C++ . MAGIC SQUARE

It should be able to answer these questions.

It asks the user for a sequence of 9 numbers. The order of the numbers is important, as the rows of the grid use this order.

It checks whether the sequence of numbers is a magic square or not. Your program should display the message Yes! if its magic, or No! if its not. I

ts very important to point out that you are not being asked to construct a magic square; only to check if a square is magic or not.

3x3 Magic Square Detection // Design Document // // 1. Application's Purpose: // To determine if a given arrangement of 9 numbers // is a magic square or not. // **Note: this program does not try to create a magic square! // // 2. Magic Square Definition: // - 3x3 grid // - contains integers 1 through 9 // - every integer in 1-9 must appear exactly once // - all rows, columns, and diagonals of the grid add up to 15 // // E.g. Magic not Magic // 8 1 6 1 9 6 // 3 5 7 5 3 7 // 4 9 2 4 8 2 // // // 3. High level behaviour (main) // Ask for the sequence of numbers ("square") // Check that it is magic! // Program should display "Yes" if it's magic, "no" otherwise //////////////////////////////////////////////////////////

/////////////////////////////////////////////////////////// // Algorithms ///////////////////////////////////////////////////////////

/////////////////////////////////////////////////////////// // Algorithm 1: main() // Pre: nothing // Post: nothing // Return: 0 // // 1. Ask for the sequence of numbers ("square") // call procedure getSquare() // // 2. Check that it is magic // call procedure checkSquare() // // 3. Display "Yes!" if it's magic, "No!" otherwise

// ///////////////////////////////////////////////////////// // Algorithm 1.1: getSquare(square) // Pre: given a 3x3 array to contain integers // Post: obtains 9 numbers from the console, storing them in the // given array // Return: Nothing // // 1. Display a friendly prompt // 2. Obtain 9 integers from the console

// ///////////////////////////////////////////////////////// // Algorithm 1.2: checkSquare(square) // Pre: given a 3x3 array of integers // Post: nothing // Return: true if the square has all the properties of a magic // square; false otherwise // // 1. To check the square has all integers 1 ... 9 // use function checkRange() // 2. To check 3 rows of the square sum to 15 // use function checkRows() // 3. To check 3 columns of the square sum to 15 // use function checkRows() // 4. To check 2 diagonals of the square sum to 15 // use function checkColumns() // 5. If all the checks are positive (true), return true //

// ///////////////////////////////////////////////////////// // Algorithm 1.2.1: checkRange(square) // Pre: given a 3x3 array of integers // Post: nothing // Return: true if the square contains all the integers 1 .. 9 // false otherwise // // 1. Declare an array of 9 boolean values, called seen // Initialize every value in seen to false // 2. for every value in the square // 2.1 seen[value-1] = true // mark it as seen // 3. if any value in seen is still false, return false // otherwise, return true // // Known Bug: checkRange() fails badly if square contains integers out of range!

// ///////////////////////////////////////////////////////// // Algorithm 1.2.2: checkRows(square) // Pre: given a 3x3 array of integers // Post: nothing // Return: true if all the rows sum to 15 // false otherwise // // 1. call function checkSum() with values from first row // 2. call function checkSum() with values from second row // 3. call function checkSum() with values from third row // 4. if any call to checkSum() returned false, return false // otherwise, return true

// ///////////////////////////////////////////////////////// // Algorithm 1.2.3: checkColumns(square) // Pre: given a 3x3 array of integers // Post: nothing // Return: true if all the columns sum to 15 // false otherwise // // 1. call function checkSum() with values from first column // 2. call function checkSum() with values from second column // 3. call function checkSum() with values from third column // 4. if any call to checkSum() returned false, return false // otherwise, return true

// ///////////////////////////////////////////////////////// // Algorithm 1.2.4: checkDiagonals(square) // Pre: given a 3x3 array of integers // Post: nothing // Return: true if all the diagonals sum to 15 // false otherwise // // 1. call function checkSum() with values from upward diagonal // 2. call function checkSum() with values from downward diagonal // 4. if any call to checkSum() returned false, return false // otherwise, return true

// ///////////////////////////////////////////////////////// // Algorithm 2: checkSum(array, N, sum) // Pre: given an array of N integers, and a value in sum // Post: nothing // Return: true if the values in the array add up to sum // false otherwise //

////////////////////////////////////////////////////////// // End of Design Document //////////////////////////////////////////////////////////