Reduce a given Binary Array to a single element by removal of Triplets

Given an binary array arr[] of size N, the task is to reduce the array to a single element by the following two operations:

• A triplet of consecutive 0‘s or 1‘s remains unchanged.
• A triplet of consecutive array elements consisting of two 0’s and a single 1 or vice versa can be converted to more frequent element.

Examples:

Input: arr[] = {0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1} 
Output: No 
Explanation:
Following are the operations performed on the array: 
{0, 1, 1} -> 1 modifies the array to {1, 1, 1, 0, 0, 1, 1, 1, 1} 
{1, 0, 0} -> 0 modifies the array to {1, 1, 0, 1, 1, 1, 1} 
{1, 0, 1} -> 1 modifies the array to {1, 1, 1, 1, 1} 
Since, all the remaining elements are 1, they remain unchanged. 
Therefore, the array cannot be reduced to a single element.

Input: arr[] = {1, 0, 0, 0, 1, 1, 1} 
Output: Yes 
Explanation:
Following are the operations performed on the array: 
{1, 0, 0} -> 0 {0, 0, 1, 1, 1} 
{0, 0, 1} -> 0 {0, 1, 1} 
{0, 1, 1} -> 1 {1}

Approach: 
Follow the steps below to solve the problem:  

• Count the frequency of 0‘s and 1‘s.
• Calculate the absolute difference their respective counts.
• If the difference is 1, only then the array can be reduced to 1. Therefore, print Yes.
• Otherwise, print No.

Below is the implementation of the above approach: 

C++

// C++ program to implement
// the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to check if it is possible to
// reduce the array to a single element
void solve(int arr[], int n)
{
    // Stores frequency of 0's
    int countzeroes = 0;

    // Stores frequency of 1's
    int countones = 0;

    for (int i = 0; i < n; i++) {

        if (arr[i] == 0)
            countzeroes++;
        else
            countones++;
    }

    // Condition for array to be reduced
    if (abs(countzeroes - countones) == 1)
        cout << "Yes";

    // Otherwise
    else
        cout << "No";
}

// Driver Code
int main()
{
    int arr[] = { 0, 1, 0, 0, 1, 1, 1 };

    int n = sizeof(arr) / sizeof(arr[0]);

    solve(arr, n);

    return 0;
}

Java

// Java program to implement
// the above approach
class GFG{

// Function to check if it is possible to
// reduce the array to a single element
static void solve(int arr[], int n)
{

    // Stores frequency of 0's
    int countzeroes = 0;

    // Stores frequency of 1's
    int countones = 0;

    for(int i = 0; i < n; i++)
    {
        if (arr[i] == 0)
            countzeroes++;
        else
            countones++;
    }

    // Condition for array to be reduced
    if (Math.abs(countzeroes - countones) == 1)
        System.out.print("Yes");

    // Otherwise
    else
        System.out.print("No");
}

// Driver Code
public static void main(String[] args)
{
    int arr[] = { 0, 1, 0, 0, 1, 1, 1 };

    int n = arr.length;

    solve(arr, n);
}
}

// This code is contributed by 29AjayKumar

Python3

# Python3 program to implement
# the above approach

# Function to check if it is possible to
# reduce the array to a single element
def solve(arr, n):

    # Stores frequency of 0's
    countzeroes = 0;

    # Stores frequency of 1's
    countones = 0;

    for i in range(n):
        if (arr[i] == 0):
            countzeroes += 1;
        else:
            countones += 1;

    # Condition for array to be reduced
    if (abs(countzeroes - countones) == 1):
        print("Yes");

    # Otherwise
    else:
        print("No");

# Driver Code
if __name__ == '__main__':

    arr = [ 0, 1, 0, 0, 1, 1, 1 ];

    n = len(arr);

    solve(arr, n);

# This code is contributed by Amit Katiyar

C#

// C# program to implement
// the above approach
using System;

class GFG{

// Function to check if it is possible to
// reduce the array to a single element
static void solve(int []arr, int n)
{

    // Stores frequency of 0's
    int countzeroes = 0;

    // Stores frequency of 1's
    int countones = 0;

    for(int i = 0; i < n; i++)
    {
        if (arr[i] == 0)
            countzeroes++;
        else
            countones++;
    }

    // Condition for array to be reduced
    if (Math.Abs(countzeroes - countones) == 1)
        Console.Write("Yes");

    // Otherwise
    else
        Console.Write("No");
}

// Driver Code
public static void Main(String[] args)
{
    int []arr = { 0, 1, 0, 0, 1, 1, 1 };

    int n = arr.Length;

    solve(arr, n);
}
}

// This code is contributed by 29AjayKumar

Javascript

<script>

// Javascript program to implement
// the above approach

// Function to check if it is possible to
// reduce the array to a single element
function solve(arr, n)
{

    // Stores frequency of 0's
    var countzeroes = 0;

    // Stores frequency of 1's
    var countones = 0;

    for(var i = 0; i < n; i++)
    {
        if (arr[i] == 0)
            countzeroes++;
        else
            countones++;
    }

    // Condition for array to be reduced
    if (Math.abs(countzeroes - countones) == 1)
        document.write( "Yes");

    // Otherwise
    else
        document.write( "No");
}

// Driver Code
var arr = [ 0, 1, 0, 0, 1, 1, 1 ];
var n = arr.length;

solve(arr, n);

// This code is contributed by rutvik_56

</script>

Output:

Yes

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