[Problem 4] Assuming that n ≥ 1, formally prove or disprove the following claims a) n²n+1 is O(n) b) 5" is O(4") c) n(log(n)) is O(n4/3)

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A:

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A: I have solved all the 3 parts and I have uploaded image for it. Hope you find it helpful.

Q: [Problem 4] Assuming that n ≥ 1, formally prove or disprove the following claims a) n²-6n +3 is O(n)…

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Q: (1) (a) show that 21 divides 4"+1 + 52n-1 for n 2 1

A: 1 (a).

Q: Q3. Find r's and (r-1)'s compliment of the following number I. (101100011)2 (78)10 II.

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Rod Cutting

A naïve solution for the above-stated problem is to evaluate all of the possible combinations of different pieces of varying size to find the maximum revenue-generating combination. Although this method seems the easiest and quick to practice, it has exponential time complexity. So there is a need to figure out a better method than this.