Python Program to Count Minimum Bits to Flip such that XOR of A and B Equal to C

In the previous article, we have discussed Python Program to Check if a Number has Bits in Alternate Pattern

Given an N-bit binary sequence consisting of three binary sequences A, B, and C. Count the minimal number of bits required to flip A and B in such a way that the XOR of A and B equals C.

X Y X XOR Y

0 0 0

0 1 1

1 0 1

1 1 0

Cases:

If A[i]==B[i] and C[i]==0 then no flip,
If A[i]==B[i] and C[i]==1 then flip either A[i] or B[i] and increase flip count by 1
If A[i]!=B[i] and C[i]==0 then flip either A[i] or B[i] and increase flip count by 1
If A[i]!=B[i] and C[i]==1 then no flip required.

Examples:

Example1:

Input:

Given number = 5
Given first string=  "11011"
Given second string= "11001"
Given third string = "11100"

Output:

The count of minimum bits to Flip in such a way that the XOR of A and B equals C =  4

Example2:

Input:

Given number = 3
Given first string= "110"
Given second string= "111"
Given third string = "101"

Output:

The count of minimum bits to Flip in such a way that the XOR of A and B equals C =  1

Program to Count Minimum Bits to Flip such that XOR of A and B Equal to C in Python

Below are the ways to Count the minimal number of bits required to flip A and B in such a way that the XOR of A and B equals C:

Using For Loop (Static Input)
Using For loop (User Input)

Method #1: Using For Loop (Static Input)

Approach:

Give the number (which is the count of bits) as static input and store it in a variable.
Give the first binary sequence string as static input and store it in another variable.
Give the second binary sequence string as static input and store it in another variable.
Give the third binary sequence string as static input and store it in another variable.
Pass the given three sequence strings and the given number as the arguments to the Flips_Count function.
Create a function to say Flips_Count which takes the given three sequence strings and the given number as the arguments and returns the count of minimum bits to Flip in such a way that the XOR of A and B equals C.
Take a variable say totl_cnt and initialize its value to 0.
Loop till the given number using the for loop.
Check if the fst_seqnce[itr] == scnd_seqnce[itr] and third_seqnce[itr] == ‘1’ using the if conditional statement.
If the statement is true, then increment the value of above totl_cnt by 1.
Store it in the same variable.
Check if the fst_seqnce[itr] != scnd_seqnce[itr] and third_seqnce[itr] == ‘0’ using the elif conditional statement.
If the statement is true, then increment the value of above totl_cnt by 1.
Store it in the same variable.
Return the value of totl_cnt.
Print the count of minimum bits to Flip in such a way that the XOR of A and B equals C.
The Exit of the Program.

Below is the implementation:

# Create a function to say Flips_Count which takes the given three sequence
# strings and the given number as the arguments and returns the count of minimum bits
# to Flip in such a way that the XOR of A and B equals C.


def Flips_Count(fst_seqnce, scnd_seqnce, third_seqnce, numb):
    # Take a variable say totl_cnt and initialize its value to 0.
    totl_cnt = 0
    # Loop till the given number using the for loop.
    for itr in range(numb):
        # Check if the fst_seqnce[itr] == scnd_seqnce[itr] and third_seqnce[itr] == '1'
        # using the if conditional statement.
        if fst_seqnce[itr] == scnd_seqnce[itr] and third_seqnce[itr] == '1':
          # If the statement is true, then increment the value of above totl_cnt by 1.
          # Store it in the same variable.
            totl_cnt = totl_cnt+1

        # Check if the fst_seqnce[itr] != scnd_seqnce[itr] and third_seqnce[itr] == '0' using
        # the elif conditional statement.
        elif fst_seqnce[itr] != scnd_seqnce[itr] and third_seqnce[itr] == '0':
          # If the statement is true, then increment the value of above totl_cnt by 1.
          # Store it in the same variable.
            totl_cnt = totl_cnt+1
    # Return the value of totl_cnt.
    return totl_cnt


# Give the number (which is the count of bits) as static input and store it in a variable.
numb = 5
# Give the first binary sequence string as static input and store it in another variable.
fst_seqnce = "11011"
# Give the second binary sequence string as static input and store it in another variable.
scnd_seqnce = "11001"
# Give the third binary sequence string as static input and store it in another variable.
third_seqnce = "11100"
# Pass the given three sequence strings and the given number as the arguments to the
# Flips_Count function.
# Print the count of minimum bits to Flip in such a way that the XOR of A and B equals C.
print("The count of minimum bits to Flip in such a way that the XOR of A and B equals C = ",
      Flips_Count(fst_seqnce, scnd_seqnce, third_seqnce, numb))

Output:

The count of minimum bits to Flip in such a way that the XOR of A and B equals C =  4

Method #2: Using For loop (User Input)

Approach:

Give the number (which is the count of bits) as user input using the int(input()) function and store it in a variable.
Give the first binary sequence string as user input using the input() function and store it in another variable.
Give the second binary sequence string as user input using the input() function and store it in another variable.
Give the third binary sequence string as user input using the input() function and store it in another variable.
Pass the given three sequence strings and the given number as the arguments to the Flips_Count function.
Create a function to say Flips_Count which takes the given three sequence strings and the given number as the arguments and returns the count of minimum bits to Flip in such a way that the XOR of A and B equals C.
Take a variable say totl_cnt and initialize its value to 0.
Loop till the given number using the for loop.
Check if the fst_seqnce[itr] == scnd_seqnce[itr] and third_seqnce[itr] == ‘1’ using the if conditional statement.
If the statement is true, then increment the value of above totl_cnt by 1.
Store it in the same variable.
Check if the fst_seqnce[itr] != scnd_seqnce[itr] and third_seqnce[itr] == ‘0’ using the elif conditional statement.
If the statement is true, then increment the value of above totl_cnt by 1.
Store it in the same variable.
Return the value of totl_cnt.
Print the count of minimum bits to Flip in such a way that the XOR of A and B equals C.
The Exit of the Program.

Below is the implementation:

# Create a function to say Flips_Count which takes the given three sequence
# strings and the given number as the arguments and returns the count of minimum bits
# to Flip in such a way that the XOR of A and B equals C.


def Flips_Count(fst_seqnce, scnd_seqnce, third_seqnce, numb):
    # Take a variable say totl_cnt and initialize its value to 0.
    totl_cnt = 0
    # Loop till the given number using the for loop.
    for itr in range(numb):
        # Check if the fst_seqnce[itr] == scnd_seqnce[itr] and third_seqnce[itr] == '1'
        # using the if conditional statement.
        if fst_seqnce[itr] == scnd_seqnce[itr] and third_seqnce[itr] == '1':
          # If the statement is true, then increment the value of above totl_cnt by 1.
          # Store it in the same variable.
            totl_cnt = totl_cnt+1

        # Check if the fst_seqnce[itr] != scnd_seqnce[itr] and third_seqnce[itr] == '0' using
        # the elif conditional statement.
        elif fst_seqnce[itr] != scnd_seqnce[itr] and third_seqnce[itr] == '0':
          # If the statement is true, then increment the value of above totl_cnt by 1.
          # Store it in the same variable.
            totl_cnt = totl_cnt+1
    # Return the value of totl_cnt.
    return totl_cnt


# Give the number (which is the count of bits) as user input using the int(input()) function 
# and store it in a variable.
numb = int(input('Enter some random number = '))
# Give the first binary sequence string as user input using the input() function and 
# store it in another variable.
fst_seqnce = input('Enter some random binary number string  = ')
# Give the second binary sequence string as user input using the input() function and 
# store it in another variable.
scnd_seqnce = input('Enter some random binary number string  = ')
# Give the third binary sequence string as user input using the input() function and 
# store it in another variable.
third_seqnce = input('Enter some random binary number string  = ')
# Pass the given three sequence strings and the given number as the arguments to the
# Flips_Count function.
# Print the count of minimum bits to Flip in such a way that the XOR of A and B equals C.
print("The count of minimum bits to Flip in such a way that the XOR of A and B equals C = ",
      Flips_Count(fst_seqnce, scnd_seqnce, third_seqnce, numb))

Output:

Enter some random number = 3
Enter some random binary number string = 110
Enter some random binary number string = 111
Enter some random binary number string = 101
The count of minimum bits to Flip in such a way that the XOR of A and B equals C = 1

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