Homework 3

Choose FIVE of the following eight problems to submit as homework. If you submit fewer than five problems, I will give you partial credit for the problems you do submit.

Each problem must be submitted as its own .cpp file. Grading for each problem is as follows:

• 1 point - problem submitted as a single .cpp files that compiles and runs
• 1 point - proper indentation and formatting of the code
• 1 point - includes the required function(s)
• 1 point - produces correct output

If two or more people submit copies of the same work, every person submitting the copied work will get a 0 for the entire homework.

You must write functions outside main for each of the following problems for full credit.

Functions

1. Write a complete C++ function that does the following:
• Prompts the user for a positive integer with 5 or more digits.
• Forces the user to enter a valid input.
• Includes a function called sumGaps that does the following:
• Computes the arithmetic difference ("gap") between adjacent digits of the input number.
• The "gap" is always the absolute value of this number.
• Returns the sum of the gaps between the adjacent digits.
• In the main function, prints the original value from the user, the gap sum, and the result when the gap sum is subtracted from the user's number .
Sample run of program:

Enter a number with five or more digits: 25361 Your original number is: 25361 The gap sum is 13 The original number minus the gap sum is 25348
2. Write a complete C++ program that does the following:
• Prompts the user for a number n between 4 and 16.
• If the user does not enter a valid input, give them two more tries (for a total of three) to enter a valid input.
• If the user does not enter a valid input, sets n equal to 10.
• Asks the user if they would like to print a triangle or a square and store the input in variable shape
• Your program must include a function called printTriangle and another function called printSquare. Each function takes n as input. Your program should then do the following;
• If the user entered "triangle", call printTriangle which prints a right triangle with n rows and n columns.
• If the user entered "square", call printSquare which prints a square with n rows and n columns.
• If the user enters something other than "triangle" or "square" your program can do whatever you want (for example, just end, print a message to a user, choose the shape to print, etc.)
Sample run of program:

Enter a number between 4 and 16: 3 Bad input! Try again: 2 Bad input! Try again: 1 Would you like a triangle or a square? triangle * ** *** **** ***** ****** ******* ******** ********* **********

Another sample run of program:

Enter a number between 4 and 16: 5 Would you like a triangle or a square? square ***** ***** ***** ***** *****
3. Write a complete C++ program that does the following:
• Prompts the user for a number with at least three digits.
• If the user enters an invalid number, say "Goodbye" and end the program.
• Includes a function called parityCheck that takes as input the user's number and does the following:
• If the digits of the user's number are all odd, prints "All odd."
• If the digits of the user's number are all even, prints "All even."
• If the digits of the user's number are not all odd or all even, prints "Mixed parity."
Sample run of program:

Enter a number with at least three digits: 1233 Mixed parity

Another sample run of program:

Enter a number with at least three digits: 22480 All even

Another sample run of program:

Enter a number with at least three digits: 333 All odd

Reference Parameters

4. Write a complete C++ program that does the following:
• Prompts the user for three integers and read the values into variables a, b and c.
• Asks the user if they would like the numbers sorted in ascending or descending order.
• Write a function called updateAscending that does the following:
• Has three integer reference parameters a, b and c.
• The function updates the variable assignments so that a stores the largest number, b stores the middle number, and c stores the smallest number.
• Write a function called updateDescending that does the following:
• Has three integer reference parameters a, b and c.
• The function updates the variable assignments so that a stores the smallest number, b stores the middle number, and c stores the largest number.
• In main, if the user chose ascending order, pass the variables to updateAscending. If the user chose descending order, pass the variables to updateDescending.
• After the function call, prints the values stored in a, b and c in main to confirm they are sorted correctly.
Sample run of program:

Enter three numbers: 1 3 2 Would you like the numbers sorted in ascending or descending order? ascending Your sorted variables now store: a = 1, b = 2, c = 3

Another sample run of program:

Enter three numbers: 7 2 4 Would you like the numbers sorted in ascending or descending order? descending Your sorted variables now store: a = 7, b = 4, c = 2
5. Write a complete C++ program that does the following:
• Prompts the user for three scores, each out of 100.
• Computes the curve by calculating the difference between 100 and the largest score.
• Write a function applyCurve that does the following:
• Takes as input three integer reference parameters (scores) and an integer curve.
• Update the scores in the function by adding the curve to them.
• In main, passes the three scores and curve to applyCurve.
• Prints the curve value and the curved scores.
Sample run of program:

Enter three scores: 87 89 82 The curve is 11. The scores after applying the curve are 98, 100, 93.

Recursion

6. Write a complete C++ function that does the following:
• Prompts the user for a number greater than or equal to 100.
• Forces the user to enter a valid input.
• Write a recursive function called getFirstThreeSum that does the following:
• Takes an integer parameter.
• Computes the sum of the leftmost three digits of the input.
• Returns this sum to the calling function.
• Write a function called printRange that does the following:
• Takes an integer parameter.
• If the integer is even, the function prints all even numbers from 0 through the number passed as input to the printRange function.
• If the integer is odd, the function prints all odd numbers from 1 through the number passed as input to the printRange function.
• The main function passes the user's input to getFirstThreeSum and prints the result to the monitor.
• The main function then takes the return value from getFirstThreeSum and passes it as the input to the printRange function.
Sample run of program:

Enter a number greater than or equal to 100: 2336 The sum of the first three digits is 8 0 2 4 6 8

Another sample run of program:

Enter a number greater than or equal to 100: 19374 The sum of the first three digits is 13 1 3 5 7 9 11 13
7. Generates the first five to twenty numbers in this sequence: a_0 = 0 (base case); a_{n} = 2*a_{n-1} + 3 (recursive definition).
• Hint: Look up recursive implementations of the Fibonacci sequence online.
• Write a recursive function called recursiveSequence that takes an integer parameter.
• This recursive function generates the ith number in the defined sequence.
• It needs two lines of code:
• The base case.
• The recursive call.
• Your main function should prompt the user for a number n between 5 and 20.
• If the user enters an invalid input, say "Goodbye" and end the program.
• If the input is valid, your program should print the first n numbers in the recursive sequence defined above.
Sample run of program:

Enter a number between 5 and 20: 7 0 3 9 21 45 93 189

Another sample run of program:

Enter a number between 5 and 20: 12 0 3 9 21 45 93 189 381 765 1533 3069 6141
8. Write a complete C++ function that does the following:
• Prompts the user for a positive integer greater than or equal to 3.
• Force the user to enter a valid input.
• Write a recursive function called changeThrees that does the following:
• Modifies the input value by changing any digit equal to 3 to a 2.
• Prints "removed a 3" every time a 3 is changed to a 2.
• Returns the modified number to the calling function.
• Your main function should print the number returned by the changeThrees function, then print "I don't like numbers with 3's in them."
Sample run of program:

Enter a number greater than or equal to 3: 23353 removed a 3 removed a 3 removed a 3 22252 I don't like numbers with 3's in them.

Another sample run of program:

Enter a number greater than or equal to 3: 5764 5764 I don't like numbers with 3's in them.