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The printing is done outside of the function. That way, we can do math with the result, like below. |ample 1 Here is a simple function that converts temperatures from Celsius to Fahrenheit.|Col2| |---|---| ||| |def convert(t): return t*9/5+32 print(convert(20))|| **print(convert(20)+5)** If we had just printed the...
Let us write our own sine function that works in degrees. **from math import pi, sin** **def deg_sin(x):** **return sin(pi*x/180)** **Example 3** A function can return multiple values as a list. Say we want to write a function that solves the system of equations ax + b y = e and cx + d y = f . It turns out that if...
We need our function to return both the x and y solutions._ |ample 2 As another example, the Python math module contains trig functions, but they only rk in radians.
Let us write our own sine function that works in degrees.|Col2| |---|---| ||| |from math import pi, sin def deg_sin(x): return sin(pi*x/180)|| |we want to write a function that solves the system of equations ax + b y = e and cx + d y = f .
urns out that if there is a unique solution, then it is given by x = (de −b f )/(ad −bc) and = (a f −ce)/(ad −bc).
We need our function to return both the x and y solutions.|Col2| |---|---| ||| |def solve(a,b,c,d,e,f): x = (d*e-b*f)/(a*d-b*c) y = (a*f-c*e)/(a*d-b*c) return [x,y]|| ----- 122 _CHAPTER 13.
FUNCTIONS_ xsol, ysol = solve(2,3,4,1,2,5) **print('The solution is x = ', xsol, 'and y = ', ysol)** ###### The solution is x = 1.3 and y = -0.2 This method uses the shortcut for assigning to lists that was mentioned in Section 10.3. **Example 4** A return statement by itself can be used to end a function early. *...
This makes it optional, and if the caller decides not to use it, then it takes the default value.
Here is an example: **def multiple_print(string, n=1)** **print(string * n)** **print()** multiple_print('Hello', 5) multiple_print('Hello') ###### HelloHelloHelloHelloHello Hello Default arguments need to come at the end of the function definition, after all of the non-default arguments. **Keyword arguments** A ...
Say we have the following function definition: |u can specify a default value for an argument. This makes it optional, and if the caller decides to use it, then it takes the default value.
Here is an example:|Col2| |---|---| ||| |def multiple_print(string, n=1) print(string * n) print() multiple_print('Hello', 5) multiple_print('Hello')|| **def fancy_print(text, color, background, style, justify):** Every time you call this function, you have to remember the correct order of the arguments.
Fortunately, Python allows you to name the arguments when calling the function, as shown below: fancy_print(text='Hi', color='yellow', background='black', style='bold', justify='left') ----- _13.5.
LOCAL VARIABLES_ 123 fancy_print(text='Hi', style='bold', justify='left', background='black', color='yellow') As we can see, the order of the arguments does not matter when you use keyword arguments. When defining the function, it would be a good idea to give defaults.
For instance, most of the time, the caller would want left justification, a white background, etc.
Using these values as defaults means the caller does not have to specify every single argument every time they call the function. Here is a example: **def fancy_print(text, color='black', background='white',** style='normal', justify='left'): _# function code goes here_ fancy_print('Hi', style='bold') fancy_print('...
For instance, most of the time, caller would want left justification, a white background, etc.
Using these values as defaults ans the caller does not have to specify every single argument every time they call the function.
re is a example:|Col2| |---|---| ||| |def fancy_print(text, color='black', background='white', style='normal', justify='left'): # function code goes here fancy_print('Hi', style='bold') fancy_print('Hi', color='yellow', background='black') fancy_print('Hi')|| **def func2():** i=100 func1() **print(i)** A problem t...
In a large program it would be a nightmare trying to make sure that we don’t repeat variable names in different functions, and, fortunately, we don’t have to worry about this.
When a variable is defined inside a function, it is local to that function, which means it essentially does not exist outside that function.
This way each function can define its own variables and not have to worry about if those variable names are used in other functions. **Global variables** On the other hand, sometimes you actually do want the same variable to be available to multiple functions.
Such a variable is called a global variable. You have to be careful using global variables, especially in larger programs, but a few global variables used judiciously are fine in smaller programs.
Here is a short example: ----- 124 _CHAPTER 13.
FUNCTIONS_ **def reset():** **global time_left** time_left = 0 **def print_time():** **print(time_left)** time_left=30 In this program we have a variable time_left that we would like multiple functions to have access to.
If a function wants to change the value of that variable, we need to tell the function that time_left is a global variable. We use a global statement in the function to do this.
On the other hand, if we just want to use the value of the global variable, we do not need a global statement. **Arguments** We finish the chapter with a bit of a technical detail.
You can skip this section for the time being if you don’t want to worry about details right now.
Here are two simple functions: **def func1(x):** x = x + 1 **def func2(L):** L = L + [1] a=3 M=[1,2,3] func1(a) func2(M) When we call func1 with a and func2 with L, a question arises: do the functions change the values of a and L?
The answer may surprise you. The value of a is unchanged, but the value of L is changed.
The reason has to do with a difference in the way that Python handles numbers and lists. Lists are said to be mutable objects, meaning they can be changed, whereas numbers and strings are _immutable, meaning they cannot be changed.
There is more on this in Section 19.1._ If we want to reverse the behavior of the above example so that a is modified and L is not, do the following: |Col1|Col2| |---|---| |def reset(): global time_left time_left = 0 def print_time(): print(time_left) time_left=30|| |guments We finish the chapter with a bit of a tec...
You can skip this section for the e being if you don’t want to worry about details right now.
Here are two simple functions:|Col2| |---|---| ||| |def func1(x): x = x + 1 def func2(L): L = L + [1] a=3 M=[1,2,3] func1(a) func2(M)|| |we want to reverse the behavior of the above example so that a is modified and L is not, do the owing:|Col2| |---|---| ||| |def func1(x): x = x + 1 return x def func2(L): copy = L[:]...
EXERCISES_ 125 func2(M) ###### 13.6 Exercises 1. Write a function called rectangle that takes two integers m and n as arguments and prints out an m _n box consisting of asterisks.
Shown below is the output of rectangle(2,4)_ _×_ **** **** 2.
(a) Write a function called add_excitement that takes a list of strings and adds an exclamation point (!) to the end of each string in the list.
The program should modify the original list and not return anything. (b) Write the same function except that it should not modify the original list and should instead return a new list. 3.
Write a function called sum_digits that is given an integer num and returns the sum of the digits of num. 4.
The digital root of a number n is obtained as follows: Add up the digits n to get a new number. Add up the digits of that to get another new number.
Keep doing this until you get a number that has only one digit. That number is the digital root. For example, if n = 45893, we add up the digits to get 4 + 5 + 8 + 9 + 3 = 29.
We then add up the digits of 29 to get 2 + 9 = 11. We then add up the digits of 11 to get 1 + 1 = 2.
Since 2 has only one digit, 2 is our digital root. Write a function that returns the digital root of an integer n.
[Note: there is a shortcut, where the digital root is equal to n mod 9, but do not use that here.] 5.
Write a function called first_diff that is given two strings and returns the first location in which the strings differ. If the strings are identical, it should return -1. 6.
Write a function called binom that takes two integers n and k and returns the binomial coef�n� �n� _n!_ ficient _k_ . The definition is _k_ = _k!(n−k)!_ [.] 7.
Write a function that takes an integer n and returns a random integer with exactly n digits.
For instance, if n is 3, then 125 and 593 would be valid return values, but 093 would not because that is really 93, which is a two-digit number. 8.
Write a function called number_of_factors that takes an integer and returns how many factors the number has. 9.
Write a function called factors that takes an integer and returns a list of its factors. 10.
Write a function called closest that takes a list of numbers L and a number n and returns the largest element in L that is not larger than n.
For instance, if L=[1,6,3,9,11] and n=8, then the function should return 6, because 6 is the closest thing in L to 8 that is not larger than 8.
Don’t worry about if all of the things in L are smaller than n. ----- 126 _CHAPTER 13. FUNCTIONS_ 11.
Write a function called matches that takes two strings as arguments and returns how many matches there are between the strings.
A match is where the two strings have the same character at the same index. For instance, 'python' and 'path' match in the first, third, and fourth characters, so the function should return 3. 12.
Recall that if s is a string, then s.find('a') will find the location of the first a in s. The problem is that it does not find the location of every a.
Write a function called findall that given a string and a single character, returns a list containing all of the locations of that character in the string.
It should return an empty list if there are no occurrences of the character in the string. 13.
Write a function called change_case that given a string, returns a string with each upper case letter replaced by a lower case letter and vice-versa. 14.
Write a function called is_sorted that is given a list and returns True if the list is sorted and False otherwise. 15.
Write a function called root that is given a number x and an integer n and returns x [1][/][n]. In the function definition, set the default value of n to 2. 16.
Write a function called one_away that takes two strings and returns True if the strings are of the same length and differ in exactly one letter, like bike/hike or water/wafer. 17.
(a) Write a function called primes that is given a number n and returns a list of the first n primes.
Let the default value of n be 100. (b) Modify the function above so that there is an optional argument called start that allows the list to start at a value other than 2.
The function should return the first n primes that are greater than or equal to start. The default value of start should be 2. 18.
Our number system is called base 10 because we have ten digits: 0, 1, ..., 9. Some cultures, including the Mayans and Celts, used a base 20 system.
In one version of this system, the 20 digits are represented by the letters A through T.
Here is a table showing a few conversions: **10** **20** **10** **20** **10** **20** **10** **20** 0 A 8 I 16 Q 39 BT 1 B 9 J 17 R 40 CA 2 C 10 K 18 S 41 CB 3 D 11 L 19 T 60 DA 4 E 12 M 20 BA 399 TT 5 F 13 N 21 BB 400 BAA 6 G 14 O 22 BC 401 BAB 7 H 15 P 23 BD 402 BAC Write a function called base20 that converts a ba...
It should return the result as a string of base 20 digits.
One way to convert is to find the remainder when the number is divided by 20, then divide the number by 20, and repeat the process until the number is 0.
The remainders are the base 20 digits in reverse order, though you have to convert them into their letter equivalents. ----- _13.6. EXERCISES_ 127 19.
Write a function called verbose that, given an integer less than 10[15], returns the name of the integer in English.
As an example, verbose(123456) should return one hundred twenty-three thousand, four hundred fifty-six. 20.
Write a function called merge that takes two already sorted lists of possibly different lengths, and merges them into a single sorted list. (a) Do this using the sort method. (b) Do this without using the sort method. 21.
In Chapter 12, the way we checked to see if a word w was a real word was: **if w in words:** where words was the list of words generated from a wordlist.
This is unfortunately slow, but there is a faster way, called a binary search. To implement a binary search in a function, start by comparing w with the middle entry in words.
If they are equal, then you are done and the function should return True. On the other hand, if w comes before the middle entry, then search the first half of the list.
If it comes after the middle entry, then search the second half of the list.
Then repeat the process on the appropriate half of the list and continue until the word is found or there is nothing left to search, in which case the function short return False.
The < and > operators can be used to alphabetically compare two strings. 22.
A Tic-tac-toe board can be represented be a 3 3 two-dimensional list, where zeroes stand for _×_ empty cells, ones stand for X’s and twos stand for O’s. (a) Write a function that is given such a list and randomly chooses a spot in which to place a 2.
The spot chosen must currently be a 0 and a spot must be chosen. (b) Write a function that is given such a list and checks to see if someone has won.
Return **True if there is a winner and False otherwise.** 23.
Write a function that is given a 9 9 potentially solved Sudoku and returns True if it is _×_ solved correctly and False if there is a mistake.
The Sudoku is correctly solved if there are no repeated numbers in any row or any column or in any of the nine “blocks.” ----- 128 _CHAPTER 13.
FUNCTIONS_ ----- ### Chapter 14 ## Object-Oriented Programming About a year or so after I started programming, I decided to make a game to play Wheel of Fortune. I wrote the program in the BASIC programming language and it got to be pretty large, a couple thousand lines.
It mostly worked, but whenever I tried to fix something, my fix would break something in a completely different part of the program. I would then fix that and break something else.
Eventually I got the program working, but after a while I was afraid to even touch it. The problem with the program was that each part of the program had access to the variables from the other parts.
A change of a variable in one part would mess up things in the others. One solution to this type of problem is object-oriented programming.
One of its chief benefits is encapsulation, where you divide your program into pieces and each piece internally operates independently of the others.
The pieces interact with each other, but they don’t need to know exactly how each one accomplishes its tasks.
This requires some planning and set-up time before you start your program, and so it is not always appropriate for short programs, like many of the ones that we have written so far. We will just cover the basics of object-oriented programming here.
Object-oriented programming is used extensively in software design and I would recommend picking up another book on programming or software design to learn more about designing programs in an object-oriented way. ###### 14.1 Python is objected-oriented Python is an object-oriented programming language, and we have in...
The key notion is that of an object. An object consists of two things: data and functions (called methods) that work with that data. As an example, strings in Python are objects.
The data of the string object is the actual characters that make up that string. The methods are things like lower, replace, and split. In Python, everything is an object.
That includes not only strings and lists, but also integers, floats, and even functions themselves. 129 ----- 130 _CHAPTER 14.
OBJECT-ORIENTED PROGRAMMING_ ###### 14.2 Creating your own classes A class is a template for objects.
It contains the code for all the object’s methods. **A simple example** Here is a simple example to demonstrate what a class looks like.
It does not do anything interesting. **class Example:** **def __init__(self, a, b):** self.a = a self.b = b **def add(self):** **return self.a + self.b** e = Example(8, 6) **print(e.add())** - To create a class, we use the class statement.
Class names usually start with a capital. - Most classes will have a method called __init__. The underscores indicate that it is a special kind of method.
It is called a constructor, and it is automatically called when someone creates a new object from your class. The constructor is usually used to set up the class’s variables.