//=========================================================================
#define PROGRAMMER "SOLUTIONS, NoFrills"
#define PROG_CODE  "soln"
#define COURSE     "ECE-1021"
#define YEAR       (2003)
#define TERM       "Fall"
#define SECTION    (0)
#define ASSIGNMENT "HW #5B"
#define REVISION   (0)
#define TITLE      "Magic Square"
#define SUBTITLE   "Problem 7.19"
#define EMAIL      "wbahn@eas.uccs.edu"
#define FILENAME   "05b0soln.txt"
//=========================================================================

// PROBLEM:
//
// Write a program to generate a 5x5 Magic Square using the following
// set of rules:
//
// 1) Place 1 in the middle of the top row.
// 2) Place successive numbers in the square up and to the left of the
//    present square subject to the following special cases:
//       Wrap around to the bottom or right side as necessary.
//       If the square is already occupied, drop to the square directly
//          below the present square instead.
//       If the present square is the top left corner, drop to the
//          square directly below it.

// SOLUTION:
//
// TOP LEVEL DECOMPOSITION:
// 1) TASK: Draw the empty boxes for the Magic Square
// 2) TASK: Generate the Magic Square
// 3) TASK: Display the Magic Sqaure
//
// The display for each element of the Magic Square will be as follows:
//
//   +----+  The vertical pitch is 2
//   | nn |  The horizontal pitch is 5
//   +----+  The top left corner is (-2,-1) relative to the number
//

// 1) TASK: Draw the empty boxes for the Magic Square
// 1.1) SET: row = 0
// 1.2) WHILE: (row < SIZE)  SIZE = 5 in this case
// 1.2.1) SET: col = 0
// 1.2.2) WHILE: (col < size)
// 1.2.2.1) TASK: Place cursor at position where number will be printed
// 1.2.2.1.1) SET: r = ROW_PITCH*row + FIRST_ROW
// 1.2.2.1.2) SET: c = COL_PITCH*col + FIRST_COL
// 1.2.2.2) TASK: Draw character box around the center
// 1.2.2.2.1) SET: cursor to (c-2, r-1)
// 1.2.2.2.2) PUT: "+----+"
// 1.2.2.2.3) SET: cursor to (c-2, r)
// 1.2.2.2.4) PUT: "|    |"
// 1.2.2.2.5) SET: cursor to (c-2, r+1)
// 1.2.2.2.6) PUT: "+----+"
// 1.2.2.3) TASK: Initial the box contents to zero
// 1.2.2.3.1) SET: array[row][col] = 0

// 2) TASK: Generate the Magic Square
// 2.1) TASK: Set cursor to middle box of top row
// 2.2) SET: n = 1
// 2.3) LOOP:
// 2.3.1) TASK: Set present box equal to n
// 2.3.1.1) SET: array[row][col] = n
// 2.3.2) TASK: Determine box to move to
// 2.3.2.1) IF: (row = 0) AND (col = 0) // present box is corner box
// 2.3.2.1.1) TASK: Impose special case for corner
// 2.3.2.1.1.1) SET: row = 1 (col is already 0)
// 2.3.2.2) ELSE:
// 2.3.2.2.1) TASK: Determine the "preferred" next box
// 2.3.2.2.1.1) SET: nextrow = row-1
// 2.3.2.2.1.2) SET: nextcol = col-1
// 2.3.2.2.2) TASK: Take care of any wrap-around issues
// 2.3.2.2.2.1) IF: nextrow < 0
// 2.3.2.2.2.1.1) SET: nextrow = SIZE - 1
// 2.3.2.2.2.1) IF: nextcol < 0
// 2.3.2.2.2.1.1) SET: nextcol = SIZE - 1
// 2.3.2.2.3) IF: array[nextrow][nextcol] != 0 // desired cell already filled
// 2.3.2.2.3.1) TASK: Move to cell directly below present cell
// 2.3.2.2.3.1.1) SET: row++ (col is already set)
// 2.3.2.2.3) ELSE: // preferred cell is the cell to use
// 2.3.2.2.3.1) SET: row = nextrow
// 2.3.2.2.3.2) SET: col = nextcol

// 2.3.3) TASK: Increment n
// 2.3.3.1) SET: n++
// 2.4) WHILE: n < SIZE*SIZE

// 3) TASK: Display the Magic Sqaure
// 3.1) SET: row = 0
// 3.2) WHILE: (row < SIZE)  SIZE = 5 in this case
// 3.2.1) SET: col = 0
// 3.2.2) WHILE: (col < size)
// 3.2.2.1) TASK: Place cursor at position where number will be printed
// 3.2.2.1.1) SET: r = ROW_PITCH*row + FIRST_ROW
// 3.2.2.1.2) SET: c = COL_PITCH*col + FIRST_COL
// 3.2.2.2) TASK: Print the number
// 3.2.2.2.1) PUT: array[row][col]