Your instructor may 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.

Project #11.1: Amagic squareis an n × 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:Here is a-------------------------- | 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 | --------------------------partialalgorithm for constructing an n × n magic square, for any odd integer n:

- Set
to 1.`i`

- Set
to be the first row; set`r`

to be the middle column.`c`

- Repeat:

- Place
in row`i`

and column`r`

.`c`

- Move
`r`

up one row, and moveone column to the right.`c`

- If the move takes you past the top,

Resetto be the last row.`r`

- If the move takes you to off the right side of the grid,

Setto be the first column.`c`

- If the move takes you to an already filled square

Move`r`

downtwo rows and`c`

to theleftone 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

= 16 is placed into the square.`i`

Write a program to construct magic squares using a two-dimensional array or a

`vector`

of`vector`

s whose dimensions are specified by an odd integer entered by the user.

Project #11.2(from Chap. 13 ofProgramming in C++ for Engineering and Science): 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:Write 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: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 0Sales 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 17

Project #11.3: Section 13.4 ofProgramming in C++ for Engineering and Sciencedescribes matrix operations — addition, subtraction, multiplication by a scalar, and multiplying two matrices. Write a program to perform these operations on matrices together with input and output operations, finding a matrix's transpose ("rotate" it 90^{o}so rows become columns), and checking if two matrices are equal. Design the program so that it implements a menu-driven matrix calculator.

Project #11.4: Develop a program to play Tic-Tac-Toe against a user.

Report errors to Larry Nyhoff (nyhl@cs.calvin.edu)