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CS 220 Python Programming Exercises

Section 1.7 HW4

Exercises Exercises

1. Between 0 and 1.

Write a function called between_zero_and_onethat takes a parameter num; num will be a number at run time.  The function should return True if num falls strictly between 0 and 1; otherwise, it should return False.
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NOTE: This function does NOT read anything from standard input.
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NOTE: Your function should not print anything to standard output. Use a return statement, not a print statement, at the end of your function.
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Hint: Do not return the strings "True", "False". Boolean values are not quoted.
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For example:
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Test Result 
between_zero_and_one(0.5)
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True
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between_zero_and_one(1.0)
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False
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between_zero_and_one(-2.2)
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False
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2. Divides.

Define a function dividesthat takes integer parameters n and d.
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-If n is a multiple of d, that is, if "d divides n" evenly, the function returns True and prints a message. For example, if n is 12 and d is 2, the message will say, "12 is divisible by 2"
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- Otherwise, the function returns False and prints  a negative message, for example, "12 is not divisible by 11"
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- Your function might  be around 7 lines long.
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Hint 1:  Use the remainder operator and an if-else conditional.
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Hint 2: Do not return the strings "True", "False". Return a Boolean constant, either True or False (no quotes)
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For example:
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Test Result 
result = divides(12, 2)
print("Return value is", result)
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12 is divisible by 2
Return value is True
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result = divides(12, 5)
print("Return value is", result)
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12 is not divisible by 5
Return value is False
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3. Num Is Even.

The function isEventakes one parameter, n (an integer). isEven returns a boolean result.
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- isEven returns Trueif n is even,
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- otherwise isEven returns False.
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Define the isEven function.
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Remember: Do not return the strings "True", "False". Return a Boolean constant, either True or False (no quotes)
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For example:
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Test Result 
print(isEven(39))
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False
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print(isEven(26))
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True
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print(isEven(11))
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False
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4. isPositive.

The function isPositivetakes one parameter, n (a number).
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- If n is positive, the function prints a message stating that n is positive and then returns True
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-  If n is zero, the function prints a message stating that n is zero and then returns False
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- If n is negative, the function prints a message stating that n is negative and then returns False
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Write a definition for isPositive.
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Remember: Do not return "True", "False". Return the Boolean constants: True, False (no quotation marks).
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For example:
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Test Result 
print(isPositive(35))
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35 is positive
True
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print(isPositive(0))
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0 is zero
False
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print(isPositive(-0.1))
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-0.1 is negative
False
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5. Divisible by 3 or 5.

This problem requires a short program, not a function definition.
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Write the code needed to get an integer from standard input.  Then, write a simple decision statement that will output a message reporting whether the number is evenly divisible by 3, or by 5, or both, or neither.  You might need about 10 lines of code.
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See the examples for the expected format of the output.
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For example:
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Input Result 
-7
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-7 is divisible by neither 3 nor 5
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60
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60 is divisible by both 3 and 5
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54
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54 is divisible by 3
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125
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125 is divisible by 5
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6. Is In Unit Circle.

Write a function called is_in_unit_circle that takes two parameters, x and y (floats), the coordinates of a point in the x-y plane.
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- The function returns Trueif (x, y) is less than one unit away from (0,0) [i.e., if the point (x, y) is inside the unit circle];
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- Otherwise, the function returns False
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Hint:Use the distance formula to calculate the distance (or the square of the distance) from (x, y) to (0, 0). Then compare that distance with 1.
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Distance between two points = \(\sqrt{(x_2-x_1)^2 + (y_2-y_2)^2}\)
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For example:
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Test Result 
is_in_unit_circle(2, .9)
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False
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is_in_unit_circle(.70, -.61)
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True
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is_in_unit_circle(.055, .81)
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True
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7. Sum over a list.

Define the function list_sum(L); it takes one parameter L, a list of numbers, and returns the sum of all the items in L.
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Hint: Use the "accumulate a sum" pattern, and use L as the sequence expression in your for loop.
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For example:
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Test Result 
L = [9, 6, 8, 5, 7]
list_sum(L)
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35
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L = [15, 7, -1, 11, 19, 3, -5]
list_sum(L)
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49
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L = []
list_sum(L)
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0
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8. List Product.

Define a function list_product(L) which takes a parameter L, a list of numbers, and returns the product of all the items in L.
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Hint: Use the accumulate-a-product pattern as discussed in class. Remember, you should not initialize your accumulator variable to 0 when it represents a product.
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For example:
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Test Result 
L = [3, 2, 7, -1, 4]
list_product(L)
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-168
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L = [55]
list_product(L)
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55
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9. Count Negatives in a list.

Define a function count_negatives(L), which takes a list of numbers, L, as its parameter. The function returns an integer count telling how many of the items in L are negative (less than zero).
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Hint: Use the accumulator pattern.
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- Initialize the accumulator to 0
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- Use a for loop to iterate over the items in L
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- Use an if statement to update the accumlator every time the current item is negative
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- Return the accumulator
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For example:
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Test Result 
L = [0, -10, 2, -8, -4, -6, -2, 6, 4]
count_negatives(L)
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5
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L = [0, 6, 4]
count_negatives(L)
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0
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L = [-10, -4, -6, -2, 6, 4]
count_negatives(L)
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4
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10. Count SPAM in list.

Define the function count_SPAM(L), which takes a list of strings, L, as its parameter. The function returns a count of how many times the word "SPAM" occurs as an item in L.
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See the examples for the expected format of the output.
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For example:
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Test Result 
L  = ["SPAM", "banana", "apple", "SPAM", "tuna"]
count_SPAM(L)
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2
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L = ["a", "stitch", "in", "time"]
count_SPAM(L)
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0
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L = ["SPAM", "SPAM", "SPAM", "egg", "and", "SPAM"]
count_SPAM(L)
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4
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11. Count Divisors.

Write a short program, approximately 12 lines of code, to read a positive integer n from the keyboard, count the number of  positive integer divisors of n, and print a message reporting that count. In addition, if n is prime, also print, "That’s a prime number!".  HINT: A positive integer n is prime provided n has exactly two positive integer divisors, 1 and n.
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For example, the divisors of 12 are 1, 2, 3, 4, 6, 12. There are 6 of them. If n = 12 is read from the keyboard, the program will print, "12 has 6 divisors."
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Warning: Notice that when n = 1, there is only one divisor. So the message needs to say, "1 has 1 divisor" (not "1 has 1 divisors").
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See the examples for the expected format of the output.
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For example:
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Input Result 
1
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1 has 1 divisor
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3
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3 has 2 divisors
That number is prime!
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6
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6 has 4 divisors
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12. Accumulate Nth Fibonacci.

Write a function Fto compute the Nth Fibonnaci number, where N is an integer parameter.
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By definition, F(1) and F(2) are both 1, while later terms are found  by adding the previous two terms to make the next. Algebraically, we define F(N) as follows:
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  • F(1) = F(2) = 1
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  • When N > 2, F(N) = F(N - 1) + F(N - 2)
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So F(3) = F(2) + F(1) = 1  + 1  = 2, F(4) = F(3) +  F(2) = 2 + 1 = 3, F(5) =  5, F(6) =  8, etc.
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When N is positive, F should return the Nth Fibonacci number, F(N); when N is not positive, F should return the Python object None.
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Big Hint: Use two accumulator variables, previousand current, since we will always add the last two terms to make the next term.
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  • Initialize previousto have the value of F(1), and initialize currentto have the value of F(2).
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  • Think about how many additional terms the for loop needs to calculate to determine F(N) when N > 2. That number is the argument for the range function call in the first line of the loop.
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  • In the body of the loop, update both accumulators: let nextbe the sum of previousand current, update previousto equal current, and update currentto equal next.
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  • When the for loop ends, return current.
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For example:
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Test Result 
F(10)
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55
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F(4)
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3
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F(3)
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2
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