Beginner struggling with Lee Algorithm on a 2D grid

Question

I am trying to implement the Lee algorithm on a 2D grid. The flood loop is however stopping too early, claiming to have not found any more "empty" cells. I am completely stumped as to why.

#define WIDTH 6
#define HEIGHT 6
int gridArray[WIDTH][HEIGHT];

void InitialiseGrid() {
    srand(time(NULL)); // initialise the randomiser

    for (int y = 0; y < HEIGHT; y++) {
        for (int x = 0; x < WIDTH; x++) {

            if (rand() % 4 == 0)
                gridArray[x][y] = -2;
            else
                gridArray[x][y] = -1;
        }
    }
}

bool foundEmpty = true;
bool foundEnd = false;

int it = 0;

while (foundEmpty && !foundEnd) {
    DrawGrid();
    cout << endl << endl;
    for (int y = 0; y < HEIGHT; y++) {
        for (int x = 0; x < WIDTH; x++) {
            if (gridArray[x][y] == it) {
                // initially assume neighbouring cells are not empty
                foundEmpty = false;

                // check east cell
                if (x < WIDTH) {
                    int *e = &gridArray[x + 1][y];
                    if (*e == -1) {
                        *e = it + 1;
                        foundEmpty = true;
                    }
                    else if (*e == -3) {
                        foundEnd = true;
                    }
                }

                // check west cell
                if (x > 0) {
                    int *w = &gridArray[x - 1][y];
                    if (*w == -1) {
                        *w = it + 1;
                        foundEmpty = true;
                    }
                    else if (*w == -3) {
                        foundEnd = true;
                    }
                }

                // check south cell
                if (y < HEIGHT) {
                    int *s = &gridArray[x][y + 1];
                    if (*s == -1) {
                        *s = it + 1;
                        foundEmpty = true;
                    }
                    else if (*s == -3) {
                        foundEnd = true;
                    }
                }

                // check north cell
                if (y > 0) {
                    int *n = &gridArray[x][y - 1];
                    if (*n == -1) {
                        *n = it + 1;
                        foundEmpty = true;
                    }
                    else if (*n == -3) {
                        foundEnd = true;
                    }
                }
            }
        }
    }
    it++;
}


void DrawGrid() {
std::string message = "";

for (int y = 0; y < HEIGHT; y++) {
    cout << endl;
    for (int x = 0; x < WIDTH; x++) {
        if (gridArray[x][y] == 0)
            message = "start";
        else if (gridArray[x][y] == -3)
            message = "end";
        else if (gridArray[x][y] == -2)
            message = "X";
        else
            message = std::to_string(gridArray[x][y]);

        cout << "|" << "\t" << message << "\t" << "|";
    }
    cout << endl;
}
}

The end on the path is specified by assigning a cell to -3. Cells that are blocked are -2. Cells that are empty are -1. The starting cell is 0.

Answer 1

Not sure what your problem is, but your algorithm seems to be solid. I have cleaned it a little and it seems to be working fine:

#include <iostream>
#include <string>
#include <iomanip>

#define WIDTH 7
#define HEIGHT 7 

int gridArray[WIDTH][HEIGHT] = 
{
    { -1,-1,-1,0,-2,-1,-2 },
    { -2,-1,-1,-1,-1,-2,-2 },
    { -2,-1,-1,-1,-1,-2,-2 },
    { -2,-2,-1,-1,-1,-2,-1 },
    { -1,-2,-2,-2,-1,-1,-2 },
    { -1,-2,-1,-1,-1,-2,-2 },
    { -2,-2,-3,-1,-1,-2,-2 }
};

void DrawGrid() 
{
    for (int x = 0; x < WIDTH; x++)  
    {
        for (int y = 0; y < HEIGHT; y++)
        {
            std::string message;

            if (gridArray[x][y] == 0)
                message = "S";
            else if (gridArray[x][y] == -3)
                message = "E";
            else if (gridArray[x][y] == -2)
                message = "#";
            else if (gridArray[x][y] == -1)
                message = ".";
            else
                message = std::to_string(gridArray[x][y]);

            std::cout << std::setw(3) << message << "  ";
        }
        std::cout << std::endl << std::endl;
    }
    std::cout << std::endl << std::endl;
}

void SolveMaze()
{
    bool foundEnd = false;
    int it = 0;

    while (!foundEnd) 
    {
        bool foundEmpty = false;
        for (int x = 0; x < WIDTH && !foundEnd; ++x)
        {
            for (int y = 0; y < HEIGHT; ++y)
            {
                if (gridArray[x][y] == it) 
                {
                    // check east cell
                    if (x < WIDTH - 1)
                    {
                        int &east = gridArray[x + 1][y];
                        if (east == -3)
                        {
                            foundEnd = true;
                            break;
                        }
                        else if (east == -1)
                        {
                            east = it + 1;
                            foundEmpty = true;
                        }
                    }

                    // check west cell
                    if (x > 0)
                    {
                        int &west = gridArray[x - 1][y];
                        if (west == -3)
                        {
                            foundEnd = true;
                            break;
                        }
                        else if (west == -1)
                        {
                            west = it + 1;
                            foundEmpty = true;
                        }
                    }

                    // check south cell
                    if (y < HEIGHT - 1)
                    {
                        int &south = gridArray[x][y + 1];
                        if (south == -3)
                        {
                            foundEnd = true;
                            break;
                        }
                        else if (south == -1)
                        {
                            south = it + 1;
                            foundEmpty = true;
                        }
                    }

                    // check north cell
                    if (y > 0)
                    {
                        int &north = gridArray[x][y - 1];
                        if (north == -3)
                        {
                            foundEnd = true;
                            break;
                        }
                        else if (north == -1)
                        {
                            north = it + 1;
                            foundEmpty = true;
                        }
                    }   
                }
            }
        }

        if (!foundEnd && !foundEmpty)
        {
            std::cout << "This maze has no solution!" << std::endl << std::endl;
            break;
        }

        it++;
    }
}

int main()
{
    DrawGrid();
    SolveMaze();
    DrawGrid();
    system("pause");
    return 0;
}