Suppose You Have an Algorithm That Tests Whether Any Element

question 11

Multiple Choice

Suppose you have an algorithm that tests whether any element of an array is duplicated elsewhere in the array. The first element must be compared with all the other array elements. The second element must be compared with all the other array elements except the first (it was already compared to the first) . The third element must be compared with all the other array elements except the first two. In the end, this algorithm makes (n - 1) + (n - 2) + … + 2 + 1
Or
N²/2 - n/2
Comparisons. Which of the following statements a) , b) or c) is false?

• A) As n increases, the n² term dominates, and the n term becomes inconsequential. O(n²) notation highlights the n² term, ignoring n/2. O(n²) is referred to as xe "quadratic run time"quadratic run time and pronounced "on the order of n-squared" or more simply "order n-squared."
• B) Big O is concerned with how an algorithm's run time grows in relation to the number of items, n, processed. When n is small, O(n²) algorithms (on today's super-fast computers) will not noticeably affect performance, but as n grows, you'll start to notice performance degradation.
• C) An O(n²) algorithm operating on a billion-element array (not unusual in today's big-data applications) would require a quintillion operations, which on today's desktop computers all the other array elements could take approximately 13.3 years to complete! O(n²) algorithms, unfortunately, are easy to write.
• D) All of the above statements are true.

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