Select the order of the algorithm for each growth-rate function (assuming that there are n inputs):  5 log n + 6n 5n log_2 n + 6n + 7n^2 5n + 9k 5n log_2 n + 6n 4n^3 - 2n 5 log_2 n + 6 42 + 99k   Options: 1. O(1) 2. O(log n) 3. O(n log n) 4. O(n) 5. O(n^2) 6. O(n^3) 7. O(nm)

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A: Solution :

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Q: a. Give three different examples of algorithms (with explanation) that run in logarithmic time.

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Q: (int i 1; i <= 2 *r pr (int j = 1; j<= n; <=D %3B cout << 2 *i+ j;

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Q: i. 100n^3/5n+ 25n+ 7 = O(n) ii. n lg n +1000 n + n2 = θ(n)

A:

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A: For the given growth-rate function: 8n3 - 9n The highest power term is 8n3.

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A: Below are the answers with reason:

Q: A.1 A.2 A.3 A.4 Expression 8 +0.081n² + 0.040n 100+ n log2 n 100n + 0.081 log³ n + n³ 0.081 log4 n +…

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A: To Do: To choose the correct option.

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A:

Q: what contributes to n on the performance n log n? in algorithm and complexity

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Q: what is the time complexity of the function given below based on n, using the big O notation?

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Problems on Turing Machines

In the computational world, the Turing machine is a powerful computation engine. The invention of the Turing Machine is done by Alan Turing in 1936. A Turing Machine (TM) is a diagrammatic model of a fictional computer. It determines an output from a set of input variables using a pre-defined set of rules. It is used to get around the limitations of finite automata and pushdown automata.