2d array maze

[dormelia]

I'm just going to go ahead and admit it, this is a homework problem. Please, please, please don't just write the answer. I do want to learn how to do this but I'm stumped.

I'm supposed to be making a maze with these symbols:

. empty spot
0 an item (can be picked up or put down)
^ NORTH
v SOUTH
< WEST
> EAST
@ mover and item in the same spot

and if the mover has passed that spot, it's replaced with a " "

I think I've got making the 2d grid but I'm really stumped on the mover. How am I supposed to store it and how to make it move? I thought I could use a switch statement to associate north, west, south, and east to their respective symbols but I just can't seem to piece it all together.

Here's what I have so far but I can't seem to move forward or understand fully without understanding the mover. I think everything will fall in place afterwards.

this is the header

#include <iostream>                 
#include <cstdlib>

using namespace std;

#define WALL '#'
#define PATH '.'
#define FREE ' ' 
#define ITEM '0'
#define NORTH '^'
#define SOUTH 'v'
#define WEST '<'
#define EAST '>'

class Maze
{
public:
   Maze(); //makes a 1 col and 1 row grid with an EAST marker
   Maze(int r, int c); //makes a grid with a random r and c
   Maze (int r, int c, int mr, int mc, int d); //makes a grid with a random r, c, mr (mover's row), mc (mover's column), and d (direction)

   bool Move(int s); //moves s spaces
   void Display() const;
   void Grow(int gr, int gc); //grow grid by gr (rows) and gc (column)
   char GetMover(); 
private:
   char maze[40][40];
   char Dir;
   int rows, columns;

and this is the cpp file

#include "maze.h"

Maze::Maze()
{
   char maze[1][1] = { '>' );
}

Maze::Maze(int r, int c)
{
   if (r < 0 || c < 0)
	{
		maze[1][1];
	}
	if (r > 40 || c > 40);
	{
		maze[40][40];
	}
	if (r > 1 && r < 40 || c > 1 && c < 40)
	{
		maze[r][c];
		rows = r;
		cols = c;
	}
}

char Maze::GetMover()
{
   switch(Dir)
   {
     case NORTH: return '^';
     case WEST: return '<';
     case SOUTH: return 'v';
     case EAST: return '>';
     default: return 0;
   }
}

void Maze::Display() const
{
	cout << "The Maze:" << endl;
	for (int i = 0; i < rows; i++)
	{
		for (int j = 0; j < cols; j++)
		{
				if (i == 0 || i == rows - 1)
					cout << WALL << ' ';
				else if (j == 0 || j == cols - 1)
					cout << WALL << ' ';
				else
					cout << PATH << ' ';
		}
		cout<< endl;
	}
}

Again, if I need help on something else I'll ask but I really want to focus on the mover since I think it might clear a few blocks. Thank you!