigned (i.e. the value of the expression on the right side of =), and C++ uses some tricky conversion rules to convert the string literal "Mai" into a bool value!?! Example: Ranges In mathematics, we often write expression like this 0 < x < 1 Let's write some C++ code that prints "x is between 0 and 1" if the above is true Assume that x is a double... Example: Ranges This is legal C++, but (0 < x < 1) doesn t mean the same as the mathematical expression 0 < x < 1!! if (0 < x < 1) { // wrong!!! Example: Ranges Let s suppose x is 0, so 0 < x is false for this example... Example: Ranges We will work out this example step by step, changing the code into equivalent but simper code at each step int x = 0; // example value of x if (0 < x < 1) { // wrong!!! int x = 0; // example value of x if (0 < x < 1) { // wrong!!!

6 int x = 0; // example value of x if (0 < x < 1) { // wrong!!! Step 1: x has value 0, so we can replace x this code does the same as this code by 0 in the expression (0 < x < 1) if (0 < 0 < 1) { // wrong!!! this code does the same as this code Step 2: (0 < 0) evaluates to false, so let s replace it if (0 < 0 < 1) { // wrong!!! if (false < 1) { // wrong!!! What is false < 1? false is a bool value, and 1 is an int C++ does not let you directly compare bools to ints, but... C++ tries to be 'helpful', and in this situation automatically converts false to the int value 0 So false < 1 is the same as 0 < 1, which is true The value of false < 1 Imagine C++ 'thinking' like this: How can I calculate false < 1? I don't know how to compare bools to ints But, I do know how to compare ints to ints And, I know how to convert a bool to an int So here s what I'll do: I'll convert false to 0, and then evaluate 0 < 1 Thus, the final answer is true! if (false < 1) { // wrong!!! this code does the same as this code Step 3: in this context, false can be converted to 0 if (0 < 1) { // wrong!!! this code does the same as this code Step 4: (0 < 1) is always true if (0 < 1) { // wrong!!! if (true) { // wrong!!!

7 if (true) { // wrong!!! this code does the same as this code, and both print x is between 0 and 1 this is the original code! Step 5: compare the simplified code to the original code int x = 0; // example value of x if (0 < x < 1) { // wrong!!! Example: Ranges if (0 < x < 1) { // wrong!!! Okay, so this is wrong, but what's the right way to handle it? The right way is to split 0 < x < 1 into two parts... Example: Ranges Other Relational Operators if ((0 < x) and (x < 1)) { // correct (x < y) true just when the value of x is less than the value of y This is the correct way to test 0 < x < 1 Moral C++'s "helpfulness" sometimes causes bugs C++ can trip you up in dozens of ways Be careful out there! (x <= y) true just when the value of x is less than the value of y, or the value of x is equal to the value of y this boolean expression can be rewritten as this equivalent one: (x < y) or (x == y) Other Relational Operators A Puzzle (x > y) true just when the value of x is greater than the value of y How can you rewrite the following C++ code without using <= or <? (x >= y) true just when the value of x is less than the value of y, or the value of x is equal to the value of y this boolean expression can be rewritten as this logically equivalent one: (x > y) or (x == y) double table_friction; double box_friction; if (table_friction <= box_friction) { get rid of this!

8 A Puzzle Here's one way to figure this out: draw number lines for (a <= b), these are the two possibilities this is the one case when (a <= b) is false, and this is the key a b a b b a A Puzzle The previous number lines show that (a <= b) is true just when (a > b) is false That means (not (a > b)) is equivalent to (a <= b) Question: why does C++ provide <=, and >= if they can be rewritten in terms of other, simpler operators? Short-circuit Evaluation In C++, (p and q) is evaluated in a very particular way First p is evaluated; if p is false, then the whole expression returns false, and q is not evaluated If p is true, then q is evaluated, and its value is returned as the value of the entire expression Short-circuit Evaluation Similarly, C++ evaluates (p or q)in a very particular way First p is evaluated; if p is true, then the whole expression returns true, and q is not evaluated If p is false, then q is evaluated, and its value is returned as the value of the entire expression Short-circuit Evaluation Short-circuit evaluation can be quite useful at times, e.g. if ((n!= 0) and (200/n > 1)) { The expression (200/n > 1) is only evaluated if n is not zero Short-circuit Evaluation Often you need not worry about shortcircuit evaluation, but sometimes it makes a big difference! Sometimes, it can speed up your programs, e.g. false and (x < 1) and (y*y > 3) and (x*y*z > z*z*z) Nothing after false is evaluated!

9 Converting an int to a bool An int can also be treated as a bool 0 means false Any other int value means true This is sometimes useful, but it's wise to use bool types whenever possible C++'s parent language, C, has no bool type, so C programs rely on this int trick all the time Once upon a time, there was this guy... Fabio his name was Fabio, and he had very long hair. There was also a seagull... who had a very sharp beak. One day the seagull started flying towards Fabio... Closer... Closer and closer...

10 Closer and closer and closer! Oh yeah, Fabio was in a roller coaster, so he couldn't move. Pow!... and closer and closer, until... Pow! Right in the kisser! The seagull hit Fabio! The Seagull s Question In C++, how can you read in 3 strings from the user, and print them out in sorted order? Fabio didn't know the answer Do you? Both Fabio and the seagull got knocked over. The seagull then asked Fabio this question...

11 Screen Layout First, here's what the user will see on the screen Please enter 3 strings: fabio bonk nose Here are those strings in sorted order: bonk fabio nose High-level Pseudocode Here's the rough structure of the program read in three strings sort those strings into alphabetical order print the strings in alphabetical order Reading in strings Reading in the strings will be easy: string A; string B; string C; cout << "Please enter 3 strings: "; cin >> A >> B >> C; Once the strings are sorted, printing them out will be easy A Note on getline cin << A will not read in spaces use getline(cin,a) to read in a string that contains spaces Be careful: getline doesn t work in some versions of BC++ (e.g. the version in the assignment lab), but if you include ccc_ansi.cpp, that should fix any problems Sorting strings The < operator works with strings string name1; string name2; if (name1 < name2) { cout << name1 << " comes before " << name2 << endl; else { cout << name2 << " comes before " << name1 << endl; Lexicographic Ordering C++ strings can consist of any sequence of characters, including numbers, punctuation, spaces, upper case and lower case letters, The < operator puts all strings into lexicographic order according to the ASCII (or ANSI) code every character has a unique integer code

12 Lexicographic Ordering Read the details of how lexicographic ordering work (p ) All the basic relational operators work with strings: ==,!=, <, <=, >, >= What we need to know is that if (str1 < str2) is true, then str1 comes before str2 Sorting Two Strings string A; string B; cin >> A >> B; if (A > B) { // swap A and B string temp = A; A = B; B = temp; cout << A << B; Sorting Three Strings Arranging 3 Strings There are a number of different ways to do this using if statements I'll do it using brute force: an if-else-if statement that considers all possible orderings You should find a shorter way to do this There are only 6 ways that the 3 strings A, B, and C can be arranged Write an if-else-if statement that recognizes each of these cases, and rearranges A, B, C Case 1: A <= B <= C Case 2: A <= C <= B Case 3: B <= A <= C Case 4: B <= C <= A Case 5: C <= A <= B Case 6: C <= B <= A if ((a <= b) and (b <= c)) { // case 1 // nothing do, already sorted else if ((a <= c) and (c <= b)) { // case 2 // swap c and b else if ((b <= a) and (a <= c)) { // case 3 // swap a and b else if ((b <= c) and (c <= a)) { // case 4 // swap a and b, then swap b and c else if ((c <= a) and (a <= b)) { // case 5 // swap a and b, then swap c and a else if ((c <= b) and (c <= a)) { // case 6 // swap a and c Filling in the Details The previous if-else-if statement shows exactly how to continue You just need to write the code to do the required swaps you already know how to swap variables! The way this program has been developed is a good example of topdown design