Maximum contiguous 1 possible in a binary string after k rotations
Given a binary string, you can rotate any substring of this string. For Example, let string be denoted by s. Let the first element of string be represented by s, second element be represented by s and so on.
s = “100110111”
Suppose, we rotate the substring starting from s and ending at s. Then the string after this operation will be:
Resultant String = “101100111”
Now, you are allowed to do at most k operations to rotate any substring. You have to tell the maximum number of contiguous 1 you can make in this string in k or less than k rotations of substring.
Input : 100011001
k = 1
Output : 3
k is 1, hence you can rotate only once. Rotate the substring starting from s and ending at s. The resultant string will be : 111000001. Hence, maximum contiguous 1 are 3.
Input : 001100111000110011100
k = 2
Output : 8
k is 2, hence you can rotate twice. Rotate the substring starting at s and ending at s. Resultant string after first rotation : 001100001100011111100. Then, rotate the substring starting at s and ending at s. Resultant string after second rotation : 001100000001111111100. Hence, maximum number of contiguous 1 are 8.
Concept For Solving:
In order to solve this problem, we will maintain the frequency of 1’s in portion of contiguous 1’s in the original string in a multiset. Then on each rotation, we will rotate that substring such that, 2 portions of contiguous 1(with maximum frequency) in the string come together. We will do this, by sorting the multiset from greatest to smallest element. We will take out top 2 elements of multiset and insert their sum back into the multiset. We will continue to do this until k rotations are completed or number of elements in multiset is reduced to 1.