Find Shortest distance from a guard in a Bank

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.
Expected Auxiliary Space is O(MN) for a M x N matrix.

Examples:

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. 

Below are implementation of above idea –  

C++

// C++ program to replace all of the O's in the matrix
// with their shortest distance from a guard
#include <bits/stdc++.h>
using namespace std;

// store dimensions of the matrix
#define M 5
#define N 5

// 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;
    }
}

// Driver code
int main()
{
    char matrix[][N] =
    {
        {'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'}
    };

    findDistance(matrix);

    return 0;
}

Java

// Java program to replace all of the O's
// in the matrix with their shortest
// distance from a guard
package Graphs;

import java.util.LinkedList;
import java.util.Queue;

public class MinDistanceFromaGuardInBank{

// Store dimensions of the matrix
int M = 5;
int N = 5;

class Node
{
    int i, j, dist;
    Node(int i, int j, int dist)
    {
        this.i = i;
        this.j = j;
        this.dist = dist;
    }
}

// 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
boolean 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
boolean isSafe(int i, int j, char matrix[][],
                              int output[][])
{
    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[][])
{
    int output[][] = new int[M][N];
    Queue<Node> q = new LinkedList<Node>();

    // 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')
            {
                q.add(new Node(i, j, 0));

                // Guard has 0 distance
                output[i][j] = 0;
            }
        }
    }

    // Do till queue is empty
    while (!q.isEmpty())
    {

        // Get the front cell in the queue
        // and update its adjacent cells
        Node curr = q.peek();
        int x = curr.i;
        int y = curr.j;
        int dist = curr.dist;

        // 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 (isValid(x + row[i], y + col[i]))
            {
                if (isSafe(x + row[i], y + col[i],
                           matrix, output))
                {
                    output[x + row[i]][y + col[i]] = dist + 1;
                    q.add(new Node(x + row[i],
                                   y + col[i],
                                   dist + 1));
                }
            }
        }

        // Dequeue the front cell as
        // its distance is found
        q.poll();
    }

    // Print output matrix
    for(int i = 0; i < M; i++)
    {
        for(int j = 0; j < N; j++)
        {
            System.out.print(output[i][j] + " ");
        }
        System.out.println();
    }
}

// Driver code
public static void main(String args[])
{
    char matrix[][] = { { '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' } };

    MinDistanceFromaGuardInBank g =
    new MinDistanceFromaGuardInBank();

    g.findDistance(matrix);
}
}

// This code is contributed by Shobhit Yadav

Python3

# Python3 program to replace all of the O's in the matrix
# with their shortest distance from a guard
from collections import deque as queue

# store dimensions of the matrix
M = 5
N = 5


# These arrays are used to get row and column
# numbers of 4 neighbors of a given cell
row = [-1, 0, 1, 0]
col = [0, 1, 0, -1]

# return true if row number and column number
# is in range
def isValid(i, j):
    if ((i < 0 or i > M - 1) or (j < 0 or 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
def isSafe(i, j,matrix, output):

    if (matrix[i][j] != 'O' or 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
def findDistance(matrix):
    output = [[ -1 for i in range(N)]for i in range(M)]
    q = queue()

    # finding Guards location and adding into queue
    for i in range(M):
        for j in range(N):

            # initialize each cell as -1
            output[i][j] = -1
            if (matrix[i][j] == 'G'):
                pos = [i, j, 0]
                q.appendleft(pos)

                # guard has 0 distance
                output[i][j] = 0



    # do till queue is empty
    while (len(q) > 0):

        # get the front cell in the queue and update
        # its adjacent cells
        curr = q.pop()
        x, y, dist = curr[0], curr[1], curr[2]

        # do for each adjacent cell
        for i in range(4):

            # if adjacent cell is valid, has path and
            # not visited yet, en-queue it.

            if isValid(x + row[i], y + col[i]) and isSafe(x + row[i], y + col[i], matrix, output) :
                output[x + row[i]][y + col[i]] = dist + 1

                pos = [x + row[i], y + col[i], dist + 1]
                q.appendleft(pos)

    # print output matrix

    for i in range(M):
        for j in range(N):
            if output[i][j] > 0:
                print(output[i][j], end=" ")
            else:
                print(output[i][j],end=" ")
        print()


# Driver code

matrix = [['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']]

findDistance(matrix)

# This code is contributed by mohit kumar 29

C#

// C# program to replace all of the O's
// in the matrix with their shortest
// distance from a guard
using System;
using System.Collections.Generic;
public class Node
{
  public int i, j, dist;
  public Node(int i, int j, int dist)
  {
    this.i = i;
    this.j = j;
    this.dist = dist;
  }
}

public class MinDistanceFromaGuardInBank
{

  // Store dimensions of the matrix
  static int M = 5;
  static int N = 5;

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

  // Return true if row number and
  // column number is in range

  static 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

  static bool isSafe(int i, int j, char[,] matrix,int[,] output)
  {
    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
  static void findDistance(char[,] matrix)
  {
    int[,] output = new int[M,N];
    Queue<Node> q = new Queue<Node>();

    // 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')
        {
          q.Enqueue(new Node(i, j, 0));

          // Guard has 0 distance
          output[i, j] = 0;
        }
      }
    }

    // Do till queue is empty
    while (q.Count != 0)
    {
      // Get the front cell in the queue
      // and update its adjacent cells
      Node curr = q.Peek();

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

      // 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 (isValid(x + row[i], y + col[i]))
        {
          if (isSafe(x + row[i], y + col[i],matrix, output))
          {
            output[x + row[i] , y + col[i]] = dist + 1;
            q.Enqueue(new Node(x + row[i],y + col[i],dist + 1));
          }
        }
      }

      // Dequeue the front cell as
      // its distance is found
      q.Dequeue();

    }

    // Print output matrix
    for(int i = 0; i < M; i++)
    {
      for(int j = 0; j < N; j++)
      {
        Console.Write(output[i,j] + " ");
      }
      Console.WriteLine();
    }
  }

  // Driver code
  static public void Main ()
  {
    char[,] matrix ={ { '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' } };

    findDistance(matrix);
  }
}

// This code is contributed by avanitrachhadiya2155

Javascript

<script>
// Javascript program to replace all of the O's
// in the matrix with their shortest
// distance from a guard

// Store dimensions of the matrix
let M = 5;
let N = 5;

class Node
{
    constructor(i,j,dist)
    {
        this.i = i;
        this.j = j;
        this.dist = dist;
    }
}

// These arrays are used to get row
// and column numbers of 4 neighbors
// of a given cell
let row=[-1, 0, 1, 0];
let col=[0, 1, 0, -1 ];

// Return true if row number and
// column number is in range
function isValid(i,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
function isSafe(i,j,matrix,output)
{
    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
function findDistance(matrix)
{
    let output = new Array(M);

    for(let i=0;i<M;i++)
    {
        output[i]=new Array(N);
    }
    let q = [];

    // Finding Guards location and
    // adding into queue
    for(let i = 0; i < M; i++)
    {
        for(let j = 0; j < N; j++)
        {

            // Initialize each cell as -1
            output[i][j] = -1;

            if (matrix[i][j] == 'G')
            {
                q.push(new Node(i, j, 0));

                // Guard has 0 distance
                output[i][j] = 0;
            }
        }
    }

    // Do till queue is empty
    while (q.length!=0)
    {

        // Get the front cell in the queue
        // and update its adjacent cells
        let curr = q[0];
        let x = curr.i;
        let y = curr.j;
        let dist = curr.dist;

        // Do for each adjacent cell
        for (let i = 0; i < 4; i++)
        {

            // If adjacent cell is valid, has
            // path and not visited yet,
            // en-queue it.
            if (isValid(x + row[i], y + col[i]))
            {
                if (isSafe(x + row[i], y + col[i],
                           matrix, output))
                {
                    output[x + row[i]][y + col[i]] = dist + 1;
                    q.push(new Node(x + row[i],
                                   y + col[i],
                                   dist + 1));
                }
            }
        }

        // Dequeue the front cell as
        // its distance is found
        q.shift();
    }

    // Print output matrix
    for(let i = 0; i < M; i++)
    {
        for(let j = 0; j < N; j++)
        {
            document.write(output[i][j] + " ");
        }
        document.write("<br>");
    }
}

// Driver code
let matrix=[[ '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' ]];
findDistance(matrix);

// This code is contributed by ab2127
</script>

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

Time Complexity: O(n*m)
Auxiliary Space: O(n*m)

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