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There is an exception if d = 29 and e = 6. In this case, Easter falls one week earlier on April 19. There is another exception if d = 28, _e = 6, and m = 2,5,10,13,16,21,24, or 39.
In this case, Easter falls one week earlier on April_ 18. Write a program that asks the user to enter a year and prints out the date of Easter in that year.
(See Tattersall, Elementary Number Theory in Nine Chapters, 2nd ed., page 167) 17.
A year is a leap year if it is divisible by 4, except that years divisible by 100 are not leap years unless they are also divisible by 400.
Ask the user to enter a year, and, using the // operator, determine how many leap years there have been between 1600 and that year. 18.
Write a program that given an amount of change less than $1.00 will print out exactly how many quarters, dimes, nickels, and pennies will be needed to efficiently make that change. [Hint: the // operator may be useful.] 19.
Write a program that draws “modular rectangles” like the ones below.
The user specifies the width and height of the rectangle, and the entries start at 0 and increase typewriter fashion from left to right and top to bottom, but are all done mod 10.
Below are examples of a 3 5 _×_ rectangle and a 4 8. _×_ ----- 26 _CHAPTER 3.
NUMBERS_ ----- ### Chapter 4 ## If statements Quite often in programs we only want to do something provided something else is true.
Python’s **if statement is what we need.** ###### 4.1 A Simple Example Let’s try a guess-a-number program.
The computer picks a random number, the player tries to guess, and the program tells them if they are correct.
To see if the player’s guess is correct, we need something new, called an if statement. **from random import randint** num = randint(1,10) guess = eval(input('Enter your guess: ')) **if guess==num:** **print('You got it!')** The syntax of the if statement is a lot like the for statement in that there is a colon at the end of the if condition and the following line or lines are indented.
The lines that are indented will be executed only if the condition is true. Once the indentation is done with, the if block is concluded. The guess-a-number game works, but it is pretty simple.
If the player guesses wrong, nothing happens.
We can add to the if statement as follows: **if guess==num:** **print('You got it!')** **else:** **print('Sorry.** The number is ', num) We have added an else statement, which is like an “otherwise.” 27 |’s try a guess-a-number program.
The computer picks a random number, the player tries to ess, and the program tells them if they are correct.
To see if the player’s guess is correct, we need mething new, called an if statement.|Col2| |---|---| ||| |from random import randint num = randint(1,10) guess = eval(input('Enter your guess: ')) if guess==num: print('You got it!')|| |e guess-a-number game works, but it is pretty simple.
If the player guesses wrong, nothing ppens. We can add to the if statement as follows:|Col2| |---|---| ||| |if guess==num: print('You got it!') else: print('Sorry.
The number is ', num)|| ----- 28 _CHAPTER 4. IF STATEMENTS_ ###### 4.2 Conditional operators The comparison operators are ==, >, <, >=, <=, and !=. That last one is for not equals.
Here are a few examples: Expression Description **if x>3:** if x is greater than 3 **if x>=3:** if x is greater than or equal to 3 **if x==3:** if x is 3 **if x!=3:** if x is not 3 There are three additional operators used to construct more complicated conditions: and, or, and **not.
Here are some examples:** **if grade>=80 and grade<90:** **print('Your grade is a B.')** **if score>1000 or time>20:** **print('Game over.')** **if not (score>1000 or time>20):** **print('Game continues.')** **Order of operations** In terms of order of operations, and is done before or, so if you have a complicated condition that contains both, you may need parentheses around the or condition. Think of and as being like multiplication and or as being like addition.
Here is an example: **if (score<1000 or time>20) and turns_remaining==0:** **print('Game over.')** ###### 4.3 Common Mistakes **Mistake 1** The operator for equality consists of two equals signs.
It is a really common error to forget one of the equals signs. Incorrect Correct **if x=1:** **if x==1:** **Mistake 2** A common mistake is to use and where or is needed or vice-versa.
Consider the following if statements: **if x>1 and x<100:** **if x>1 or x<100:** |t.
Here are some examples:|Col2| |---|---| ||| |if grade>=80 and grade<90: print('Your grade is a B.') if score>1000 or time>20: print('Game over.') if not (score>1000 or time>20): print('Game continues.')|| |nk of and as being like multiplication and or as being like addition.
Here is an example:|Col2| |---|---| ||| |if (score<1000 or time>20) and turns_remaining==0: print('Game over.')|| ----- _4.4. ELIF_ 29 The first statement is the correct one.
If x is any value between 1 and 100, then the statement will be true. The idea is that x has to be both greater than 1 and less than 100.
On the other hand, the second statement is not what we want because for it to be true, either x has to be greater than 1 or x has to be less than 100. But every number satisfies this.
The lesson here is if your program is not working correctly, check your and’s and or’s. **Mistake 3** Another very common mistake is to write something like below: **if grade>=80 and <90:** This will lead to a syntax error.
We have to be explicit.
The correct statement is **if grade>=80 and grade<90:** On the other hand, there is a nice shortcut that does work in Python (though not in many other programming languages): **if 80<=grade<90:** ###### 4.4 elif A simple use of an if statement is to assign letter grades.
Suppose that scores 90 and above are A’s, scores in the 80s are B’s, 70s are C’s, 60s are D’s, and anything below 60 is an F.
Here is one way to do this: grade = eval(input('Enter your score: ')) **if grade>=90:** **print('A')** **if grade>=80 and grade<90:** **print('B')** **if grade>=70 and grade<80:** **print('C')** **if grade>=60 and grade<70:** **print('D')** **if grade<60:** **print('F')** The code above is pretty straightforward and it works.
However, a more elegant way to do it is shown below. |imple use of an if statement is to assign letter grades.
Suppose that scores 90 and above are A’s, res in the 80s are B’s, 70s are C’s, 60s are D’s, and anything below 60 is an F.
Here is one way to this:|Col2| |---|---| ||| |grade = eval(input('Enter your score: ')) if grade>=90: print('A') if grade>=80 and grade<90: print('B') if grade>=70 and grade<80: print('C') if grade>=60 and grade<70: print('D') if grade<60: print('F')|| |e code above is pretty straightforward and it works.
However, a more elegant way to do it is wn below.|Col2| |---|---| ||| |grade = eval(input('Enter your score: ')) if grade>=90: print('A') elif grade>=80: print('B') elif grade>=70: print('C')|| ----- 30 _CHAPTER 4.
IF STATEMENTS_ **elif grade>=60:** **print('D')** **else:** **print('F')** With the separate if statements, each condition is checked regardless of whether it really needs to be.
That is, if the score is a 95, the first program will print an A but then continue on and check to see if the score is a B, C, etc., which is a bit of a waste.
Using elif, as soon as we find where the score matches, we stop checking conditions and skip all the way to the end of the whole block of statements.
An added benefit of this is that the conditions we use in the elif statements are simpler than in their if counterparts.
For instance, when using elif, the second part of the second if statement condition, grade<90, becomes unnecessary because the corresponding elif does not have to worry about a score of 90 or above, as such a score would have already been caught by the first if statement. You can get along just fine without elif, but it can often make your code simpler. ###### 4.5 Exercises 1.
Write a program that asks the user to enter a length in centimeters. If the user enters a negative length, the program should tell the user that the entry is invalid.
Otherwise, the program should convert the length to inches and print out the result. There are 2.54 centimeters in an inch. 2. Ask the user for a temperature.
Then ask them what units, Celsius or Fahrenheit, the temperature is in. Your program should convert the temperature to the other unit.
The conversions are F = 5[9] _[C][ +][ 32][ and][ C][ =][ 5]9_ [(][F][ −] [32][)][.] 3. Ask the user to enter a temperature in Celsius.
The program should print a message based on the temperature: - If the temperature is less than -273.15, print that the temperature is invalid because it is below absolute zero. - If it is exactly -273.15, print that the temperature is absolute 0. - If the temperature is between -273.15 and 0, print that the temperature is below freezing. - If it is 0, print that the temperature is at the freezing point. - If it is between 0 and 100, print that the temperature is in the normal range. - If it is 100, print that the temperature is at the boiling point. - If it is above 100, print that the temperature is above the boiling point. 4.
Write a program that asks the user how many credits they have taken. If they have taken 23 or less, print that the student is a freshman.
If they have taken between 24 and 53, print that they are a sophomore. The range for juniors is 54 to 83, and for seniors it is 84 and over. ----- _4.5. EXERCISES_ 31 5.
Generate a random number between 1 and 10. Ask the user to guess the number and print a message based on whether they get it right or not. 6.
A store charges $12 per item if you buy less than 10 items. If you buy between 10 and 99 items, the cost is $10 per item. If you buy 100 or more items, the cost is $7 per item.
Write a program that asks the user how many items they are buying and prints the total cost. 7.
Write a program that asks the user for two numbers and prints Close if the numbers are within .001 of each other and Not close otherwise. 8.
A year is a leap year if it is divisible by 4, except that years divisible by 100 are not leap years unless they are also divisible by 400.
Write a program that asks the user for a year and prints out whether it is a leap year or not. 9. Write a program that asks the user to enter a number and prints out all the divisors of that number.
[Hint: the % operator is used to tell if a number is divisible by something. See Section 3.2.] 10. Write a multiplication game program for kids.
The program should give the player ten randomly generated multiplication questions to do.
After each, the program should tell them whether they got it right or wrong and what the correct answer is. ###### Question 1: 3 x 4 = 12 Right! Question 2: 8 x 6 = 44 Wrong. The answer is 48. ...
... Question 10: 7 x 7 = 49 Right. 11. Write a program that asks the user for an hour between 1 and 12, asks them to enter am or pm, and asks them how many hours into the future they want to go.
Print out what the hour will be that many hours into the future, printing am or pm as appropriate. An example is shown below. ###### Enter hour: 8 am (1) or pm (2)? 1 How many hours ahead?
5 New hour: 1 pm 12. A jar of Halloween candy contains an unknown amount of candy and if you can guess exactly how much candy is in the bowl, then you win all the candy.
You ask the person in charge the following: If the candy is divided evenly among 5 people, how many pieces would be left over? The answer is 2 pieces.
You then ask about dividing the candy evenly among 6 people, and the amount left over is 3 pieces. Finally, you ask about dividing the candy evenly among 7 people, and the amount left over is 2 pieces.
By looking at the bowl, you can tell that there are less than 200 pieces. Write a program to determine how many pieces are in the bowl. ----- 32 _CHAPTER 4. IF STATEMENTS_ 13.
Write a program that lets the user play Rock-Paper-Scissors against the computer.
There should be five rounds, and after those five rounds, your program should print out who won and lost or that there is a tie. ----- ### Chapter 5 ## Miscellaneous Topics I This chapter consists of a several common techniques and some other useful information. ###### 5.1 Counting Very often we want our programs to count how many times something happens.
For instance, a video game may need to keep track of how many turns a player has used, or a math program may want to count how many numbers have a special property.
The key to counting is to use a variable to keep the count. **Example 1** This program gets 10 numbers from the user and counts how many of those numbers are greater than 10. count = 0 **for i in range(10):** num = eval(input('Enter a number: ')) **if num>10:** count=count+1 **print('There are', count, 'numbers greater than 10.')** Think of the count variable as if we are keeping a tally on a piece of paper.
Every time we get a number larger than 10, we add 1 to our tally. In the program, this is accomplished by the line count=count+1. The first line of the program, count=0, is important.
Without it, the Python interpreter would get to the count=count+1 line and spit out an error saying something about not knowing what count is.
This is because the first time the program gets to this line, it tries to do what it says: take the old value of count, add 1 to it, and store the result in count.
But the first time the program gets there, there is no old value of count to use, so the Python interpreter doesn’t know what to do.
To avoid the error, we need to define count, and that is what the first 33 |ample 1 This program gets 10 numbers from the user and counts how many of those numbers greater than 10.|Col2| |---|---| ||| |count = 0 for i in range(10): num = eval(input('Enter a number: ')) if num>10: count=count+1 print('There are', count, 'numbers greater than 10.')|| ----- 34 _CHAPTER 5.
MISCELLANEOUS TOPICS I_ line does. We set it to 0 to indicate that at the start of the program no numbers greater than 10 have been found. Counting is an extremely common thing.
The two things involved are: 1. count=0 — Start the count at 0. 2.
count=count+1 — Increase the count by 1. **Example 2** This modification of the previous example counts how many of the numbers the user enters are greater than 10 and also how many are equal to 0.
To count two things we use two count variables. count1 = 0 count2 = 0 **for i in range(10):** num = eval(input('Enter a number: ')) **if num>10:** count1=count1+1 **if num==0:** count2=count2+1 **print('There are', count1, 'numbers greater than 10.')** **print('There are', count2, 'zeroes.')** **Example 3** Next we have a slightly trickier example.
This program counts how many of the squares from 1[2] to 100[2] end in a 4. count = 0 **for i in range(1,101):** **if (i**2)%10==4:** count = count + 1 **print(count)** A few notes here: First, because of the aforementioned quirk of the range function, we need to use **range(1,101) to loop through the numbers 1 through 100.
The looping variable i takes on those** values, so the squares from 1[2] to 100[2] are represented by i**2.
Next, to check if a number ends in 4, a nice mathematical trick is to check if it leaves a remainder of 4 when divided by 10.
The modulo operator, %, is used to get the remainder. ###### 5.2 Summing Closely related to counting is summing, where we want to add up a bunch of numbers. |ample 2 This modification of the previous example counts how many of the numbers the user ers are greater than 10 and also how many are equal to 0.
To count two things we use two count iables.|Col2| |---|---| ||| |count1 = 0 count2 = 0 for i in range(10): num = eval(input('Enter a number: ')) if num>10: count1=count1+1 if num==0: count2=count2+1 print('There are', count1, 'numbers greater than 10.') print('There are', count2, 'zeroes.')|| |ample 3 Next we have a slightly trickier example.
This program counts how many of the ares from 12 to 1002 end in a 4.|Col2| |---|---| ||| |count = 0 for i in range(1,101): if (i**2)%10==4: count = count + 1 print(count)|| ----- _5.3.
SWAPPING_ 35 **Example 1** This program will add up the numbers from 1 to 100.
The way this works is that each time we encounter a new number, we add it to our running total, s. s = 0 **for i in range(1,101):** s = s + i **print('The sum is', s)** **Example 2** This program that will ask the user for 10 numbers and then computes their average. s = 0 **for i in range(10):** num = eval(input('Enter a number: ')) s = s + num **print('The average is', s/10)** **Example 3** A common use for summing is keeping score in a game.
Near the beginning of the game we would set the score variable equal to 0.
Then when we want to add to the score we would do something like below: |ample 1 This program will add up the numbers from 1 to 100.
The way this works is that each e we encounter a new number, we add it to our running total, s.|Col2| |---|---| ||| |s = 0 for i in range(1,101): s = s + i print('The sum is', s)|| |ample 2 This program that will ask the user for 10 numbers and then computes their average.|Col2| |---|---| ||| |s = 0 for i in range(10): num = eval(input('Enter a number: ')) s = s + num print('The average is', s/10)|| score = score + 10 ###### 5.3 Swapping Quite often we will want to swap the values of two variables, x and y.
It would be tempting to try the following: x = y y = x But this will not work. Suppose x is 3 and y is 5.
The first line will set x to 5, which is good, but then the second line will set y to 5 also because x is now 5.
The trick is to use a third variable to save the value of x: hold = x x = y y = hold In many programming languages, this is the usual way to swap variables.
Python, however, provides a nice shortcut: x,y = y,x We will learn later exactly why this works.
For now, feel free to use whichever method you prefer. The latter method, however, has the advantage of being shorter and easier to understand. ----- 36 _CHAPTER 5.
MISCELLANEOUS TOPICS I_ ###### 5.4 Flag variables A flag variable can be used to let one part of your program know when something happens in another part of the program.
Here is an example that determines if a number is prime. num = eval(input('Enter number: ')) flag = 0 **for i in range(2,num):** **if num%i==0:** flag = 1 **if flag==1:** **print('Not prime')** **else:** **print('Prime')** Recall that a number is prime if it has no divisors other than 1 and itself.
The way the program above works is flag starts off at 0. We then loop from 2 to num-1. If one of those values turns out to be a divisor, then flag gets set to 1.
Once the loop is finished, we check to see if the flag got set or not. If it did, we know there was a divisor, and num isn’t prime.
Otherwise, the number must be prime. ###### 5.5 Maxes and mins A common programming task is to find the largest or smallest value in a series of values.
Here is an example where we ask the user to enter ten positive numbers and then we print the largest one. largest = eval(input('Enter a positive number: ')) **for i in range(9):** num = eval(input('Enter a positive number: ')) **if num>largest:** largest=num **print('Largest number:', largest)** The key here is the variable largest that keeps track of the largest number found so far.