Minimize hamming distance in Binary String by setting only one K size substring bits
Given two binary strings S and T of length N and a positive integer K. Initially, all characters of T are ‘0’. The task is to find the minimum Hamming distance after choosing a substring of size K and making all elements of string T as ‘1’ only once.
Input: S = “101”, K = 2
Explanation: Initially string T = “000”, one possible way is to change all 0s in range [0, 1] to 1. Thus string T becomes “110” and the hamming distance between S and T is 2 which is the minimum possible.
Input: S = “1100”, K=3
Naive Approach: The simplest approach is to consider every substring of size K and make all the elements as 1 and then check the hamming distance with string, S. After checking all the substrings, print the minimum hamming distance.
Time Complexity: O(N×K)
Auxiliary Space: O(1)
- Create a prefix sum array pref of string S by initializing pref as 0 updating pref[i] as pref[i-1] +(S[i] – ‘0’) for every index i.
- Store the total count of ones in the string, S in a variable cnt.
- Initialize a variable ans as cnt to store the required result.
- Iterate in the range [0, N-K] using the variable i
- Initialize a variable val as pref[i+K-1] – pref[i-1] to store the count of ones in the substring S[i, i+K-1].
- Create two variables A and B to store the hamming distance outside the current substring and the hamming distance inside the current substring and initialize A with cnt – K and B with K – val.
- Update the value of ans with the minimum of ans and (A + B).
- Print the value of ans as the result.
Below is the implementation of the above approach:
Time Complexity: O(N)
Auxiliary Space: O(N)
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready. To complete your preparation from learning a language to DS Algo and many more, please refer Complete Interview Preparation Course.