Minimum swaps required to make a binary string divisible by 2^k
Given a binary string S of length N and an integer K, the task is to find the minimum number of adjacent swaps required to make the binary string divisible by 2K. If it is not possible then print -1.
Input: S = “100111”, K = 2
Swapping the right-most zero 3 times
to the right, we get “101110”.
Swapping the second right-most zero
3 times to the right, we get “111100”.
Input: S = “1011”, K = 2
Method 1: An approach will be swapping from the right-most zero. So, let’s rephrase the problem to something simpler. The minimum number of swaps are required such that at least K consecutive zeros are made available at the right end.
One way will be to simulate the swapping. Starting from the right-most zero, swap it till it has 1 at its right, and it’s not the end of the string. This will be performed for the K rightmost zeros. The time complexity of this approach will be O(N * K).
Method 2: The key to performing better here will be to avoid doing the simulation.
Among the K right-most zeros, each zero will need to be swapped X number of times, where X is the number of 1s to the right of that zero.
Thus, for the K right-most zeros, the task is to find the sum of the number of 1s to the right of each of them.
- Initialize variable c_zero = 0, c_one = 0 and ans = 0.
- Run a loop from i = N – 1 to i = 0.
- If S[i] = 0 then update c_zero = c_zero + 1 and ans = ans + c_one.
- If S[i] = 1 then update c_one = c_one + 1.
- If c_zero = K then break.
- If c_zero < K then return -1.
- Finally, return the ans.
Thus, the time complexity of this approach will be O(N).
Below is the implementation of the above approach:
Time Complexity: O(|s|)
Auxiliary Space: O(1)