Question: (a) Consider the following algorithm. Input: A non-negative integer n. (1) If 0 n < 10, output n and stop. Otherwise, go to step

(a) Consider the following algorithm. Input: A non-negative integer n. (1) If 0 n < 10, output n and stop.

(a) Consider the following algorithm. Input: A non-negative integer n. (1) If 0 n < 10, output n and stop. Otherwise, go to step (2). n- (n% 10) and go to step (1). 10 (2) Replace n by Prove that this algorithm enters step (2) at most log10 (n) times. (b) Consider the following algorithm, in which f(n) = n-3n+2. Input: An integer n. (1) If f(n) = 0, stop and output n. Otherwise, go to step (2). (2) Replace n by f(n) % 5 and go to step (1). Prove that this algorithm terminates for every choice of input.

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