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##### week 6 problem 2

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solution

**Question**

NOTE: Remember that you are NOT allowed to use the break, return, or exit statements to exit from a loop. All loops must exit ONLY via their test condition.;Program #2;Mathematically, given a number, we can define a sequence,,... where is the sum of the squares of the digits of. n is happy if and only if there exists i such that.;Here is an example;First, take each digit of any positive integer, square them and add them together. We will use the number nineteen as an example;19 ? 1 2 + 9 2 = 82;Then take each digit of this number, square them and add them together;82 ? 8 2 + 2 2 = 68;And repeat until the result is 1;68 ? 6 2 + 8 2 = 100;100 ? 1 2 + 0 2 + 0 2 = 1;So when the sum of the squares of the digits in the last member in the sequence starting with n eventually reduces to 1, n is happy.;Additionally;If a number is happy, then all members of its sequence are happy. If a number is unhappy, all members of its sequence are unhappy.;The above example sequence: 19, 82, 68, 100 is happy, and so all of the terms within the sequence are also happy.;Write a program that determines which numbers produce a happy sequence, within a series of test numbers.;The user will provide a first number to test and a last number to test. The program will test the numbers starting with the first number, incrementing by one, and repeating until the last number.;Program Implementation Requirements;1. Tell the user what the program does before prompting for input.;2. main will call a user-defined function to read the first and last numbers for the range to test from the user.;? The user-defined function will;o Separately read and validate each number. Both the first and last numbers must be at least 1 and can be up to 9999 (remember to define constants for these values!);? If the first number is not in the correct range, issue an error message and then re-prompt until the number entered is valid.;o The last number cannot be smaller than the first number.;? If the last number is not in the correct range or is smaller than the first number, issue an error message and then re-prompt until the number entered is valid.;o Pass back both values to main using reference parameters.;3. main will start with the first number as the test number, and loop until all numbers including the last number have been tested. Each time the loop runs, main will;o Call a user-defined function to test if the number is happy.;o Display the results (whether the sequence is happy or unhappy), and pause so the results can be read by the user.;o Increment the test number.;? The user-defined function to test whether a number is happy must implement nested loops, as follows;o A test number will be passed into the function.;o The function?s outer loop will test the number, as follows;o Use an inner loop to compute the sum of the squares of the digits in the current term. NOTE: You must use a loop, so this program will still work for larger numbers, if the maximum value of the last number constant is modified.;o Count and display each term.;o Each term displayed should be formatted to a width of 8, and 10 terms should be displayed per line.;o Repeat with the sum of the squares of the digits in the current term becoming the next term to test, until it is determined;? The test number is happy (when the sum of the square of the digits is 1);? The test number is unhappy (when 50 terms have been computed, without reaching 1).;o After the outer loop exits, the function shall display the number of terms in the sequence.;o A boolean value will be returned to main, indicating whether the displayed sequence is happy or not.;Program to test for Happy numbers;Enter the first number to test: 79;Enter the last number to test: 1;Invalid -- must be between 79 and 9999. Try again.;Enter the last number to test: 82;Test sequence for 79 is;79 130 10 1;4 sequence terms computed;The above sequence of numbers is happy;Press any key to continue...;Test sequence for 80 is;80 64 52 29 85 89 145 42 20 4;16 37 58 89 145 42 20 4 16 37;58 89 145 42 20 4 16 37 58 89;145 42 20 4 16 37 58 89 145 42;20 4 16 37 58 89 145 42 20 4;50 sequence terms computed;The above sequence of numbers is unhappy;Press any key to continue...;Test sequence for 81 is;81 65 61 37 58 89 145 42 20 4;16 37 58 89 145 42 20 4 16 37;58 89 145 42 20 4 16 37 58 89;145 42 20 4 16 37 58 89 145 42;20 4 16 37 58 89 145 42 20 4;50 sequence terms computed;The above sequence of numbers is unhappy;Press any key to continue...;Test sequence for 82 is;82 68 100 1;4 sequence terms computed;The above sequence of numbers is happy;Press any key to continue...;Testing of numbers 79 to 82 complete.;NOTES;o If the first and last numbers are the same, and only the first number will be tested.;o For testing purposes, it may help to know that the happy numbers up to 100 are;1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100;Program and Function Documentation (both programs);1) Include top of program comments as specified in course Content section 1.8.;2) Comment any constants/variables whose names are not completely descriptive.;3) Include prototypes for all of your user-defined functions. The prototypes should be placed above main, and the function definitions should be placed below main.;4) Provide a comment above each user-defined function definition that includes;o Dividing lines;o A description of what the function does;o The name and a description of each input parameter, used to pass values into the function;o The name and a description of each output parameter, used to pass values back from the function;o The name (if there is one), and a description of what is returned from the function via the return statement (if anything).;Examples;// ----------------------------------------------------------;// Task: Reads a positive and negative number from the user;// and error checks them;// Input parameters: prompt ? prompt to display;// Output parameters: posValue, negValue ? valid numbers read;// ----------------------------------------------------------;voidgetData (string prompt, int&posValue, int&negValue)

Paper#66609 | Written in 18-Jul-2015

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