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8 April, 23:40

What is the f (n) runtime of the following pseudocode: sum = 0 for A = N/2 downto 1 for B = 1 to 4N increment sum by B

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  1. 9 April, 02:35
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    f (N) = 2 + N/2 + 6N² units of time.

    Step-by-step explanation:

    Assigning 0 to the variable sum takes one unit of time.

    Each time you increment sum by B, you need to call the value of sum, sum it to B and assign it to sum, which takes three units of time in total. You are repeating this process for each value of B which ranges from 1 to 4n and for each value of A which ranges from 1 to n/2. Opening the FOR takes also another unit of time, so, as a result, we have

    f (N) 1 + 1 (open the FOR in A) + N/2 * (1 (open the FOR in B) + 4N*3) = 2 + N/2 + 6N² units of time. It has order complexity O (N²).
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