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The order of an algorithm that finds whether a given Boolean function of ‘n’ variables, produces a 1 is
- a)Constant
- b)Linear
- c)Logarithmic
- d)Exponential
Correct answer is option 'D'. Can you explain this answer?
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The order of an algorithm that finds whether a given Boolean function ...
In the worst case it has to check all the 2n possible input combinations, which is exponential.
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The order of an algorithm that finds whether a given Boolean function ...
$n$ variables is true or false can vary depending on the specific algorithm used.
One possible algorithm is the brute force method, which involves evaluating the function for all possible input combinations of the $n$ variables. This would require $2^n$ evaluations and therefore has a worst-case time complexity of $O(2^n)$.
However, there are more efficient algorithms that can solve this problem in polynomial time. For example, the Quine-McCluskey algorithm can find the minimal form of a Boolean function in polynomial time, and therefore can determine whether a Boolean function is true or false in polynomial time as well. The time complexity of this algorithm is $O(2^{2n})$, which is much better than the brute force method for large values of $n$.
Overall, the order of an algorithm that finds whether a given Boolean function of $n$ variables is true or false can range from exponential to polynomial, depending on the specific algorithm used.
One possible algorithm is the brute force method, which involves evaluating the function for all possible input combinations of the $n$ variables. This would require $2^n$ evaluations and therefore has a worst-case time complexity of $O(2^n)$.
However, there are more efficient algorithms that can solve this problem in polynomial time. For example, the Quine-McCluskey algorithm can find the minimal form of a Boolean function in polynomial time, and therefore can determine whether a Boolean function is true or false in polynomial time as well. The time complexity of this algorithm is $O(2^{2n})$, which is much better than the brute force method for large values of $n$.
Overall, the order of an algorithm that finds whether a given Boolean function of $n$ variables is true or false can range from exponential to polynomial, depending on the specific algorithm used.
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The order of an algorithm that finds whether a given Boolean function of ‘n’ variables, produces a 1 isa)Constantb)Linearc)Logarithmicd)ExponentialCorrect answer is option 'D'. Can you explain this answer?
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