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Maximum flips possible such that no pair of adjacent elements are both 1

  • Last Updated : 23 Apr, 2021
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Given a binary array arr[] of size N, the task is to find the maximum count of 0s that can be converted into 1s such that no pair of adjacent array elements are 1.

Examples:

Input: arr[] = { 1, 0, 0, 0, 1 } 
Output:
Explanation: 
Updating arr[2] to 1 modifies arr[] to { 1, 0, 1, 0, 1 } 
Therefore, the required output is 1

Input: arr[] = { 0, 0, 1, 0, 0, 0, 0, 1, 0, 0 } 
Output:
Explanation: 
Updating arr[0], arr[5] and arr[9] modifies arr[] to { 1, 0, 1, 0, 0, 1, 0, 1, 0, 1 } 
Therefore, the required output is 3

 

Approach: The problem can be solved using Greedy technique. Follow the steps below to solve the problem:



Below is the implementation of the above approach:

C++




// C++ program for the above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the maximum count of 0s
// required to be converted into 1s such
// no pair of adjacent elements are 1
void maxPositionsOccupied(vector<int>& arr)
{
 
    // Base Case
    if (arr.size() == 0) {
        cout << 0;
        return;
    }
 
    // Insert 0 at the end
    // of the array
    arr.push_back(0);
 
    // Insert 0 at the front
    // of the array
    arr.insert(arr.begin(), 0);
 
    // Stores the maximum count of of 0s
    // that can be converted into 1s
    int ans = 0;
 
    // Stores index of array elements
    int i = 0;
 
    // Traverse the array
    while ((i < arr.size() - 2)) {
 
        // If adjacent elements are 0s
        if ((arr[i] == 0) && (arr[i + 1] == 0)
            && (arr[i + 2] == 0)) {
 
            // Update ans
            ans++;
 
            // Update arr[i + 1]
            arr[i + 1] = 1;
        }
 
        // Update i
        i++;
    }
 
    // Print the answer
    cout << ans;
}
 
// Driver Code
int main()
{
    // Given binary array
    vector<int> arr = { 1, 0, 0, 0, 1 };
 
    // Prints the maximum 0 to 1
    // conversions required
    maxPositionsOccupied(arr);
 
    return 0;
}

Java




// Java program for the above approach
public class GFG
{
 
  // Function to find the maximum count of 0s
  // required to be converted into 1s such
  // no pair of adjacent elements are 1
  static void maxPositionsOccupied(int[] arr)
  {
 
    // Base Case
    if (arr.length == 0)
    {
      System.out.print(0);
      return;
    }
 
    // Stores the maximum count of of 0s
    // that can be converted into 1s
    int ans = 0;
 
    // Stores index of array elements
    int i = 0;
 
    // Traverse the array
    while ((i < arr.length - 2))
    {
 
      // If adjacent elements are 0s
      if ((arr[i] == 0) &&
          (arr[i + 1] == 0) &&
          (arr[i + 2] == 0))
      {
 
        // Update ans
        ans++;
 
        // Update arr[i + 1]
        arr[i + 1] = 1;
      }
 
      // Update i
      i++;
    }
 
    // Print the answer
    System.out.print(ans);
  }
 
  // Driver code
  public static void main(String[] args)
  {
 
    // Given binary array
    int[] arr = { 1, 0, 0, 0, 1 };
 
    // Prints the maximum 0 to 1
    // conversions required
    maxPositionsOccupied(arr);
  }
}
 
// This code is contributed by divyeshrabadiya07.

Python3




# Python3 program for the above approach
 
# Function to find the maximum count of 0s
# required to be converted into 1s such
# no pair of adjacent elements are 1
def maxPositionsOccupied(arr):
     
    # Base Case
    if (len(arr) == 0):
        print(0)
 
    # Insert 0 at the end
    # of the array
    arr.append(0)
 
    # Insert 0 at the front
    # of the array
    arr.insert(0, 0)
 
    # Stores the maximum count of of 0s
    # that can be converted into 1s
    ans = 0
 
    # Stores index of array elements
    i = 0
 
    # Traverse the array
    while((i < len(arr) - 2)):
         
        # If adjacent elements are 0s
        if ((arr[i] == 0) and
            (arr[i + 1] == 0) and
            (arr[i + 2] == 0)):
 
            # Update ans
            ans += 1
 
            # Update arr[i + 1]
            arr[i + 1] = 1
 
        # Update i
        i += 1
 
    # Print the answer
    print(ans)
 
# Driver Code
if __name__ == '__main__':
     
    # Given binary array
    arr =  [ 1, 0, 0, 0, 1 ]
 
    # Prints the maximum 0 to 1
    # conversions required
    maxPositionsOccupied(arr)
 
# This code is contributed by SURENDRA_GANGWAR

C#




// C# program for the above approach
using System;
 
class GFG{
 
// Function to find the maximum count of 0s
// required to be converted into 1s such
// no pair of adjacent elements are 1
static void maxPositionsOccupied(int[] arr)
{
     
    // Base Case
    if (arr.Length == 0)
    {
        Console.Write(0);
        return;
    }
     
    // Stores the maximum count of of 0s
    // that can be converted into 1s
    int ans = 0;
   
    // Stores index of array elements
    int i = 0;
   
    // Traverse the array
    while ((i < arr.Length - 2))
    {
         
        // If adjacent elements are 0s
        if ((arr[i] == 0) &&
            (arr[i + 1] == 0) &&
            (arr[i + 2] == 0))
        {
             
            // Update ans
            ans++;
             
            // Update arr[i + 1]
            arr[i + 1] = 1;
        }
         
        // Update i
        i++;
    }
     
    // Print the answer
    Console.Write(ans);
}  
 
// Driver code
static void Main()
{
     
    // Given binary array
    int[] arr = { 1, 0, 0, 0, 1 };
     
    // Prints the maximum 0 to 1
    // conversions required
    maxPositionsOccupied(arr);
}
}
 
// This code is contributed by divyesh072019

Javascript




<script>
 
    // Javascript program for the above approach
     
    // Function to find the maximum count of 0s
    // required to be converted into 1s such
    // no pair of adjacent elements are 1
    function maxPositionsOccupied(arr)
    {
 
        // Base Case
        if (arr.length == 0)
        {
            document.write(0);
            return;
        }
 
        // Stores the maximum count of of 0s
        // that can be converted into 1s
        let ans = 0;
 
        // Stores index of array elements
        let i = 0;
 
        // Traverse the array
        while ((i < arr.length - 2))
        {
 
            // If adjacent elements are 0s
            if ((arr[i] == 0) &&
                (arr[i + 1] == 0) &&
                (arr[i + 2] == 0))
            {
 
                // Update ans
                ans++;
 
                // Update arr[i + 1]
                arr[i + 1] = 1;
            }
 
            // Update i
            i++;
        }
 
        // Print the answer
        document.write(ans);
    }
     
    // Given binary array
    let arr = [ 1, 0, 0, 0, 1 ];
      
    // Prints the maximum 0 to 1
    // conversions required
    maxPositionsOccupied(arr);
   
</script>
Output: 
1

 

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

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