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Algorithms HW#3 Solution

A solution guide to problems 2(a), 1, 4, and 5 from Algorithm Homework 3, including proofs and bounding summations.

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Algorithms HW#3 Solution

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  1. Algorithms HW#3Solution 李孟、施舜元 2014

  2. HW#3 Problem 2

  3. HW#3 Problem 2(a) , 1 * 1000 ,

  4. HW#3 Problem 2(b) • f • f , ,

  5. HW#3 Problem 4 • Let , and T(1) = 1, T(2) = 3 • , 3

  6. HW#3 Problem 4 (cont.) • -3

  7. HW#3 Problem 1 • Below is a theorem from Manber'sbook:For all constants and , and for all monotonically increasing functions , we have . • Prove, by using the above theorem, that for all constants , .

  8. HW#3 Problem 1 (cont.) • let , is monotonically increasing function • Proved.

  9. HW#3 Problem 3

  10. HW#3 Problem 5 • Use Equation 1, shown below, to prove that satisfies • Bounding a summation by an integral • If f (x) is a monotonically increasing continuous function, then

  11. HW#3 Problem 5 (cont.) f(n) S(n) = O(n)

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