Efficiency Of Algorithms
Overzicht
Ask a class of thirty to add up the numbers from 1 to 100 and most of them start at the left and work along. One of them writes 5050 after a few seconds, because 1 and 100 make 101, and so do 2 and 99, and there are fifty such pairs. Both people solve the same problem. Both get the same answer. One did ninety-nine additions and the other did about three operations, and that gap is the entire content of this lesson.
You will learn why more than one algorithm can solve the same problem, what makes one of them more efficient than another, and how to compare two algorithms by counting the work they do rather than by timing them on a stopwatch. You will also learn where this specification stops: it asks only about time efficiency, and it never asks for a formal mathematical comparison. Knowing the boundary of a topic is worth marks, because it tells you what a question can and cannot be asking.
Doelstellingen
- Understand that more than one algorithm can be used to solve the same problem. Compare the efficiency of algorithms explaining how some algorithms are more efficient than others in solving the same problem.
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- On this specification, exam questions about the efficiency of algorithms refer only to: A. Memory efficiency B. Network efficiency C. Storage efficiency D. Time efficiency Answer: D
- An algorithm takes 2 seconds on 1000 items and 8 seconds on 2000 items. Approximately how long would it take on 4000 items? A. 10 seconds B. 16 seconds C. 32 seconds D. 64 seconds Answer: C
- A binary search is used on a sorted list of 1000 items. What is the maximum number of comparisons it will make? A. 3 B. 10 C. 500 D. 1000 Answer: B
- Which statement about two algorithms that solve the same problem is correct? A. The faster algorithm is always the better choice B. Two correct algorithms must do the same amount of work C. Only one algorithm can be correct for any problem D. The faster algorithm may have a condition on the data that the slower one does not Answer: D
- Algorithm A adds up the numbers from 1 to N with a loop. Algorithm B calculates N * (N + 1) DIV 2. Which statement is true when N is very large? A. Algorithm A does far more work than Algorithm B B. Algorithm B does far more work than Algorithm A C. Both do the same amount of work D. Algorithm B gives a different answer Answer: A
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