What is the worst-case time complexity of the Karatsuba algorithm for multiplying two n-digit numbers?
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O(n^log2(3))
Karatsuba is a divide-and-conquer algorithm that reduces four sub-multiplications to three. Its complexity is approximately O(n^1.585), significantly faster than the O(n^2) schoolbook multiplication.
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- What is the worst-case time complexity of Karatsuba's multiplication algorithm for two n-digit numbers?