Question

Consider the following algorithm. First, explain what exactly it computes. Then, use the 5 steps in the General Plan to analyze the time efficiency of the algorithm. Algorithm 1: A pseudocode of an algorithm whose time efficiency is of interest Data: a non-negative integer n Result: to be answered by you s ← 0; for i ← 1 to n do s ← s + i * i end return s (Hint: Note that this is a non-recursive algorithm. So, follow the procedure in the General Plan for non-recursive algorithms.) For each of the following recurrence relations, first, write down explicitly what sequence they represent, and then solve them. a. x(n) = 3x(n − 1) for n > 1, with the initial condition x(1) = 5 b. x(n) = x(n/2) + n, for n > 1, with the initial condition x(1) = 1 (solve for n = 2^k)

          Consider the following algorithm. First, explain what exactly it computes. Then, use the 5 steps in the General Plan to analyze the time efficiency of the algorithm.

Algorithm 1: A pseudocode of an algorithm whose time efficiency is of interest

Data: a non-negative integer n
Result: to be answered by you

s ← 0;
for i ← 1 to n do
    s ← s + i * i
end
return s

(Hint: Note that this is a non-recursive algorithm. So, follow the procedure in the General Plan for non-recursive algorithms.)

For each of the following recurrence relations, first, write down explicitly what sequence they represent, and then solve them.

a. x(n) = 3x(n − 1) for n > 1, with the initial condition x(1) = 5

b. x(n) = x(n/2) + n, for n > 1, with the initial condition x(1) = 1 (solve for n = 2^k)

Added by Linda U.

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