## Tuesday, May 17, 2016

### Shortest path in a Binary Maze - GeeksforGeeks

Shortest path in a Binary Maze - GeeksforGeeks
Given a MxN matrix where each element can either be 0 or 1. We need to find the shortest path between a given source cell to a destination cell. The path can only be created out of a cell if its value is 1.
Expected time complexity is O(MN).
The idea is inspired from Lee algorithm and uses BFS.
1. We start from the source cell and calls BFS procedure.
2. We maintain a queue to store the coordinates of the matrix and initialize it with the source cell.
3. We also maintain a Boolean array visited of same size as our input matrix and initialize all its elements to false.
1. We LOOP till queue is not empty
2. Dequeue front cell from the queue
3. Return if the destination coordinates have reached.
4. For each of its four adjacent cells, if the value is 1 and they are not visited yet, we enqueue it in the queue and also mark them as visited.
struct Point
{
int x;
int y;
};

// An Data Structure for queue used in BFS
struct queueNode
{
Point pt;  // The cordinates of a cell
int dist;  // cell's distance of from the source
};

// check whether given cell (row, col) is a valid
// cell or not.
bool isValid(int row, int col)
{
// return true if row number and column number
// is in range
return (row >= 0) && (row < ROW) &&
(col >= 0) && (col < COL);
}

// These arrays are used to get row and column
// numbers of 4 neighbours of a given cell
int rowNum[] = {-1, 0, 0, 1};
int colNum[] = {0, -1, 1, 0};

// function to find the shortest path between
// a given source cell to a destination cell.
int BFS(int mat[][COL], Point src, Point dest)
{
// check source and destination cell
// of the matrix have value 1
if (!mat[src.x][src.y] || !mat[dest.x][dest.y])
return INT_MAX;

bool visited[ROW][COL];
memset(visited, false, sizeof visited);

// Mark the source cell as visited
visited[src.x][src.y] = true;

// Create a queue for BFS
queue<queueNode> q;

// distance of source cell is 0
queueNode s = {src, 0};
q.push(s);  // Enqueue source cell

// Do a BFS starting from source cell
while (!q.empty())
{
queueNode curr = q.front();
Point pt = curr.pt;

// If we have reached the destination cell,
// we are done
if (pt.x == dest.x && pt.y == dest.y)
return curr.dist;

// Otherwise dequeue the front cell in the queue
// and enqueue its adjacent cells
q.pop();

for (int i = 0; i < 4; i++)
{
int row = pt.x + rowNum[i];
int col = pt.y + colNum[i];

// if adjacent cell is valid, has path and
// not visited yet, enqueue it.
if (isValid(row, col) && mat[row][col] &&
!visited[row][col])
{
// mark cell as visited and enqueue it
visited[row][col] = true;
queueNode Adjcell = { {row, col},
curr.dist + 1 };
}
}
}

//return -1 if destination cannot be reached
return INT_MAX;
}