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Bitwise AND of N binary strings

  • Difficulty Level : Hard
  • Last Updated : 28 Jun, 2021

Given an array arr[] of binary strings, the task is to calculate the bitwise AND of all of these strings and print the resultant string.

Examples: 

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Input: arr[] = {"101", "110110", "111"}
Output: 000100
(000101) & (110110) & (000111) = 000100

Input: arr[] = {"110010101", "111101001"}
Output: 110000001
 

Approach 1: Similar to Add two bit strings(https://www.geeksforgeeks.org/add-two-bit-strings/) 
Given an array of N binary strings. We first compute the AND operation of the first two binary strings and then perform this “Result” with third binary string and so on till the last binary string. 
For Example, string arr[] = {“101”, “110110”, “111”}; 
Step 1: Result = 101 AND 110110; 
Step 2: Result = Result(Step1) AND 111; 
So on.. 



Below is the implementation of the above approach:  

C++




// C++ implementation of the above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Helper method: given two unequal sized
// bit strings, converts them to
// same length by adding leading 0s in the
// smaller string. Returns the the new length
int makeEqualLength(string &a, string &b)
{
    int len_a = a.length();
    int len_b = b.length();
     
    int num_zeros = abs(len_a-len_b);
     
    if (len_a<len_b)
    {
        for (int i = 0 ; i<num_zeros; i++)
        {
            a = '0' + a;
        }
        // Return len_b which is highest.
        // No need to proceed further!
        return len_b;
    }
    else
    {
        for (int i = 0 ; i<num_zeros; i++)
        {
            b = '0' + b;
        }
    }
    // Return len_a which is greater or
    // equal to len_b
    return len_a;
}
 
// The main function that performs AND
// operation of two-bit sequences
// and returns the resultant string
string andOperationBitwise(string s1, string s2)
{
    // Make both strings of same length with the
    // maximum length of s1 & s2.
    int length = makeEqualLength(s1,s2);
 
    // Initialize res as NULL string
    string res = "";
 
    // We start from left to right as we have
    // made both strings of same length.
    for (int i = 0 ; i<length; i++)
    {
        // Convert s1[i] and s2[i] to int and perform
        // bitwise AND operation, append to "res" string
        res = res + (char)((s1[i] - '0' & s2[i]-'0')+'0');
    }
    return res;
}
 
//Driver Code
int main()
{
    string arr[] = {"101", "110110", "111"};
    int n = sizeof(arr)/sizeof(arr[0]);
     
    string result;
     
    // Check corner case: If there is just one
    // binary string, then print it and return.
    if (n<2)
    {
        cout<<arr[n-1]<<endl;
        return 0;
    }
    result = arr[0];
    for (int i = 1; i<n; i++)
    {
        result = andOperationBitwise(result, arr[i]);
    }
    cout <<result<<endl;
}
// This code has been contributed by sharathmaidargi

Python3




# Python3 implementation of above approach
 
# this function takes two unequal sized
# bit strings, converts them to
# same length by adding leading 0s in the
# smaller string. Returns the the new length
def makeEqualLength(a, b):
    len_a = len(a)
    len_b = len(b)
     
    num_zeros = abs(len_a - len_b)
     
    if (len_a < len_b):
        for i in range(num_zeros):
            a = '0' + a
             
        # Return len_b which is highest.
        # No need to proceed further!
        return len_b, a, b
 
    else:
        for i in range(num_zeros):
            b = '0' + b
             
    # Return len_a which is greater or
    # equal to len_b
    return len_a, a, b
 
# The main function that performs AND
# operation of two-bit sequences
# and returns the resultant string
def andOperationBitwise(s1, s2):
     
    # Make both strings of same length
    # with the maximum length of s1 & s2.
    length, s1, s2 = makeEqualLength(s1, s2)
 
    # Initialize res as NULL string
    res = ""
 
    # We start from left to right as we have
    # made both strings of same length.
    for i in range(length):
         
        # Convert s1[i] and s2[i] to int
        # and perform bitwise AND operation,
        # append to "res" string
        res = res + str(int(s1[i]) & int(s2[i]))
         
    return res
 
# Driver Code
arr = ["101", "110110", "111"]
n = len(arr)
if (n < 2):
    print(arr[n - 1])
     
else:
    result = arr[0]
    for i in range(n):
        result = andOperationBitwise(result, arr[i]);
 
    print(result)
     
# This code is contributed by
# ANKITKUMAR34

Javascript




<script>
 
// Javascript implementation of the above approach
 
// Helper method: given two unequal sized
// bit strings, converts them to
// same length by adding leading 0s in the
// smaller string. Returns the the new length
let s1, s2;
 
function makeEqualLength()
{
    let len_a = s1.length;
    let len_b = s2.length;
 
    let num_zeros = Math.abs(len_a - len_b);
 
    if (len_a < len_b)
    {
        for(let i = 0; i < num_zeros; i++)
        {
            s1 = '0' + s1;
        }
         
        // Return len_b which is highest.
        // No need to proceed further!
        return len_b;
    }
    else
    {
        for(let i = 0; i < num_zeros; i++)
        {
            s2 = '0' + s2;
        }
    }
     
    // Return len_a which is greater or
    // equal to len_b
    return len_a;
}
 
// The main function that performs AND
// operation of two-bit sequences
// and returns the resultant string
function andOperationBitwise()
{
     
    // Make both strings of same length with the
    // maximum length of s1 & s2.
    let length = makeEqualLength();
 
    // Initialize res as NULL string
    let res = "";
 
    // We start from left to right as we have
    // made both strings of same length.
    for(let i = 0 ; i<length; i++)
    {
         
        // Convert s1[i] and s2[i] to int
        // and perform bitwise AND operation,
        // append to "res" string
        res = res + String.fromCharCode((s1[i].charCodeAt() -
                                           '0'.charCodeAt() &
                                         s2[i].charCodeAt() -
                                           '0'.charCodeAt()) +
                                           '0'.charCodeAt());
    }
    return res;
}
 
// Driver code
let arr = [ "101", "110110", "111" ];
let n = arr.length;
let result;
  
// Check corner case: If there is just one
// binary string, then print it and return.
if (n < 2)
{
    document.write(arr[n - 1] + "</br>");
}
result = arr[0];
for(let i = 1; i<n; i++)
{
    s1 = result;
    s2 = arr[i];
    result = andOperationBitwise();
}
document.write(result);
 
// This code is contributed by vaibhavrabadiya3
 
</script>
Output: 
000100

 

Approach 2: Find the size of the smallest and the largest string. We need this to add (largest-smallest) zeroes to our result. For example, if we have 0010 and 11, then AND on these strings will be 0010 (since we can write 11 as 0011). Then perform AND operation on each bit.
We can achieve this by only finding if the current bit in any string is 0 or not. If current bit is 0 in any of the given strings, then AND operation on that bit will be 0. If all bits at the current position are 1, then AND operation will be 1.

Below is the implementation of the above approach:  

C++




// C++ implementation of the above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the bitwise AND of
// all the binary strings
string strBitwiseAND(string* arr, int n)
{
    string res;
 
    // To store the largest and the smallest
    // string's size, We need this to add '0's
    // in the resultant string
    int smallest_size = INT_MAX;
    int largest_size = INT_MIN;
 
    // Reverse each string
    // Since we need to perform AND operation
    // on bits from Right to Left
    for (int i = 0; i < n; i++) {
        reverse(arr[i].begin(), arr[i].end());
 
        // Update the respective length values
        smallest_size = min(smallest_size, (int)arr[i].size());
        largest_size = max(largest_size, (int)arr[i].size());
    }
 
    // Traverse bits from 0 to smallest string's size
    for (int i = 0; i < smallest_size; i++) {
        bool all_ones = true;
 
        for (int j = 0; j < n; j++) {
 
            // If at this bit position, there is a 0
            // in any of the given strings then AND
            // operation on current bit position
            // will be 0
            if (arr[j][i] == '0') {
 
                all_ones = false;
                break;
            }
        }
 
        // Add resultant bit to result
        res += (all_ones ? '1' : '0');
    }
 
    // Add 0's to the string.
    for (int i = 0; i < largest_size - smallest_size; i++)
        res += '0';
 
    // Reverse the string
    // Since we started from LEFT to RIGHT
    reverse(res.begin(), res.end());
 
    // Return the resultant string
    return res;
}
 
// Driver code
int main()
{
    string arr[] = { "101", "110110", "111" };
 
    int n = sizeof(arr) / sizeof(arr[0]);
 
    cout << strBitwiseAND(arr, n);
 
    return 0;
}

Java




// Java implementation of the above approach
class GfG
{
 
    // Function to find the bitwise AND of
    // all the binary strings
    static String strBitwiseAND(String[] arr, int n)
    {
        String res = "";
     
        // To store the largest and the smallest
        // string's size, We need this to add
        // '0's in the resultant string
        int smallest_size = Integer.MAX_VALUE;
        int largest_size = Integer.MIN_VALUE;
     
        // Reverse each string
        // Since we need to perform AND operation
        // on bits from Right to Left
        for (int i = 0; i < n; i++)
        {
             
            StringBuilder temp = new StringBuilder();
            temp.append(arr[i]);
            arr[i] = temp.reverse().toString();
     
            // Update the respective length values
            smallest_size = Math.min(smallest_size, arr[i].length());
            largest_size = Math.max(largest_size, arr[i].length());
        }
     
        // Traverse bits from 0 to smallest string's size
        for (int i = 0; i < smallest_size; i++)
        {
            boolean all_ones = true;
     
            for (int j = 0; j < n; j++)
            {
     
                // If at this bit position, there is a 0
                // in any of the given strings then AND
                // operation on current bit position
                // will be 0
                if (arr[j].charAt(i) == '0')
                {
     
                    all_ones = false;
                    break;
                }
            }
     
            // Add resultant bit to result
            res += (all_ones ? '1' : '0');
        }
     
        // Add 0's to the string.
        for (int i = 0; i < largest_size - smallest_size; i++)
            res += '0';
     
        // Reverse the string
        // Since we started from LEFT to RIGHT
        StringBuilder temp = new StringBuilder();
        temp.append(res);
        res = temp.reverse().toString();
     
        // Return the resultant string
        return res;
    }
 
    // Driver code
    public static void main(String []args)
    {
         
        String arr[] = { "101", "110110", "111" };
        int n = arr.length;
     
        System.out.println(strBitwiseAND(arr, n));
    }
}
 
// This code is contributed by Rituraj Jain

Python3




# Python3 implementation of the above approach
import sys;
 
# Function to find the bitwise AND of
# all the binary strings
def strBitwiseAND(arr, n) :
     
    res = ""
     
    # To store the largest and the smallest
    # string's size, We need this to add '0's
    # in the resultant string
    smallest_size = sys.maxsize;
    largest_size = -(sys.maxsize - 1);
     
    # Reverse each string
    # Since we need to perform AND operation
    # on bits from Right to Left
    for i in range(n) :
        arr[i] = arr[i][::-1] ;
         
        # Update the respective length values
        smallest_size = min(smallest_size, len(arr[i]));
        largest_size = max(largest_size, len(arr[i]));
     
    # Traverse bits from 0 to smallest string's size
    for i in range(smallest_size) :
        all_ones = True;
         
        for j in range(n) :
             
            # If at this bit position, there is a 0
            # in any of the given strings then AND
            # operation on current bit position
            # will be 0
            if (arr[j][i] == '0') :
                all_ones = False;
                break;
         
        # Add resultant bit to result
        if all_ones :
            res += '1' ;
        else :
            res += '0' ;
     
    # Add 0's to the string.
    for i in range(largest_size - smallest_size) :
        res += '0';
     
    # Reverse the string
    # Since we started from LEFT to RIGHT
    res = res[::-1];
 
    # Return the resultant string
    return res;
 
 
# Driver code
if __name__ == "__main__" :
 
    arr = [ "101", "110110", "111" ];
 
    n = len(arr) ;
 
    print(strBitwiseAND(arr, n));
     
# This code is contributed by Ryuga

C#




// C# implementation of the above approach:
using System;
 
class GfG
{
 
    // Function to find the bitwise AND of
    // all the binary strings
    static String strBitwiseAND(String[] arr, int n)
    {
        String res = "";
     
        // To store the largest and the smallest
        // string's size, We need this to add
        // '0's in the resultant string
        int smallest_size = int.MaxValue;
        int largest_size = int.MinValue;
     
        // Reverse each string
        // Since we need to perform AND operation
        // on bits from Right to Left
        String temp ="";
        for (int i = 0; i < n; i++)
        {
             
             
            temp+=arr[i];
            arr[i] = reverse(temp);
     
            // Update the respective length values
            smallest_size = Math.Min(smallest_size, arr[i].Length);
            largest_size = Math.Max(largest_size, arr[i].Length);
        }
     
        // Traverse bits from 0 to smallest string's size
        for (int i = 0; i < smallest_size; i++)
        {
            bool all_ones = true;
     
            for (int j = 0; j < n; j++)
            {
     
                // If at this bit position, there is a 0
                // in any of the given strings then AND
                // operation on current bit position
                // will be 0
                if (arr[j][i] == '0')
                {
     
                    all_ones = false;
                    break;
                }
            }
     
            // Add resultant bit to result
            res += (all_ones ? '1' : '0');
        }
     
        // Add 0's to the string.
        for (int i = 0; i < largest_size - smallest_size; i++)
            res += '0';
     
        // Reverse the string
        // Since we started from LEFT to RIGHT
        String temp1 = "";
        temp1+=res;
        res = reverse(temp1);
     
        // Return the resultant string
        return res;
    }
     
    static String reverse(String input)
    {
        char[] temparray = input.ToCharArray();
        int left, right = 0;
        right = temparray.Length - 1;
 
        for (left = 0; left < right; left++, right--)
        {
            // Swap values of left and right
            char temp = temparray[left];
            temparray[left] = temparray[right];
            temparray[right] = temp;
        }
        return String.Join("",temparray);
    }
     
    // Driver code
    public static void Main(String []args)
    {
         
        String []arr = { "101", "110110", "111" };
        int n = arr.Length;
     
        Console.WriteLine(strBitwiseAND(arr, n));
    }
}
 
// This code has been contributed by 29AjayKumar

Javascript




<script>
 
    // JavaScript implementation of the above approach:
     
    // Function to find the bitwise AND of
    // all the binary strings
    function strBitwiseAND(arr, n)
    {
        let res = "";
       
        // To store the largest and the smallest
        // string's size, We need this to add
        // '0's in the resultant string
        let smallest_size = Number.MAX_VALUE;
        let largest_size = Number.MIN_VALUE;
       
        // Reverse each string
        // Since we need to perform AND operation
        // on bits from Right to Left
        let temp ="";
        for (let i = 0; i < n; i++)
        {
               
               
            temp+=arr[i];
            arr[i] = reverse(temp);
       
            // Update the respective length values
            smallest_size = Math.min(smallest_size, arr[i].length);
            largest_size = Math.max(largest_size, arr[i].length);
        }
       
        // Traverse bits from 0 to smallest string's size
        for (let i = 0; i < smallest_size; i++)
        {
            let all_ones = true;
       
            for (let j = 0; j < n; j++)
            {
       
                // If at this bit position, there is a 0
                // in any of the given strings then AND
                // operation on current bit position
                // will be 0
                if (arr[j][i] == '0')
                {
       
                    all_ones = false;
                    break;
                }
            }
       
            // Add resultant bit to result
            res += (all_ones ? '1' : '0');
        }
       
        // Add 0's to the string.
        for (let i = 0; i < largest_size - smallest_size; i++)
            res += '0';
       
        // Reverse the string
        // Since we started from LEFT to RIGHT
        let temp1 = "";
        temp1+=res;
        res = reverse(temp1);
       
        // Return the resultant string
        let temparray1 = res;
        let Temparray = "";
        for(let i = 6; i < temparray1.length; i++)
        {
            Temparray = Temparray + temparray1[i];
        }
        return Temparray;
    }
       
    function reverse(input)
    {
        let temparray = input.split('');
        let left, right = 0;
        right = temparray.length - 1;
   
        for (left = 0; left < right; left++, right--)
        {
            // Swap values of left and right
            let temp = temparray[left];
            temparray[left] = temparray[right];
            temparray[right] = temp;
        }
        return temparray.join("");
    }
     
    let arr = [ "101", "110110", "111" ];
    let n = arr.length;
 
    document.write(strBitwiseAND(arr, n));
     
</script>
Output: 
000100

 




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