Maximum time required for all patients to get infected

Given a matrix arr[][], consisting of only 0, 1, and 2, that represents an empty ward, an uninfected patient, and an infected patient respectively. In one unit of time, an infected person at index (i, j) can infect an uninfected person adjacent to it i.e., at index (i – 1, j), (i + 1, j), (i, j – 1), and (i, j + 1). The task is to find the minimum amount of time required to infect all the patients. If it is impossible to infect all the patients, then print “-1”.

Examples:

Input: arr[][] = {{2, 1, 0, 2, 1}, {1, 0, 1, 2, 1}, {1, 0, 0, 2, 1}}
Output: 2
Explanation:
At time t = 1: The patients at positions {0, 0}, {0, 3}, {1, 3} and {2, 3} will infect patient at {{0, 1}, {1, 0}, {0, 4}, {1, 2}, {1, 4}, {2, 4}} during 1st unit time.
At time t = 2: The patient at {1, 0} will get infected and will infect patient at {2, 0}.
After the above time intervals all the uninfected patients are infected. Therefore, the total amount of time required is 2.
Input: arr[][] = {{2, 1, 0, 2, 1}, {0, 0, 1, 2, 1}, {1, 0, 0, 2, 1}}
Output: -1

Approach: The given problem can be solved by using BFS Traversal on the 2D matrix. Follow the steps below to solve the given problem:

Initialize a 2D array, say timeofinfection[][] with -1, such that timeofinfection[i][j] stores the time when the patient at index (i, j) was infected.
Initialize a queue to store indices of infected patients and their time of infection.
Traverse the given matrix arr[][] and perform the following operations:
- If the value at cell (i, j) is 2, then push that cell into the queue with the time of infection as 0 i.e., {i, j, 0}.
- Iterate until the queue is non-empty and perform the following steps:
  - Pop the front element of the queue and store it in a variable, say current.
  - From the current popped cell (i, j), if the adjacent cell has an infected person which is unvisited, then push the index of the adjacent cell with (1 + time of infection of the current popped cell) into the queue.
After completing the above steps, if all the infected persons are visited, i.e. the time of infection of all the infected persons is non-negative, then print the maximum element present in the matrix timeofinfection[][] as the maximum unit of time required to infect all the patients.
Otherwise, print “-1”.

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Direction arrays
vector<pair<int, int> > direction
    = { { 1, 0 }, { 0, -1 }, { -1, 0 }, { 0, 1 } };
 
// Function to find the maximum time
// required for all patients to get infected
int maximumTime(vector<vector<int> > arr)
{
    // Stores the number of rows
    int n = arr.size();
 
    // Stores the number of columns
    int m = arr[0].size();
 
    // Stores the time of infection
    // of the patient at index (i, j)
    int timeofinfection[n][m];
 
    // Stores index and time of
    // infection of infected persons
    queue<pair<pair<int, int>, int> > q;
 
    // Traverse the matrix
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
 
            // Set the cell as unvisited
            timeofinfection[i][j] = -1;
 
            // If the current patient
            // is already infected
            if (arr[i][j] == 2) {
 
                // Push the index and time of
                // infection of current patient
                q.push({ { i, j }, 0 });
                timeofinfection[i][j] = 0;
            }
        }
    }
 
    // Iterate until queue becomes empty
    while (!q.empty()) {
        // Stores the front element of queue
        pair<pair<int, int>, int> current
            = q.front();
 
        // Pop out the front element
        q.pop();
 
        // Check for all four
        // adjacent indices
        for (auto it : direction) {
 
            // Find the index of the
            // adjacent cell
            int i = current.first.first
                    + it.first;
            int j = current.first.second
                    + it.second;
 
            // If the current adjacent
            // cell is invalid or it
            // contains an infected patient
            if (i < 0 || j < 0 || i >= n
                || j >= m || arr[i][j] != 1
                || timeofinfection[i][j] != -1) {
 
                // Continue to the next
                // neighbouring cell
                continue;
            }
 
            // Push the infected
            // neighbour into queue
            q.push({ { i, j },
                     current.second + 1 });
            timeofinfection[i][j]
                = current.second + 1;
        }
    }
 
    // Stores the maximum time
    int maxi = INT_MIN;
 
    // Stores if any uninfected
    // patient exists or not
    int flag = 0;
 
    // Traverse the matrix
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
            // If no patient is
            // present at index (i, j)
            if (arr[i][j] != 1)
                continue;
 
            // If an uninfected patient
            // is present at index (i, j)
            if (arr[i][j] == 1
                && timeofinfection[i][j] == -1) {
                // Set flag as true
                flag = 1;
                break;
            }
 
            // Update the maximum time of infection
            maxi = max(maxi, timeofinfection[i][j]);
        }
    }
 
    // If an uninfected patient is present
    if (flag)
        return -1;
 
    // Return the final result
    return maxi;
}
 
// Driver Code
int main()
{
    vector<vector<int> > arr
        = { { 2, 1, 0, 2, 1 },
            { 1, 0, 1, 2, 1 },
            { 1, 0, 0, 2, 1 } };
    cout << maximumTime(arr);
 
    return 0;
}

Java

// Java program for the above approach
import java.util.*;
 
class GFG {
     
static class pair
{
    int first, second, third;
     
    pair(int first,int second,int third)
    {
         this.first = first;
         this.second = second;
         this.third = third;
    }
}   
     
// Direction arrays
static int[][] direction = { { 1, 0 }, { 0, -1 },
                             { -1, 0 }, { 0, 1 } };
 
// Function to find the maximum time
// required for all patients to get infected
static int maximumTime(int[][] arr)
{
     
    // Stores the number of rows
    int n = arr.length;
 
    // Stores the number of columns
    int m = arr[0].length;
 
    // Stores the time of infection
    // of the patient at index (i, j)
    int[][] timeofinfection = new int[n][m];
 
    // Stores index and time of
    // infection of infected persons
    Queue<pair> q = new LinkedList<>();
 
    // Traverse the matrix
    for(int i = 0; i < n; i++)
    {
        for(int j = 0; j < m; j++)
        {
 
            // Set the cell as unvisited
            timeofinfection[i][j] = -1;
 
            // If the current patient
            // is already infected
            if (arr[i][j] == 2)
            {
                 
                // Push the index and time of
                // infection of current patient
                q.add(new pair(i, j, 0));
                timeofinfection[i][j] = 0;
            }
        }
    }
 
    // Iterate until queue becomes empty
    while (!q.isEmpty())
    {
         
        // Stores the front element of queue
        pair current = q.peek();
 
        // Pop out the front element
        q.poll();
 
        // Check for all four
        // adjacent indices
        for(int[] it : direction)
        {
             
            // Find the index of the
            // adjacent cell
            int i = current.first + it[0];
            int j = current.second + it[1];
 
            // If the current adjacent
            // cell is invalid or it
            // contains an infected patient
            if (i < 0 || j < 0 || i >= n ||
               j >= m || arr[i][j] != 1 ||
               timeofinfection[i][j] != -1)
            {
 
                // Continue to the next
                // neighbouring cell
                continue;
            }
 
            // Push the infected
            // neighbour into queue
            q.add(new pair(i, j ,
                           current.second + 1 ));
            timeofinfection[i][j] = current.third + 1;
        }
    }
 
    // Stores the maximum time
    int maxi = Integer.MIN_VALUE;
 
    // Stores if any uninfected
    // patient exists or not
    int flag = 0;
 
    // Traverse the matrix
    for(int i = 0; i < n; i++)
    {
        for(int j = 0; j < m; j++)
        {
             
            // If no patient is
            // present at index (i, j)
            if (arr[i][j] != 1)
                continue;
 
            // If an uninfected patient
            // is present at index (i, j)
            if (arr[i][j] == 1 && timeofinfection[i][j] == -1)
            {
                 
                // Set flag as true
                flag = 1;
                break;
            }
 
            // Update the maximum time of infection
            maxi = Math.max(maxi, timeofinfection[i][j]);
        }
    }
 
    // If an uninfected patient is present
    if (flag == 1)
        return -1;
 
    // Return the final result
    return maxi;
}
 
// Driver code
public static void main(String[] args)
{
    int[][] arr = { { 2, 1, 0, 2, 1 },
                    { 1, 0, 1, 2, 1 },
                    { 1, 0, 0, 2, 1 } };
    System.out.print(maximumTime(arr));
}
}
 
// This code is contributed by offbeat

Javascript

<script>
 
// JavaScript program for the above approach
 
// Direction arrays
var direction
    = [ [ 1, 0 ], [ 0, -1 ], [ -1, 0 ], [ 0, 1 ] ];
 
// Function to find the maximum time
// required for all patients to get infected
function maximumTime(arr)
{
    // Stores the number of rows
    var n = arr.length;
 
    // Stores the number of columns
    var m = arr[0].length;
 
    // Stores the time of infection
    // of the patient at index (i, j)
    var timeofinfection = Array.from(Array(n), ()=>Array(m));
 
    // Stores index and time of
    // infection of infected persons
    var q = [];
 
    // Traverse the matrix
    for (var i = 0; i < n; i++) {
        for (var j = 0; j < m; j++) {
 
            // Set the cell as unvisited
            timeofinfection[i][j] = -1;
 
            // If the current patient
            // is already infected
            if (arr[i][j] == 2) {
 
                // Push the index and time of
                // infection of current patient
                q.push([ [ i, j ], 0 ]);
                timeofinfection[i][j] = 0;
            }
        }
    }
 
    // Iterate until queue becomes empty
    while (q.length!=0) {
        // Stores the front element of queue
        var current
            = q[0];
 
        // Pop out the front element
        q.shift();
 
        // Check for all four
        // adjacent indices
        for(var it of direction) {
 
            // Find the index of the
            // adjacent cell
            var i = current[0][0]
                    + it[0];
            var j = current[0][1]
                    + it[1];
 
            // If the current adjacent
            // cell is invalid or it
            // contains an infected patient
            if (i < 0 || j < 0 || i >= n
                || j >= m || arr[i][j] != 1
                || timeofinfection[i][j] != -1) {
 
                // Continue to the next
                // neighbouring cell
                continue;
            }
 
            // Push the infected
            // neighbour into queue
            q.push([[i, j],
                     current[1] + 1 ]);
            timeofinfection[i][j]
                = current[1] + 1;
        }
    }
 
    // Stores the maximum time
    var maxi = -1000000000;
 
    // Stores if any uninfected
    // patient exists or not
    var flag = 0;
 
    // Traverse the matrix
    for (var i = 0; i < n; i++) {
        for (var j = 0; j < m; j++) {
            // If no patient is
            // present at index (i, j)
            if (arr[i][j] != 1)
                continue;
 
            // If an uninfected patient
            // is present at index (i, j)
            if (arr[i][j] == 1
                && timeofinfection[i][j] == -1) {
                // Set flag as true
                flag = 1;
                break;
            }
 
            // Update the maximum time of infection
            maxi = Math.max(maxi, timeofinfection[i][j]);
        }
    }
 
    // If an uninfected patient is present
    if (flag)
        return -1;
 
    // Return the final result
    return maxi;
}
 
// Driver Code
var arr
    = [ [ 2, 1, 0, 2, 1 ],
        [ 1, 0, 1, 2, 1 ],
        [ 1, 0, 0, 2, 1 ] ];
document.write( maximumTime(arr));
 
</script>

Python

# function to traverse to nearby possible directions
def bfs(i, j, mat, time):
    # marking position as visited
    mat[i][j] = 0
 
# stack to store positions that got infected in one unit time
    stack = []
 
# direction arrays
    row = [-1, 0, 0, 1]
    col = [0, -1, 1, 0]
 
# traversing to nearby uninfected beds
    for k in range(4):
        x = i+row[k]
        y = j+col[k]
 
        if x >= 0 and x < r and y >= 0 and y < c and mat[x][y] == 1:
            mat[x][y] = 0
            stack.append((x, y))
 
# storing the time at which the patient got infected
            time[x][y] = time[i][j]+1
 
    return stack
 
 
# function to calculate maximum time
def maxTime(hospital):
 
    # array to store the time at which the patients got infected
    time = [[0 for i in range(c)] for j in range(r)]
 
# to store newly infected ones
    que = []
 
# initial run
    for i in range(r):
        for j in range(c):
            if hospital[i][j] == 2:
                que += bfs(i, j, hospital, time)
 
# iterate till every infected patient has done spreading
    while(len(que) != 0):
        for x, y in que:
            temp = bfs(x, y, hospital, time)
        que = temp
 
# finally calculating maximum time
    res = 0
    for i in range(r):
        for j in range(c):
 
            # checking if there is any uninfected person
            if hospital[i][j] == 1:
                return -1
            res = max(res, time[i][j])
 
    return res
 
 
# Driver Code Starts
hospital = [[2, 1, 0, 2, 1],
            [1, 0, 1, 2, 1],
            [1, 0, 0, 2, 1]]
 
r = len(hospital)
c = len(hospital[0])
print(maxTime(hospital))
 
# Driver Code Ends

C#

using System;
using System.Collections.Generic;
 
 
    class GFG
    {
        public class pair
{
    public int first;
    public int second;
    public int third;
 
    public pair(int first, int second, int third)
    {
        this.first = first;
        this.second = second;
        this.third = third;
    }
}
 
 
        // Direction arrays
        static int[][] direction = {
            new int[] { 1, 0 },
            new int[] { 0, -1 },
            new int[] { -1, 0 },
            new int[] { 0, 1 }
        };
 
        // Function to find the maximum time
        // required for all patients to get infected
        static int maximumTime(int[][] arr)
        {
 
            // Stores the number of rows
            int n = arr.Length;
 
            // Stores the number of columns
            int m = arr[0].Length;
 
            // Stores the time of infection
            // of the patient at index (i, j)
            int[][] timeofinfection = new int[n][];
            for (int i = 0; i < n; i++)
                timeofinfection[i] = new int[m];
 
            // Stores index and time of
            // infection of infected persons
            Queue<pair> q = new Queue<pair>();
 
            // Traverse the matrix
            for (int i = 0; i < n; i++)
            {
                for (int j = 0; j < m; j++)
                {
 
                    // Set the cell as unvisited
                    timeofinfection[i][j] = -1;
 
                    // If the current patient
                    // is already infected
                    if (arr[i][j] == 2)
                    {
 
                        // Push the index and time of
                        // infection of current patient
                        q.Enqueue(new pair(i, j, 0));
                        timeofinfection[i][j] = 0;
                    }
                }
            }
 
            // Iterate until queue becomes empty
            while (q.Count != 0)
            {
 
                // Stores the front element of queue
                pair current = q.Peek();
 
                // Pop out the front element
                q.Dequeue();
 
                // Check for all four
                // adjacent indices
                foreach (int[] it in direction)
                {
 
                    // Find the index of the
                    // adjacent cell
                    int i = current.first + it[0];
                    int j = current.second + it[1];
 
                    // If the current adjacent
                    // cell is invalid or it
                    // contains an infected patient
                    if (i < 0 || j < 0 || i >= n ||
                        j >= m || arr[i][j] != 1 ||
                        timeofinfection[i][j] != -1)
                    {
 
                        // Continue to the next
                        // neighbouring cell
                        continue;
                    }
 
                    // Push the infected
                    // patient into queue
                    q.Enqueue(new pair(i, j,
                        current.second + 1));
                    timeofinfection[i][j] = current.third + 1;
                }
            }
 
            // Stores the maximum time
          int maxi = int.MinValue;
 
 
        // Stores if any uninfected
        // patient exists or not
        int flag = 0;
 
        // Traverse the matrix
        for (int i = 0; i < n; i++)
        {
            for (int j = 0; j < m; j++)
            {
 
                // If no patient is
                // present at index (i, j)
                if (arr[i][j] != 1)
                    continue;
 
                // If an uninfected patient
                // is present at index (i, j)
                if (arr[i][j] == 1 && timeofinfection[i][j] == -1)
                {
 
                    // Set flag as true
                    flag = 1;
                    break;
                }
 
                // Update the maximum time of infection
                maxi = Math.Max(maxi, timeofinfection[i][j]);
            }
        }
 
        // If an uninfected patient is present
        if (flag == 1)
            return -1;
 
        // Return the final result
        return maxi;
    }
 
    // Driver code
    static void Main(string[] args)
    {
        int[][] arr = {
            new int[]{ 2, 1, 0, 2, 1 },
            new int[]{ 1, 0, 1, 2, 1 },
            new int[]{ 1, 0, 0, 2, 1 }
        };
        Console.WriteLine(maximumTime(arr));
    }
}

Output

Time Complexity: O(N * M)
Auxiliary Space: O(N * M)

Approach 2:This uses the same BFS traversal technique but instead of using an array of integers to keep track of whether all patients are infected, it uses a single integer which reduces overall space consumption and overhead of doing an extra check for uninfected patients.

The basic idea is we will store the count of uninfected persons at the start and as an individual will got infected we will decrement this count. This will remove the overhead of checking for uninfected persons at the end. And the time at which the last person got infected will be our final answer.

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Direction arrays
vector<pair<int, int> > direction
    = { { 1, 0 }, { 0, -1 }, { -1, 0 }, { 0, 1 } };
 
// Function to find the maximum time
// required for all patients to get infected
int maximumTime(vector<vector<int> > arr)
{
    // Stores the number of rows
    int n = arr.size();
 
    // Stores the number of columns
    int m = arr[0].size();
 
    // Stores whether particular index(i, j)
    // is visited or not 
    vector<vector<bool>> visited(n,vector<bool>(m,0));
 
    // Stores index and time of
    // infection of infected persons
    queue<pair<pair<int, int>, int> > q;
   
    //Stores uninfected patients count 
      int uninfected_count=0;
     
      //Stores time at which last person got infected
      int time = 0;
    // Traverse the matrix
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
 
            // If the current patient
            // is already infected
            if (arr[i][j] == 2) {
 
                // Push the index of current patient
                // and mark it as visited
                q.push({ { i, j }, 0 });
                visited[i][j] =  1;
            }
           
            //If current patient is uninfected
              //increment uninfected count
              if(arr[i][j] == 1){
                uninfected_count++;
            }
        }
    }
 
    // Iterate until queue becomes empty
    while (!q.empty()) {
        // Stores the front element of queue
        pair<pair<int, int>, int> current
            = q.front();
           
        time = current.second;
        // Pop out the front element
        q.pop();
 
        // Check for all four
        // adjacent indices
        for (auto it : direction) {
 
            // Find the index of the
            // adjacent cell
            int i = current.first.first
                    + it.first;
            int j = current.first.second
                    + it.second;
 
            // If the current adjacent
            // cell is invalid or it
            // contains an infected patient
            if (i < 0 || j < 0 || i >= n
                || j >= m || arr[i][j] != 1
                || visited[i][j] != 0) {
 
                // Continue to the next
                // neighbouring cell
                continue;
            }
 
            // Push the infected
            // neighbour into queue
            q.push({ { i, j }, time + 1 });
            visited[i][j] = 1;
              uninfected_count--;
        }
    }
 
    // If an uninfected patient is present
    if (uninfected_count != 0)
        return -1;
 
      // Return the final result
    return time;
}
 
// Driver Code
int main()
{
    vector<vector<int> > arr
        = { { 2, 1, 0, 2, 1 },
            { 1, 0, 1, 2, 1 },
            { 1, 0, 0, 2, 1 } };
    cout << maximumTime(arr);
 
    return 0;
}
// Contributed By Devendra Kolhe

Java

// Java program for the above approach
import java.util.*;
 
public class GFG{
     
    static class pair
    {
        int first, second, third;
          
        pair(int first,int second,int third)
        {
             this.first = first;
             this.second = second;
             this.third = third;
        }
    }
     
    // Direction arrays
    static int direction[][] = { { 1, 0 }, { 0, -1 },
                            { -1, 0 }, { 0, 1 } };
     
    // Function to find the maximum time
    // required for all patients to get infected
    static int maximumTime(int arr[][])
    {
        // Stores the number of rows
        int n = arr.length;
     
        // Stores the number of columns
        int m = arr[0].length;
     
        // Stores whether particular index(i, j)
        // is visited or not
        boolean visited[][] = new boolean[n][m];
     
        // Stores index and time of
        // infection of infected persons
        Queue<pair> q = new LinkedList<>();
     
        //Stores uninfected patients count
        int uninfected_count=0;
         
        //Stores time at which last person got infected
        int time = 0;
        // Traverse the matrix
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
     
                // If the current patient
                // is already infected
                if (arr[i][j] == 2) {
     
                    // Push the index of current patient
                    // and mark it as visited
                    q.add( new pair(i, j, 0 ));
                    visited[i][j] = true;
                }
             
                //If current patient is uninfected
                //increment uninfected count
                if(arr[i][j] == 1){
                    uninfected_count++;
                }
            }
        }
     
        // Iterate until queue becomes empty
        while (!q.isEmpty()) {
            // Stores the front element of queue
            pair current = q.peek();
             
            time = current.third;
            // Pop out the front element
            q.poll();
     
            // Check for all four
            // adjacent indices
            for (int[] it : direction) {
     
                // Find the index of the
                // adjacent cell
                int i = current.first
                        + it[0];
                int j = current.second
                        + it[1];
     
                // If the current adjacent
                // cell is invalid or it
                // contains an infected patient
                if (i < 0 || j < 0 || i >= n
                    || j >= m || arr[i][j] != 1
                    || visited[i][j]) {
     
                    // Continue to the next
                    // neighbouring cell
                    continue;
                }
     
                // Push the infected
                // neighbour into queue
                q.add( new pair( i, j, time + 1 ));
                visited[i][j] = true;
                uninfected_count--;
            }
        }
     
        // If an uninfected patient is present
        if (uninfected_count != 0)
            return -1;
     
        // Return the final result
        return time;
    }
     
    // Driver Code
    public static void main(String args[])
    {
        int arr[][] = { { 2, 1, 0, 2, 1 },
                    { 1, 0, 1, 2, 1 },
                    { 1, 0, 0, 2, 1 } };
                     
        System.out.println(maximumTime(arr));
     
    }
}
 
// This code is contributed by adityapande88.

Python

# Python program for the above approach
 
# Direction arrays
direction = [(1, 0), (0, -1), (-1, 0), (0, 1)]
 
# Function to find the maximum time
# required for all patients to get infected
def maximumTime(arr):
    # Stores the number of rows
    n = len(arr)
 
    # Stores the number of columns
    m = len(arr[0])
 
    # Stores whether particular index(i, j)
    # is visited or not
    visited = [[False for j in range(m)] for i in range(n)]
 
    # Stores index and time of
    # infection of infected persons
    q = []
 
    # Stores uninfected patients count
    uninfected_count = 0
 
    # Stores time at which last person got infected
    time = 0
 
    # Traverse the matrix
    for i in range(n):
        for j in range(m):
 
            # If the current patient
            # is already infected
            if arr[i][j] == 2:
 
                # Push the index of current patient
                # and mark it as visited
                q.append(((i, j), 0))
                visited[i][j] = True
 
            # If current patient is uninfected
            # increment uninfected count
            if arr[i][j] == 1:
                uninfected_count += 1
 
    # Iterate until queue becomes empty
    while q:
        # Stores the front element of queue
        current = q.pop(0)
 
        time = current[1]
        # Check for all four
        # adjacent indices
        for it in direction:
 
            # Find the index of the
            # adjacent cell
            i = current[0][0] + it[0]
            j = current[0][1] + it[1]
 
            # If the current adjacent
            # cell is invalid or it
            # contains an infected patient
            if i < 0 or j < 0 or i >= n or j >= m or arr[i][j] != 1 or visited[i][j]:
 
                # Continue to the next
                # neighbouring cell
                continue
 
            # Push the infected
            # neighbour into queue
            q.append(((i, j), time + 1))
            visited[i][j] = True
            uninfected_count -= 1
 
    # If an uninfected patient is present
    if uninfected_count != 0:
        return -1
 
    # Return the final result
    return time
 
# Driver Code
arr = [[2, 1, 0, 2, 1], [1, 0, 1, 2, 1], [1, 0, 0, 2, 1]]
print(maximumTime(arr))
 
# This code is contributed by divyansh2212

Javascript

// JavaScript program for the above approach
 
// Direction arrays
let direction = [
    [1, 0],
    [0, -1],
    [-1, 0],
    [0, 1]
];
 
// Function to find the maximum time
// required for all patients to get infected
function maximumTime(arr) {
    // Stores the number of rows
    let n = arr.length;
    // Stores the number of columns
    let m = arr[0].length;
 
    // Stores whether particular index(i, j)
    // is visited or not
    let visited = Array(n).fill().map(() => Array(m).fill(false));
 
    // Stores index and time of
    // infection of infected persons
    let q = [];
 
    // Stores uninfected patients count
    let uninfected_count = 0;
 
    // Stores time at which last person got infected
    let time = 0;
 
    // Traverse the matrix
    for (let i = 0; i < n; i++) {
        for (let j = 0; j < m; j++) {
 
            // If the current patient
            // is already infected
            if (arr[i][j] === 2) {
 
                // Push the index of current patient
                // and mark it as visited
                q.push([
                    [i, j], 0
                ]);
                visited[i][j] = true;
 
            }
 
            // If current patient is uninfected
            // increment uninfected count
            if (arr[i][j] === 1) {
                uninfected_count += 1;
            }
        }
    }
 
    // Iterate until queue becomes empty
    while (q.length > 0) {
        // Stores the front element of queue
        let current = q.shift();
 
        time = current[1];
 
        // Check for all four
        // adjacent indices
        for (let it of direction) {
 
            // Find the index of the
            // adjacent cell
            let i = current[0][0] + it[0];
            let j = current[0][1] + it[1];
 
            // If the current adjacent
            // cell is invalid or it
            // contains an infected patient
            if (i < 0 || j < 0 || i >= n || j >= m || arr[i][j] !== 1 || visited[i][j]) {
 
                // Continue to the next
                // neighbouring cell
                continue;
            }
 
            // Push the infected
            // neighbour into queue
            q.push([
                [i, j], time + 1
            ]);
            visited[i][j] = true;
            uninfected_count -= 1;
        }
    }
 
    // If an uninfected patient is present
    if (uninfected_count !== 0) {
        return -1;
    }
 
    // Return the final result
    return time;
}
 
// Driver Code
let arr = [
    [2, 1, 0, 2, 1],
    [1, 0, 1, 2, 1],
    [1, 0, 0, 2, 1]
];
console.log(maximumTime(arr));
 
// This code is contributed by adityasharmadev01

C#

// Online C# Editor for free
// Write, Edit and Run your C# code using C# Online Compiler
using System;
using System.Collections.Generic;
 
public struct Pair
{
    public int first, second, third;
 
    public Pair(int first, int second, int third)
    {
        this.first = first;
        this.second = second;
        this.third = third;
    }
}
 
public class GFG {
    // Direction arrays
 
    static int[][] direction
        = { new int[] { 1, 0 }, new int[] { 0, -1 },
            new int[] { -1, 0 }, new int[] { 0, 1 } };
 
    // Function to calculate maximum time required to infect
    // all uninfected cells
    static int MaximumTime(int[][] arr)
    {
        // Stores the number of rows
 
        int n = arr.Length;
 
        // Stores the number of columns
        int m = arr[0].Length;
 
        // Stores whether particular index(i, j)
        // is visited or not
        bool[, ] visited = new bool[n, m];
 
        // Stores index and time of
        // infection of infected persons
        var q = new Queue<Pair>();
 
        // Stores uninfected patients count
        int uninfected_count = 0;
 
        int time = 0;
 
        // Add infected cells to the queue and mark them as
        // visited Count the number of uninfected cells
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
 
                // If the current patient
                // is already infected
                if (arr[i][j] == 2) {
                    // Push the index of current patient
                    // and mark it as visited
                    q.Enqueue(new Pair(i, j, 0));
                    visited[i, j] = true;
                }
 
                // If current patient is uninfected
                // increment uninfected count
                if (arr[i][j] == 1) {
                    uninfected_count++;
                }
            }
        }
 
        // Perform BFS until all uninfected cells are
        // infected
        while (q.Count > 0) {
            var current = q.Peek();
 
            time = current.third;
            q.TryDequeue(out current);
 
            for (int i = 0; i < 4; i++) {
                int x = current.first + direction[i][0];
                int y = current.second + direction[i][1];
 
                // Check if new cell is within bounds and
                // uninfected and Not Visited
                if (x < 0 || y < 0 || x >= n || y >= m
                    || arr[x][y] != 1 || visited[x, y]) {
                    continue;
                }
 
                // Add new cell to the queue, mark as
                // visited and decrement uninfected count
                q.Enqueue(new Pair(x, y, time + 1));
                visited[x, y] = true;
                uninfected_count--;
            }
        }
 
        // If there are uninfected cells remaining, return
        // -1 to indicate infection failure
        if (uninfected_count != 0) {
            return -1;
        }
 
        // Return time taken to infect all uninfected cells
        return time;
    }
 
    public static void Main(string[] args)
    {
        int[][] arr = { new int[] { 2, 1, 0, 2, 1 },
                        new int[] { 1, 0, 1, 2, 1 },
                        new int[] { 1, 0, 0, 2, 1 } };
        Console.WriteLine(MaximumTime(arr));
    }
    // Code is Contributed By Vikas Bishnoi
}