The Lee algorithm is one possible solution for maze routing problems. It always gives an optimal solution, if one exists, but is slow and requires large memory for dense layout.

### Understanding how it works

The algorithm is a `breadth-first`

based algorithm that uses `queues`

to store the steps. It usually uses the following steps:

- Choose a starting point and add it to the queue.
- Add the valid neighboring cells to the queue.
- Remove the position you are on from the queue and continue to the next element.
- Repeat steps 2 and 3 until the queue is empty.

### Implementation

C++ has the queue already implemented in the `<queue>`

library, but if you are using something else you are welcome to implement your own version of queue.

C++ code:

```
int dl[] = {-1, 0, 1, 0}; // these arrays will help you travel in the 4 directions more easily
int dc[] = {0, 1, 0, -1};
queue<int> X, Y; // the queues used to get the positions in the matrix
X.push(start_x); // initialize the queues with the start position
Y.push(start_y);
void lee()
{
int x, y, xx, yy;
while(!X.empty()) // while there are still positions in the queue
{
x = X.front(); // set the current position
y = Y.front();
for(int i = 0; i < 4; i++)
{
xx = x + dl[i]; // travel in an adiacent cell from the current position
yy = y + dc[i];
if('position is valid') //here you should insert whatever conditions should apply for your position (xx, yy)
{
X.push(xx); // add the position to the queue
Y.push(yy);
mat[xx][yy] = -1; // you usually mark that you have been to this position in the matrix
}
}
X.pop(); // eliminate the first position, as you have no more use for it
Y.pop();
}
}
```