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+It can be established that the rows that become 1 in the end are same in the beginning. So, keep a count of the frequency of every distinct row and since we have to perform exactly k operations, find the row with maximum frequency and (noOfZeros — k)%2 == 0. The answer is the frequency of that row.
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Men's restroom problem : It is a well-researched fact that men in a restroom generally prefer to maximize their distance from already occupied stalls, by occupying the middle of the longest sequence of unoccupied places. For detailed version, check the following link.
Link : https://stackoverflow.com/questions/32645046/urinal-algorithm-a-simple-optimization
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+ Hint : Use priority_queue to store distances