Find Shortest distance from a guard in a Bank - GeeksforGeeks

Find Shortest distance from a guard in a Bank - GeeksforGeeks
Given a matrix that is filled with 'O', 'G', and 'W' where 'O' represents open space, 'G' represents guards and 'W' represents walls in a Bank. Replace all of the O's in the matrix with their shortest distance from a guard, without being able to go through any walls. Also, replace the guards with 0 and walls with -1 in output matrix.
Expected Time complexity is O(MN) for a M x N matrix.

O ==> Open Space
G ==> Guard
W ==> Wall

Input: 
  O  O  O  O  G
  O  W  W  O  O
  O  O  O  W  O
  G  W  W  W  O
  O  O  O  O  G

Output:  
  3  3  2  1  0
  2 -1 -1  2  1
  1  2  3 -1  2
  0 -1 -1 -1  1
  1  2  2  1  0

The idea is to do BFS. We first enqueue all cells containing the guards and loop till queue is not empty. For each iteration of the loop, we dequeue the front cell from the queue and for each of its four adjacent cells, if cell is an open area and its distance from guard is not calculated yet, we update its distance and enqueue it. Finally after BFS procedure is over, we print the distance matrix.

// An Data Structure for queue used in BFS

struct queueNode

{

    // i, j and distance stores x and y-coordinates

    // of a matrix cell and its distance from guard

    // respectively

    int i, j, distance;

};

 

// These arrays are used to get row and column

// numbers of 4 neighbors of a given cell

int row[] = { -1, 0, 1, 0};

int col[] = { 0, 1, 0, -1 };

 

// return true if row number and column number

// is in range

bool isValid(int i, int j)

{

    if ((i < 0 || i > M - 1) || (j < 0 || j > N - 1))

        return false;

 

    return true;

}

 

// return true if current cell is an open area and its

// distance from guard is not calculated yet

bool isSafe(int i, int j, char matrix[][N], int output[][N])

{

    if (matrix[i][j] != 'O' || output[i][j] != -1)

        return false;

 

    return true;

}

 

// Function to replace all of the O's in the matrix

// with their shortest distance from a guard

void findDistance(char matrix[][N])

{

    int output[M][N];

    queue<queueNode> q;

 

    // finding Guards location and adding into queue

    for (int i = 0; i < M; i++)

    {

        for (int j = 0; j < N; j++)

        {

            // initialize each cell as -1

            output[i][j] = -1;

            if (matrix[i][j] == 'G')

            {

                queueNode pos = {i, j, 0};

                q.push(pos);

                // guard has 0 distance

                output[i][j] = 0;

            }

        }

    }

 

    // do till queue is empty

    while (!q.empty())

    {

        // get the front cell in the queue and update

        // its adjacent cells

        queueNode curr = q.front();

        int x = curr.i, y = curr.j, dist = curr.distance;

 

        // do for each adjacent cell

        for (int i = 0; i < 4; i++)

        {

            // if adjacent cell is valid, has path and

            // not visited yet, en-queue it.

            if (isSafe(x + row[i], y + col[i], matrix, output)

                && isValid(x + row[i], y + col[i]))

            {

                output[x + row[i]][y + col[i]] = dist + 1;

 

                queueNode pos = {x + row[i], y + col[i], dist + 1};

                q.push(pos);

            }

        }

 

        // dequeue the front cell as its distance is found

        q.pop();

    }

 

    // print output matrix

    for (int i = 0; i < M; i++)

    {

        for (int j = 0; j < N; j++)

            cout << std::setw(3) << output[i][j];

        cout << endl;

    }

}

Read full article from Find Shortest distance from a guard in a Bank - GeeksforGeeks