Witty Timmy

Timmy has two n n digit numbers. Using the long division method he learned in kindergarten, he divides the larger number by the smaller one. He wants to know roughly how much time this process takes. Which computational complexity best describes the long division of two n n digit numbers?

Details and assumptions

  • Any multiplication is carried out via school book multiplication.
O ( n ) O(n) O ( n 2 ) O(n^2) O ( n 2 n + 1 n ) O(n^{\frac{2n+1}{n}} ) O ( lg ( n ) ) O(\lg(n))

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