Fill array with 1's using minimum iterations of filling neighbors

Given an array of 0s and 1s, in how many iterations the whole array can be filled with 1s if in a single iteration immediate neighbors of 1s can be filled.

Note: if we cannot fill array with 1s, then print "-1" .

Examples : 

Input : arr[] = {1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1}
Output : 1
Explanation: 
To convert the whole array into 1s, one iteration is required. Between indexes i=2 and i=5, the zero at i=3 would be converted to '1' due to its neighbours at i=2 similarly the zero at i=4 would be converted into '1' due to its neighbor at i=5, all this can be done in a single iteration.
Similarly all 0's can be converted to 1 in single iteration.

Input : arr[] = {0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1}
Output : 2

Asked in : Amazon

It is given that a single 1 can convert both its 0 neighbours to 1. This problem boils down to three cases : 

Case 1 : A block of 0s has 1s on both sides

Let count_zero be the count of zeros in the block.

Number of iterations are always equal to : 
              count_zero/2   if (count_zero is even)
              count_zero+1)/2    if(count_zero is odd).

Case 2 : Either single 1 at the end or in 
         the starting. For example 0 0 0 0 1 and 
         1 0 0 0 0
In this case the number of iterations required will 
always be equal to number of zeros.

Case 3 : There are no 1s (Array has only 0s)
In this case array can't be filled with all 1's. 
So print -1.

Algorithm : 

1-Start traversing the array.
  (a) Traverse until a 0 is found.
     while (i < n && a[i] == 1)
     {
        i++;
        flag=true;
     }
   Flag is set to true just to check at 
   the last if array contains any 1 or not.

  (b) Traverse until a 1 is found and Count 
     contiguous 0 .
     while (i < n && a[i] == 0)
     {
         count_zero++;
         i++;
     }

  (c) Now check which case is satisfied by 
     current subarray. And update iterations 
     using count and update max iterations.    

Implementation:

// C++ program to find number of iterations
// to fill with all 1s
#include<bits/stdc++.h>
using namespace std;

// Returns count of iterations to fill arr[]
// with 1s.
int countIterations(int arr[], int n)
{
    bool oneFound = false;
    int res = 0;
    // Start traversing the array
    for (int i=0; i<n; )
    {
        if (arr[i] == 1)
          oneFound = true;

        // Traverse until a 0 is found
        while (i<n && arr[i]==1)
            i++;

        // Count contiguous 0s
        int count_zero = 0;
        while (i<n && arr[i]==0)
        {
            count_zero++;
            i++;
        }

        // Condition for Case 3
        if (oneFound == false && i == n)
            return -1;

        // Condition to check if Case 1 satisfies:
        int curr_count;
        if (i < n && oneFound == true)
        {
            // If count_zero is even
            if (count_zero & 1 == 0)
                curr_count = count_zero/2;

            // If count_zero is odd
            else
                curr_count = (count_zero+1)/2;

            // Reset count_zero
            count_zero = 0;
        }

        // Case 2
        else
        {
            curr_count = count_zero;
            count_zero = 0;
        }

        // Update res
        res = max(res, curr_count);
    }

    return res;
}

// Driver code
int main()
{
    int arr[] = {0, 1, 0, 0, 1, 0, 0,
                 0, 0, 0, 0, 0, 1, 0};
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << countIterations(arr, n);
    return 0;
}

// Java program to find number of iterations
// to fill with all 1s

class Test
{
    // Returns count of iterations to fill arr[]
    // with 1s.
    static int countIterations(int arr[], int n)
    {
        boolean oneFound = false;
        int res = 0;
        
        // Start traversing the array
        for (int i=0; i<n; )
        {
            if (arr[i] == 1)
              oneFound = true;
     
            // Traverse until a 0 is found
            while (i<n && arr[i]==1)
                i++;
     
            // Count contiguous 0s
            int count_zero = 0;
            while (i<n && arr[i]==0)
            {
                count_zero++;
                i++;
            }
     
            // Condition for Case 3
            if (oneFound == false && i == n)
                return -1;
     
            // Condition to check if Case 1 satisfies:
            int curr_count;
            if (i < n && oneFound == true)
            {
                // If count_zero is even
                if ((count_zero & 1) == 0)
                    curr_count = count_zero/2;
     
                // If count_zero is odd
                else
                    curr_count = (count_zero+1)/2;
     
                // Reset count_zero
                count_zero = 0;
            }
     
            // Case 2
            else
            {
                curr_count = count_zero;
                count_zero = 0;
            }
     
            // Update res
            res = Math.max(res, curr_count);
        }
     
        return res;
    }
    
    // Driver method
    public static void main(String[] args) 
    {
        int arr[] = {0, 1, 0, 0, 1, 0, 0,
                0, 0, 0, 0, 0, 1, 0};
        
        System.out.println(countIterations(arr, arr.length));
        
    }
}

# Python3 program to find number 
# of iterations to fill with all 1s 

# Returns count of iterations 
# to fill arr[] with 1s. 
def countIterations(arr, n): 

    oneFound = False; 
    res = 0;
    i = 0;
    
    # Start traversing the array 
    while (i < n): 
        if (arr[i] == 1):
            oneFound = True; 

        # Traverse until a 0 is found 
        while (i < n and arr[i] == 1): 
            i += 1; 

        # Count contiguous 0s 
        count_zero = 0; 
        while (i < n and arr[i] == 0):
            count_zero += 1; 
            i += 1; 

        # Condition for Case 3 
        if (oneFound == False and i == n): 
            return -1; 

        # Condition to check 
        # if Case 1 satisfies: 
        curr_count = 0; 
        if (i < n and oneFound == True):
            
            # If count_zero is even 
            if ((count_zero & 1) == 0): 
                curr_count = count_zero // 2; 

            # If count_zero is odd 
            else:
                curr_count = (count_zero + 1) // 2; 

            # Reset count_zero 
            count_zero = 0; 

        # Case 2 
        else:
            curr_count = count_zero; 
            count_zero = 0; 

        # Update res 
        res = max(res, curr_count); 

    return res; 

# Driver code 
arr = [0, 1, 0, 0, 1, 0, 0,
       0, 0, 0, 0, 0, 1, 0]; 
n = len(arr); 
print(countIterations(arr, n)); 

# This code is contributed by mits

// C# program to find number of 
// iterations to fill with all 1s
using System;

class Test {
    
    // Returns count of iterations 
    // to fill arr[] with 1s.
    static int countIterations(int []arr, int n)
    {
        bool oneFound = false;
        int res = 0;
        
        // Start traversing the array
        for (int i = 0; i < n; )
        {
            if (arr[i] == 1)
            oneFound = true;
    
            // Traverse until a 0 is found
            while (i < n && arr[i] == 1)
                i++;
    
            // Count contiguous 0s
            int count_zero = 0;
            while (i < n && arr[i] == 0)
            {
                count_zero++;
                i++;
            }
    
            // Condition for Case 3
            if (oneFound == false && i == n)
                return -1;
    
            // Condition to check if
            // Case 1 satisfies:
            int curr_count;
            if (i < n && oneFound == true)
            {
                
                // If count_zero is even
                if ((count_zero & 1) == 0)
                    curr_count = count_zero / 2;
    
                // If count_zero is odd
                else
                    curr_count = (count_zero + 1) / 2;
    
                // Reset count_zero
                count_zero = 0;
            }
    
            // Case 2
            else
            {
                curr_count = count_zero;
                count_zero = 0;
            }
    
            // Update res
            res = Math.Max(res, curr_count);
        }
    
        return res;
    }
    
    // Driver code
    public static void Main() 
    {
        int []arr = {0, 1, 0, 0, 1, 0, 0,
                0, 0, 0, 0, 0, 1, 0};
        
        Console.Write(countIterations(arr, arr.Length));
        
    }
}

// This code is contributed by nitin mittal.

<?php
// PHP program to find number 
// of iterations to fill with all 1s

// Returns count of iterations 
// to fill arr[] with 1s.
function countIterations($arr, $n)
{
    $oneFound = false;
    $res = 0;
    // Start traversing the array
    for ( $i = 0; $i < $n; )
    {
        if ($arr[$i] == 1)
        $oneFound = true;

        // Traverse until a 0 is found
        while ($i < $n && $arr[$i] == 1)
            $i++;

        // Count contiguous 0s
        $count_zero = 0;
        while ($i < $n && $arr[$i] == 0)
        {
            $count_zero++;
            $i++;
        }

        // Condition for Case 3
        if ($oneFound == false && $i == $n)
            return -1;

        // Condition to check 
        // if Case 1 satisfies:
        $curr_count;
        if ($i < $n && $oneFound == true)
        {
            // If count_zero is even
            if ($count_zero & 1 == 0)
                $curr_count = $count_zero / 2;

            // If count_zero is odd
            else
                $curr_count = ($count_zero + 1) / 2;

            // Reset count_zero
            $count_zero = 0;
        }

        // Case 2
        else
        {
            $curr_count = $count_zero;
            $count_zero = 0;
        }

        // Update res
        $res = max($res, $curr_count);
    }

    return $res;
}

// Driver code
$arr = array(0, 1, 0, 0, 1, 0, 0,
            0, 0, 0, 0, 0, 1, 0);
$n = sizeof($arr) / sizeof($arr[0]);
echo countIterations($arr, $n);

// This code is contributed by nitin mittal.
?>

<script>

// Javascript program to find number of
// iterations to fill with all 1s

// Returns count of iterations to fill arr[]
// with 1s.
function countIterations(arr, n)
{
    var oneFound = false;
    var res = 0;
    
    // Start traversing the array
    for(var i = 0; i < n; )
    {
        if (arr[i] == 1)
          oneFound = true;
 
        // Traverse until a 0 is found
        while (i < n && arr[i] == 1)
            i++;
 
        // Count contiguous 0s
        var count_zero = 0;
        while (i < n && arr[i] == 0)
        {
            count_zero++;
            i++;
        }
 
        // Condition for Case 3
        if (oneFound == false && i == n)
            return -1;
 
        // Condition to check if Case 1 satisfies:
        var curr_count;
        if (i < n && oneFound == true)
        {
            
            // If count_zero is even
            if ((count_zero & 1) == 0)
                curr_count = count_zero / 2;
 
            // If count_zero is odd
            else
                curr_count = (count_zero + 1) / 2;
 
            // Reset count_zero
            count_zero = 0;
        }
 
        // Case 2
        else
        {
            curr_count = count_zero;
            count_zero = 0;
        }
 
        // Update res
        res = Math.max(res, curr_count);
    }
 
    return res;
}

// Driver Code
var arr = [ 0, 1, 0, 0, 1, 0, 0,
            0, 0, 0, 0, 0, 1, 0 ];
        
document.write(countIterations(arr, arr.length));
        
// This code is contributed by Ankita saini

</script>

4

Time Complexity: O(n)
Auxiliary Space: O(1)