Your instructor will assign you one of the problems below. To solve your problem, write a program that reads the necessary information to compute and output the indicated values, as efficiently as possible. Following the pattern in the lab exercise, first, design using OCD; then code your design in C++ using stepwise translation; finally, test your program thoroughly.
Project #13.1: A magic square is an n-by-n table in which the integers 1, 2, 3, ..., n^2 appear exactly once, and all column sums, row sums and diagonal sums are equal. For example, here is a 5-by-5 magic square in which all the rows, columns and diagonals add up to 65:-------------------------- | 17 | 24 | 1 | 8 | 15 | -------------------------- | 23 | 5 | 7 | 14 | 16 | -------------------------- | 4 | 6 | 13 | 20 | 22 | -------------------------- | 10 | 12 | 19 | 21 | 3 | -------------------------- | 11 | 18 | 25 | 2 | 9 | --------------------------Here is a partial algorithm for constructing an n-by-n magic square, for any odd integer n:
- Set
i
to 1.- Set
r
to be the first row; setc
to be the middle column.- Repeat:
- Place
i
in rowr
and columnc
.- Move
r
up one row, and movec
one column to the right.- If the move takes you past the top,
Resetr
to be the last row.- If the move takes you to off the right side of the grid,
Setc
to be the first column.- If the move takes you to an already filled square
Mover
down two rows andc
to the left one column.The algorithm is missing two crucial steps: (1) when should the loop terminate? and (2) what happens when the algorithm tries to work its way up the main diagonal a second time? Both of these steps are fixed with one statement each, although the second problem will require a bit more thought---consider the example above when
i
= 16 is placed into the square.Build a
MagicSquare
class as avector
ofvector
s. Given an odd integer n, its constructor should use the preceding algorithm to initialize the two-dimensional structure. Provide an output operator to display the magic square using the format shown above. Then write a driver program that inputs the value n and, using yourMagicSquare
class, constructs and outputs the corresponding magic square.
Project #13.2: A certain automobile dealership sells ten different models of automobiles, and employs eight salespeople. Each month, the sales are recorded in a table in entry [r][c] corresponds to the number of sales of model r by salesperson c. For example, a typical sales table might appear as follows:0 0 2 0 5 6 3 0 5 1 9 0 0 2 3 2 0 0 0 1 0 0 0 0 1 1 1 0 2 2 2 1 5 3 2 0 0 2 5 5 2 2 1 0 1 1 0 0 3 2 5 0 1 2 0 4 3 0 7 1 3 5 2 4 0 2 6 1 0 5 2 1 4 0 2 0 3 2 1 0Write a program that, given such a sales table, produces a monthly sales report, displaying the monthly sales and the totals for each model and salesperson in easy-to-read format:Sales Person Model : 1 2 3 4 5 6 7 8 : Totals ------------------------------------------------------ 1 : 0 0 2 0 5 6 3 0 : 16 2 : 5 1 9 0 0 2 3 2 : 22 3 : 0 0 0 1 0 0 0 0 : 1 4 : 1 1 1 0 2 2 2 1 : 10 5 : 5 3 2 0 0 2 5 5 : 22 6 : 2 2 1 0 1 1 0 0 : 7 7 : 3 2 5 0 1 2 0 4 : 17 8 : 3 0 7 1 3 5 2 4 : 25 9 : 0 2 6 1 0 5 2 1 : 17 10 : 4 0 2 0 3 2 1 0 : 12 ------------------------------------------------------ Totals : 23 11 35 3 15 27 18 17Use object-centered design to design and implement aSalesTable
class and use it to solve this problem. In addition to an output operation that displays aSalesTable
in a format like that shown above, its constructor should allow aSalesTable
object to be initialized with data from a file. It should also provide operations to determine the total sales for a given salesperson, as well as the total sales for a particular model of automobile.
Project #13.3: In Chapter 13 of C++: An Introduction to Computing, aMatrix
data type is presented. Get this data type fully operational, including functions (or methods if you define it as a class) to perform the addition, subtraction, multiplication, transpose, test equality, input, and output operations forMatrix
objects. To test your class, create a driven driver program that implements a menu-drivenMatrix
calculator.
Project #13.4: Create a TicTacToeGame
class that stores the 3-by-3 board,
and methods to initialize the board, display the board, and take a
turn. Add a driver program that uses your class to allow a person
to play Tic-Tac-Toe against the computer.
Turn the following things: