Number of days until all chocolates become unhealthy

Pablo has square chocolate Box of size n x n in which a variety of healthy chocolates are present denoted by ‘H’ initially but he finds out that some of the chocolates are rotten and are unhealthy denoted by ‘U’. In one day the rotten chocolates make all its neighbouring chocolates as unhealthy. This goes on and on until all chocolates present in the chocolate box becomes Unhealthy to eat. Find out the number of days in which the whole chocolate box becomes Unhealthy.
(Note : It is guaranteed that atleast one of the chocolate is Unhealthy)

Examples:

Input :  n = 3
         H H H
         H U H
         H H H
Output : 1
Only 1 day is required to turn all the
chocolates unhealthy in the chocolate box.

Input :  n = 4
         H H H U
         H H H H
         H U H H
         H H H H
Output : 2
Explanation:
In first day chocolate at (0, 0), (0, 1),
(2, 3), (3, 3) will remain healthy and in
the second day all the chocolates will
become unhealthy.

Asked in Amazon, Accolite, Arcesium.



Brute Force Approach:
Initialize a flag = 1. Use a while loop, inside that while search for an H (searching requires O(n^2) time complexity if we are unable to find a H in the 2-D character array stop incrementing the day counter and set flag as 0 to break the loop.

Below is the implementation of above approach:

// CPP program to find number of days before
// all chocolates become unhealthy.
#include <bits/stdc++.h>
using namespace std;

// Validates out of bounds indexing
bool isValid(int i, int j, int n)
{
    if (i < 0 || j < 0 || i >= n || j >= n)
        return false;
    return true;
}

// function for returning number of days
int numdays(char arr[][4], int n)
{
    int numdays = 0;

    while (true)
    {
        // Traverse matrix to look for unhealthy
        // chocolates and mark their neighbors.
        for (int i = 0; i < n; i++)
        {
            for (int j = 0; j < n; j++)
            {
                if (arr[i][j] == 'U')
                {

                    if (isValid(i - 1, j - 1, n) &&
                        arr[i - 1][j - 1] == 'H')
                        arr[i - 1][j - 1] = 'V';

                    if (isValid(i - 1, j, n) &&
                        arr[i - 1][j] == 'H')
                        arr[i - 1][j] = 'V';

                    if (isValid(i - 1, j + 1, n) &&
                        arr[i - 1][j + 1] == 'H')
                        arr[i - 1][j + 1] = 'V';

                    if (isValid(i, j - 1, n) &&
                        arr[i][j - 1] == 'H')
                        arr[i][j - 1] = 'V';

                    if (isValid(i, j + 1, n) &&
                        arr[i][j + 1] == 'H')
                        arr[i][j + 1] = 'V';

                    if (isValid(i + 1, j - 1, n) &&
                        arr[i + 1][j - 1] == 'H')
                        arr[i + 1][j - 1] = 'V';

                    if (isValid(i + 1, j, n) &&
                            arr[i + 1][j] == 'H')
                        arr[i + 1][j] = 'V';

                    if (isValid(i + 1, j + 1, n) &&
                        arr[i + 1][j + 1] == 'H')
                        arr[i + 1][j + 1] = 'V';
                }

                /*Here we are assigning the neighbours of U
                with the character V because we don't want
                these neighbours to be counted in that
                particular day. If we do not do so, in the
                next iteration that neighbour will also get
                counted which was supposed to be counted in
                the next day. */
            }
        }

        // Mark chocolates unhealthy which are made
        // unhealthy in current day.
        bool Hflag = false;
        for (int i = 0; i < n; i++)
        {
            for (int j = 0; j < n; j++)
            {
                if (arr[i][j] == 'V')
                {
                    arr[i][j] = 'U';
                    Hflag = true;
                }
            }
        }

        // Check if there was any chocoloate
        // marked unhealthy in current day
        if (Hflag)
            numdays++;
        else
            break;
    }
    return numdays;
}

// Driver function
int main()
{
    int n = 4;
    char arr[4][4] = { 'H', 'H', 'H', 'U',
                       'H', 'H', 'H', 'H',
                       'H', 'U', 'H', 'H',
                       'H', 'H', 'H', 'H'
                     };
    int ans = numdays(arr, n);
    cout << "number of days taken : "
         << ans << "\n";
    return 0;
}

Output:

 number of days taken : 2

Efficient Approach (Uses BFS)
In this approach, declare a queue which inputs pairs which corresponds to the index of the unhealthy chocolates and then as soon as the index (-1, -1) is reached we increment the numdays counter. This Solution is basically based on calculating levels in level order traversal (Iterative version) of a binary tree in which we push the initial indexes of the unhealthy chocolates instead of root node and incrementing numdays instead of level counter as soon as the index (-1, -1) is reached instead of NULL. As soon as the counter of the flag reaches 2 we break the loop denoting that queue has encoutered two consecutive (-1, -1) pair.

Below is the implementation of above approach:

// CPP program using Efficient approach
// to find number of days
#include <bits/stdc++.h>
using namespace std;

// Validates out of bounds indexing
bool isValid(int i, int j, int n)
{
    if (i < 0 || j < 0 || i >= n || j >= n)
        return false;
    return true;
}

// function for returning number of days
int numdays(char arr[][4], int n)
{
    int numdays = 0;
    int i, j;
    queue<pair<int, int> > q;

    // Initializing queue with initial
    // positions of unhealthy chocolates
    for (i = 0; i < n; i++)
        for (j = 0; j < n; j++) {
            if (arr[i][j] == 'U')
                q.push(make_pair(i, j));
        }

    q.push(make_pair(-1, -1));

    // (-1, -1) is used as a checkpoint
    // to count the number of days
    pair<int, int> temp;

    // temporary pair to store the indexes
    int flag = 0;
    while (!q.empty()) {
        temp = q.front();
        i = temp.first;
        j = temp.second;
        q.pop();
        if (i == -1 && j == -1) {
            flag++;
            q.push(make_pair(-1, -1));

            // pushing the respective
           // checkpoint
            if (flag == 2)
                break;
            numdays++;
        }
        else {
            flag = 0;
            if (isValid(i - 1, j - 1, n) &&
                arr[i - 1][j - 1] == 'H') {
                q.push(make_pair(i - 1, j - 1));
                arr[i - 1][j - 1] = 'U';
            }

            if (isValid(i - 1, j, n) &&
                arr[i - 1][j] == 'H') {
                q.push(make_pair(i - 1, j));
                arr[i - 1][j] = 'U';
            }

            if (isValid(i - 1, j + 1, n) &&
                arr[i - 1][j + 1] == 'H') {
                q.push(make_pair(i - 1, j + 1));
                arr[i - 1][j + 1] = 'U';
            }

            if (isValid(i, j - 1, n) &&
                arr[i][j - 1] == 'H') {
                q.push(make_pair(i, j - 1));
                arr[i][j - 1] = 'U';
            }

            if (isValid(i, j + 1, n) &&
                arr[i][j + 1] == 'H') {
                q.push(make_pair(i, j + 1));
                arr[i][j + 1] = 'U';
            }

            if (isValid(i + 1, j - 1, n) &&
                arr[i + 1][j - 1] == 'H') {
                q.push(make_pair(i + 1, j - 1));
                arr[i + 1][j - 1] = 'U';
            }

            if (isValid(i + 1, j, n) &&
                arr[i + 1][j] == 'H') {
                q.push(make_pair(i + 1, j));
                arr[i + 1][j] = 'U';
            }

            if (isValid(i + 1, j + 1, n) &&
                arr[i + 1][j + 1] == 'H') {
                q.push(make_pair(i + 1, j + 1));
                arr[i + 1][j + 1] = 'U';
            }
        }
    }

    return numdays - 1;
}

// Driver function
int main()
{
    int n = 4;
    char arr[4][4] = { 'H', 'H', 'H', 'U',
                       'H', 'H', 'H', 'H',
                       'H', 'H', 'U', 'H',
                       'H', 'H', 'H', 'H' };
    int ans = numdays(arr, n);
    cout << "number of days taken : "
         << ans << "\n";
    return 0;
}

Output:

number of days taken : 2



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