C++

Write a program to construct an n x n magic square for any odd value of n. The problem will require a double indexed array and integer pair to keep track of the current position on the grid. You should also have a method for testing that the matrix created is correct by adding the columns and rows to ensure they all have the same sum.

A magic square is an n x n matrix in which each of the integers 1, 2, 3, ...n² appears exactly once and all column sums, row sums, and diagonal sums are equal.

The following is a procedure for constructing a n x n magic square for any odd integer n. Place 1 in the middle of the top row. Then, after integer k has been placed, move up one row and one column to the right to place the next integer k+1, unless one of the following occurs:

- If a move takes you above the top row in the jth column, move to the bottom of the jth column and place k+1 there.

- If a move takes you outside to the right of the square in the ith row, place k+1 in the ith row at the left side.

-If a move takes you to an already filled square or if you move out of the square at the upper right hand corner, place k+1 immediately below k.