Put the follow BigO categories in order Top label: Least Efficient Algorithm (Most number of steps)Least Efficient Algorithm (Most number of steps) position 11 O(n^2) position 22 O(n) position 33 O(1) position 44 O(logn)
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Rank the following functions in ascending order; that is, find an arrangement f1, f2, ..., f8 of the functions satisfying f1 = O(f2), f2 = O(f3), ..., f7 = O(f8). Briefly show your work for this problem. (2pts)
Adi S.
The following are examples of computing times in algorithm analysis. To make the difference clearer, let's compare based on the execution time where n = 1,000,000 and time = 1 millisecond: Big-Oh Description Algorithm Running Time Sample Code Implementation O(1) Constant return n (n+1)/2 O(log2 n) Logarithmic Binary Search 19.93 microseconds while n > 1 count < count + 1 n = n / 2 O(n) Linear Sequential 1.00 seconds for i = 1 to n search sum < sum + i O(n log2 n) Heapsort 19.93 seconds O(n^2) Quadratic Insertion Sort 11.57 days for i = 1 to n for j = 1 to n sum = sum + i O(n^3) Cubic Floyd's Algorithm O(2^n) Exponential 317.10 centuries O(n^n) Eternity O(log2 log2 n) Operations on the O-Notation: Rule for Sums Suppose that T(n) = O(f(n)) and Tz(n) = O(g(n)): Then, t(n) = Ti(n) + Tz(n) = O(max(f(n), g(n))).
Madhur L.
Suppose we have a collection of algorithm that runs on O(1), O(n), O(n^2), O(n log n), and O(2^n). Which of the following list them from fastest to slowest? a) O(1), O(n log n), O(n), O(n^2), O(2^n) b) O(1), O(n), O(n log n), O(n^2), O(2^n) c) O(1), O(n), O(n^2), O(n log n), O(2^n) d) None of the above
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