Given a binary string and a number k, task is to check whether the binary string is evenly divisible by 2k or not.
Input : 11000 k = 2 Output : Yes Explanation : (11000)2 = (24)10 24 is evenly divisible by 2k i.e. 4. Input : 10101 k = 3 Output : No Explanation : (10101)2 = (21)10 21 is not evenly divisible by 2k i.e. 8.
Naive Approach : Compute the binary string into decimal and then simply check whether it is divisible by 2k. But, this approach is not feasible for long binary string as time complexity will be high for computing decimal number from binary string and then dividing it by 2k.
Efficient Approach : In the binary string, check for last k bits. If the all the last k bits are 0, then the binary number is evenly divisible by 2k else it is not evenly divisible. Time complexity using this approach is O(k).
Below is the implementation of the approach.
Time Complexity: O(k)
- Check divisibility in a binary stream
- Python | Check if a given string is binary string or not
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- Check if a binary string has a 0 between 1s or not | Set 2 (Regular Expression Approach)
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