Given a sequence of three binary sequences A, B and C of N bits. Count the minimum bits required to flip in A and B such that XOR of A and B is equal to C. For Example :
Input: N = 3 A = 110 B = 101 C = 001 Output: 1 We only need to flip the bit of 2nd position of either A or B, such that A ^ B = C i.e., 100 ^ 101 = 001
A Naive approach is to generate all possible combination of bits in A and B and then XORing them to Check whether it is equal to C or not. Time complexity of this approach grows exponentially so it would not be better for large value of N.
An Efficient approach is to use concept of XOR.
XOR Truth Table Input Output X Y Z 0 0 - 0 0 1 - 1 1 0 - 1 1 1 - 0
If we generalize, we will find that at any position of A and B, we just only need to flip ith (0 to N-1) position of either A or B otherwise we will not able to achieve minimum no of Bits.
So at any position of i (0 to N-1) you will encounter two type of situation i.e., either A[i] == B[i] or A[i] != B[i]. Let’s discuss it one by one.
If A[i] == B[i] then XOR of these bits will be 0, two cases arise in C: C[i]==0 or C[i]==1.
If C[i] == 0, then no need to flip the bit but if C[i] == 1 then we have to flip the bit either in A[i] or B[i] so that 1^0 == 1 or 0^1 == 1.
If A[i] != B[i] then XOR of these Bits gives a 1, In C two cases again arise i.e., either C[i] == 0 or C[i] == 1.
Therefore if C[i] == 1, then we need not to flip the bit but if C[i] == 0, then we need to flip the bit either in A[i] or B[i] so that 0^0==0 or 1^1==0
Time Complexity: O(N)
Auxiliary space: O(1)
This article is contributed by Shubham Bansal. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.”
- Count pairs in an array such that both elements has equal set bits
- Check if bits of a number has count of consecutive set bits in increasing order
- XOR of all elements of array with set bits equal to K
- Sorting array elements with set bits equal to K
- Count set bits in a range
- Count set bits in an integer
- Range query for count of set bits
- Sort an array according to count of set bits | Set 2
- Count total set bits in all numbers from 1 to N | Set 3
- Count pairs (A, B) such that A has X and B has Y number of set bits and A+B = C
- Count unset bits of a number
- Count total bits in a number
- Count unset bits in a range
- Count total set bits in all numbers from 1 to n
- Python | Count set bits in a range
Improved By : nitin mittal