The following algorithm is given: int foo(int x; y) if x == 0 return y y = 2 · y + x%2 return foo(x=2; y) (i) Compute foo(5, 0), foo(6, 0), foo(7, 0). (ii) What is the time complexity of the call foo(n, 0)? (iii) Let f1(n) = 12n + 11log(n) and f2(n) = 11 n + 12log(n). For each function, find to which of the following families it belongs: O(n); Ω(n); Θ(n); O(log n); Ω(log n); Θ(log n):

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Problems on numbers

Number theory is one of the most appealing topics in mathematics. Given one or more numeric values, a numeric algorithm performs some computation. The use of number theory in computing is important for applications like in the case of cryptographic algorithms. Number theory is also used in various applications such as calculating hash functions or in information security. Euclid’s algorithm is one of the oldest number-theoretic algorithms which is used to calculate the greatest common divisor of two numbers.