Datasets:
lhn004
/
python_textbooks

Dataset card Data Studio Files
xet
 Community
1
Text
stringlengths
1
9.41k
For instance, range(5) produces five values: 0, 1, 2, 3, and 4. |ere is one part of a for loop that is a little tricky, and that is the loop variable.
In the example ow, the loop variable is the variable i.
The output of this program will be the numbers 0, 1, ..., each printed on its own line.|Col2| |---|---| ||| |for i in range(100): print(i)|| |ce the loop variable, i, gets increased by 1 each time through the loop, it can be used to keep ck of where we are in the looping process.
Consider the example below:|Col2| |---|---| ||| |for i in range(3): print(i+1, '-- Hello')|| |mes There’s nothing too special about the name i for our variable.
The programs below will ve the exact same result.|Col2| |---|---| ||| |for i in range(100): for wacky_name in range(100): print(i) print(wacky_name)|| ----- 14 _CHAPTER 2.
FOR LOOPS_ If we want the list of values to start at a value other than 0, we can do that by specifying the starting value. The statement range(1,5) will produce the list 1, 2, 3, 4.
This brings up one quirk of the **range function—it stops one short of where we think it should.
If we wanted the list to contain the** numbers 1 through 5 (including 5), then we would have to do range(1,6). Another thing we can do is to get the list of values to go up by more than one at a time.
To do this, we can specify an optional step as the third argument.
The statement range(1,10,2) will step through the list by twos, producing 1, 3, 5, 7, 9. To get the list of values to go backwards, we can use a step of -1.
For instance, range(5,1,-1) will produce the values 5, 4, 3, 2, in that order. (Note that the range function stops one short of the ending value 1).
Here are a few more examples: Statement Values generated **range(10)** 0,1,2,3,4,5,6,7,8,9 **range(1,10)** 1,2,3,4,5,6,7,8,9 **range(3,7)** 3,4,5,6 **range(2,15,3)** 2,5,8,11,14 **range(9,2,-1)** 9,8,7,6,5,4,3 Here is an example program that counts down from 5 and then prints a message. **for i in range(5,0,-1)...
The program below prints a rectangle of stars that is 4 rows tall and 6 rows wide. **for i in range(4):** **print('*'*6)** The rectangle produced by this code is shown below on the left.
The code '*'*6 is something we’ll cover in Section 6.2; it just repeats the asterisk character six times. |re is an example program that counts down from 5 and then prints a message.|Col2| |---|---| ||| |for i in range(5,0,-1): print(i, end=' ') print('Blast off!!')|| |’s look at a problem where we will make use of t...
The program below prints a tangle of stars that is 4 rows tall and 6 rows wide.|Col2| |---|---| ||| |for i in range(4): print('*'*6)|| ----- _2.5.
EXERCISES_ 15 Suppose we want to make a triangle instead. We can accomplish this with a very small change to the rectangle program.
Looking at the program, we can see that the for loop will repeat the print statement four times, making the shape four rows tall.
It’s the 6 that will need to change. The key is to change the 6 to i+1. Each time through the loop the program will now print i+1 stars instead of 6 stars.
The loop counter variable i runs through the values 0, 1, 2, and 3. Using it allows us to vary the number of stars.
Here is triangle program: **for i in range(4):** **print('*'*(i+1))** ###### 2.5 Exercises 1. Write a program that prints your name 100 times. 2.
Write a program to fill the screen horizontally and vertically with your name. [Hint: add the option end='' into the print function to fill the screen horizontally.] 3.
Write a program that outputs 100 lines, numbered 1 to 100, each with your name on it. The output should look like the output below. ###### 1 Your name 2 Your name 3 Your name 4 Your name ...
100 Your name 4. Write a program that prints out a list of the integers from 1 to 20 and their squares. The output should look like this: ###### 1 --- 1 2 --- 4 3 --- 9 ... 20 --- 400 5.
Write a program that uses a for loop to print the numbers 8, 11, 14, 17, 20, ..., 83, 86, 89. 6. Write a program that uses a for loop to print the numbers 100, 98, 96, ..., 4, 2. 7.
Write a program that uses exactly four for loops to print the sequence of letters below. ###### AAAAAAAAAABBBBBBBCDCDCDCDEFFFFFFG 8.
Write a program that asks the user for their name and how many times to print it. The program should print out the user’s name the specified number of times. |e key is to change the 6 to i+1.
Each time through the loop the program will now print i+1 stars tead of 6 stars. The loop counter variable i runs through the values 0, 1, 2, and 3. Using it allows to vary the number of stars.
Here is triangle program:|Col2| |---|---| ||| |for i in range(4): print('*'*(i+1))|| ----- 16 _CHAPTER 2. FOR LOOPS_ 9.
The Fibonacci numbers are the sequence below, where the first two numbers are 1, and each number thereafter is the sum of the two preceding numbers.
Write a program that asks the user how many Fibonacci numbers to print and then prints that many. 1,1,2,3,5,8,13,21,34,55,89... 10. Use a for loop to print a box like the one below.
Allow the user to specify how wide and how high the box should be.
[Hint: print('*'*10) prints ten asterisks.] ###### ******************* ******************* ******************* ******************* 11. Use a for loop to print a box like the one below.
Allow the user to specify how wide and how high the box should be. ###### ******************* * * * * ******************* 12. Use a for loop to print a triangle like the one below.
Allow the user to specify how high the triangle should be. ###### * ** *** **** 13. Use a for loop to print an upside down triangle like the one below.
Allow the user to specify how high the triangle should be. ###### **** *** ** * 14. Use for loops to print a diamond like the one below.
Allow the user to specify how high the diamond should be. ----- _2.5. EXERCISES_ 17 15. Write a program that prints a giant letter A like the one below.
Allow the user to specify how large the letter should be. ----- 18 _CHAPTER 2.
FOR LOOPS_ ----- ### Chapter 3 ## Numbers This chapter focuses on numbers and simple mathematics in Python. ###### 3.1 Integers and Decimal Numbers Because of the way computer chips are designed, integers and decimal numbers are represented differently on computers.
Decimal numbers are represented by what are called floating point numbers. The important thing to remember about them is you typically only get about 15 or so digits of precision.
It would be nice if there were no limit to the precision, but calculations run a lot more quickly if you cut off the numbers at some point. On the other hand, integers in Python have no restrictions.
They can be arbitrarily large. For decimal numbers, the last digit is sometimes slightly off due to the fact that computers work in binary (base 2) whereas our human number system is base 10.
As an example, mathematically, we know that the decimal expansion of 7/3 is 2.333, with the threes repeating forever. But when _···_ we type 7/3 into the Python shell, we get 2.3333333333333335.
This is called roundoff error. For most practical purposes this is not too big of a deal, but it actually can cause problems for some mathematical and scientific calculations.
If you really need more precision, there are ways. See Section 22.5. ###### 3.2 Math Operators Here is a list of the common operators in Python: 19 ----- 20 _CHAPTER 3.
NUMBERS_ Operator Description + addition - subtraction - multiplication / division ** exponentiation // integer division % modulo (remainder) **Exponentiation** Python uses ** for exponentiation.
The caret, ^, is used for something else. **Integer division** The integer division operator, //, requires some explanation.
Basically, for positive numbers it behaves like ordinary division except that it throws away the decimal part of the result. For instance, while 8/5 is 1.6, we have 8//5 equal to 1.
We will see uses for this operator later.
Note that in many other programming languages and in older versions of Python, the usual division operator / actually does integer division on integers. **Modulo** The modulo operator, %, returns the remainder from a division.
For instance, the result of 18%7 is 4 because 4 is the remainder when 18 is divided by 7. This operation is surprisingly useful.
For instance, a number is divisible by n precisely when it leaves a remainder of 0 when divided by n. Thus to check if a number, n, is even, see if n%2 is equal to 0.
To check if n is divisible by 3, see if n%3 is 0. One use of this is if you want to schedule something in a loop to happen only every other time through the loop, you could check to see if the loop variable modulo 2 is equal to 0, and if it is, then do that something. The modulo operator shows up surprisingly often i...
If you need to “wrap around” and come back to the start, the modulo is useful. For example, think of a clock. If you go six hours past 8 o’clock, the result is 2 o’clock.
Mathematically, this can be accomplished by doing a modulo by 12. That is, (8+6)%12 is equal to 2. As another example, take a game with players 1 through 5.
Say you have a variable player that keeps track of the current player. After player 5 goes, it’s player 1’s turn again.
The modulo operator can be used to take care of this: player = player%5+1 When player is 5, player%5 will be 0 and expression will set player to 1. ----- _3.3.
ORDER OF OPERATIONS_ 21 ###### 3.3 Order of operations Exponentiation gets done first, followed by multiplication and division (including // and %), and addition and subtraction come last.
The classic math class mnemonic, PEMDAS (Please Excuse My Dear Aunt Sally), might be helpful. This comes into play in calculating an average.
Say you have three variables x, y, and z, and you want to calculate the average of their values. To expression x+y+z/3 would not work.
Because division comes before addition, you would actually be calculating x + y + 3[z] [instead of][ x][+]3[y][+][z] .
This is easily fixed by using parentheses: (x+y+z)/3. In general, if you’re not sure about something, adding parentheses might help and usually doesn’t do any harm. ###### 3.4 Random numbers To make an interesting computer game, it’s good to introduce some randomness into it.
Python comes with a module, called random, that allows us to use random numbers in our programs. Before we get to random numbers, we should first explain what a module is.
The core part of the Python language consists of things like for loops, if statements, math operators, and some functions, like print and input.
Everything else is contained in modules, and if we want to use something from a module we have to first import it—that is, tell Python that we want to use it. At this point, there is only one function, called randint, that we will need from the random module.
To load this function, we use the following statement: **from random import randint** Using randint is simple: randint(a,b) will return a random integer between a and b including both a and b.
(Note that randint includes the right endpoint b unlike the range function).
Here is a short example: **from random import randint** x = randint(1,10) **print('A random number between 1 and 10: ', x)** ###### A random number between 1 and 10: 7 The random number will be different every time we run the program. ###### 3.5 Math functions **The math module** Python has a module called math th...
There are also the inverse trig functions, hyperbolic functions, and the constants pi and e. Here is a short example: ----- 22 _CHAPTER 3.
NUMBERS_ **from math import sin, pi** **print('Pi is roughly', pi)** **print('sin(0) =', sin(0))** ###### Pi is roughly 3.14159265359 sin(0) = 0.0 **Built-in math functions** There are two built in math functions, abs (absolute value) and round that are available without importing the math module.
Here are some examples: **print(abs(-4.3))** **print(round(3.336, 2))** **print(round(345.2, -1))** ###### 4.3 3.34 350.0 The round function takes two arguments: the first is the number to be rounded and the second is the number of decimal places to round to.
The second argument can be negative. ###### 3.6 Getting help from Python There is documentation built into Python.
To get help on the math module, for example, go to the Python shell and type the following two lines: >>> import math >>> dir(math) ###### ['__doc__', '__name__', '__package__', 'acos', 'acosh', 'asin', 'asinh', 'atan', 'atan2', 'atanh', 'ceil', 'copysign', 'cos', 'cosh', 'degrees', 'e', 'exp', 'fabs', 'factorial', '...
You can ignore all of the ones that start with underscores. To get help on a specific function, say the floor function, you can type help(math.floor).
Typing help(math) will give you help for everything in the math module. ###### 3.7 Using the Shell as a Calculator The Python shell can be used as a very handy and powerful calculator.
Here is an example session: ----- _3.8.
EXERCISES_ 23 ###### >>> 23**2 529 >>> s = 0 >>> for n in range(1,10001): s = s + 1/n**2 >>> s 1.6448340718480652 >>> from math import * >>> factorial(10) 3628800 The second example here sums the numbers 1 + 1/4 + 1/9 + ··· + 1/10000[2].
The result is stored in the variable s. To inspect the value of that variable, just type its name and press enter. Inspecting variables is useful for debugging your programs.
If a program is not working properly, you can type your variable names into the shell after the program has finished to see what their values are. The statement from math import* imports every function from the math module, which can make the shell a lot like a scientific calculator. **Note** Under the Shell menu, se...
Write a program that generates and prints 50 random integers, each between 3 and 6. 2.
Write a program that generates a random number, x, between 1 and 50, a random number y between 2 and 5, and computes x _[y]_ . 3.
Write a program that generates a random number between 1 and 10 and prints your name that many times. 4.
Write a program that generates a random decimal number between 1 and 10 with two decimal places of accuracy. Examples are 1.23, 3.45, 9.80, and 5.00. 5.
Write a program that generates 50 random numbers such that the first number is between 1 and 2, the second is between 1 and 3, the third is between 1 and 4, ..., and the last is between 1 and 51. 6.
Write a program that asks the user to enter two numbers, x and y, and computes _[|][x]x[−]+_ _[y]y[|]_ [.] 7. Write a program that asks the user to enter an angle between 180[◦] and 180[◦].
Using an _−_ expression with the modulo operator, convert the angle to its equivalent between 0[◦] and 360[◦]. ----- 24 _CHAPTER 3. NUMBERS_ 8.
Write a program that asks the user for a number of seconds and prints out how many minutes and seconds that is. For instance, 200 seconds is 3 minutes and 20 seconds.
[Hint: Use the // operator to get minutes and the % operator to get seconds.] 9. Write a program that asks the user for an hour between 1 and 12 and for how many hours in the future they want to go.
Print out what the hour will be that many hours into the future. An example is shown below. ###### Enter hour: 8 How many hours ahead? 5 New hour: 1 o'clock 10.
(a) One way to find out the last digit of a number is to mod the number by 10. Write a program that asks the user to enter a power.
Then find the last digit of 2 raised to that power. (b) One way to find out the last two digits of a number is to mod the number by 100. Write a program that asks the user to enter a power.
Then find the last two digits of 2 raised to that power. (c) Write a program that asks the user to enter a power and how many digits they want. Find the last that many digits of 2 raised to the power the user entered. 11.
Write a program that asks the user to enter a weight in kilograms. The program should convert it to pounds, printing the answer rounded to the nearest tenth of a pound. 12.
Write a program that asks the user for a number and prints out the factorial of that number. 13.
Write a program that asks the user for a number and then prints out the sine, cosine, and tangent of that number. 14.
Write a program that asks the user to enter an angle in degrees and prints out the sine of that angle. 15.
Write a program that prints out the sine and cosine of the angles ranging from 0 to 345[◦] in 15[◦] increments. Each result should be rounded to 4 decimal places.
Sample output is shown below: ###### 0 --- 0.0 1.0 15 --- 0.2588 0.9659 30 --- 0.5 0.866 ... 345 --- -0.2588 0.9659 16. Below is described how to find the date of Easter in any year.
Despite its intimidating appearance, this is not a hard problem. Note that _x_ is the floor function, which for positive numbers _⌊_ _⌋_ just drops the decimal part of the number.
For instance ⌊3.14⌋ = 3. The floor function is part of the math module. _C = century (1900’s →_ _C = 19)_ ----- _3.8.
EXERCISES_ 25 _Y = year (all four digits)_ _m = (15 + C −⌊_ _[C]4_ _[⌋−⌊]_ [8][C]25[+][13] _⌋) mod 30_ _n = (4 + C −⌊_ _[C]4_ _[⌋][)][ mod 7]_ _a = Y mod 4_ _b = Y mod 7_ _c = Y mod 19_ _d = (19c + m) mod 30_ _e = (2a + 4b + 6d + n) mod 7_ Easter is either March (22 + _d +_ _e) or April (d +_ _e_ _−_ 9).