Algorithm 1 does a particular task in a \"time\" of N3, where N is the number of

Question

Algorithm 1 does a particular task in a "time" of N3, where N is the number of elements processed. Algorithm 2 does the same task in a "time" of 3N + 1000. a. What is the Big-O efficiency of each algorithm? b. Which algorithm is more efficient by Big-O standards? (need a short explanation as to why) c. Under what conditions if any, would the "less efficient" algorithm execute more quickly than the "more efficient algorithm? (for this question I need to show what values of N work better with the less efficient algorithm and how you figure it out) Thanks in advance for any help. Algorithm 1 does a particular task in a "time" of N3, where N is the number of elements processed. Algorithm 2 does the same task in a "time" of 3N + 1000. a. What is the Big-O efficiency of each algorithm? b. Which algorithm is more efficient by Big-O standards? (need a short explanation as to why) c. Under what conditions if any, would the "less efficient" algorithm execute more quickly than the "more efficient algorithm? (for this question I need to show what values of N work better with the less efficient algorithm and how you figure it out) Thanks in advance for any help.

Explanation / Answer

Dear user, (a) Algorithm 1 does a particular task in a time of N3 So the order of algorithm 1 is N3 Hence the Big-O efficiency of algorithm 1 is O (N3) Algorithm 2 does the same task in a time of 3N + 1000. It does the task in a linear time. The order of this algorithm is N So the Big-O efficiency of algorithm 2 is O (N) (b) Algorithm 2 is more efficient than algorithm 1 by Big-O standards. The value of N3 increases as N increases. That means the time increases and efficiency decreases. The value of 3N + 1000 is a linear function and it is very much less than the value of N3. However, Big-O notation is generally applied to larger values of N (c) For smaller values of N, algorithm 2 would be less efficient than algorithm 1. For example, if we take N as 2, the time taken by algorithm 1 will be 8 (23) which is very much less than the time taken by algorithm2 (3x2 + 1000 = 1006).

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