CMSC 351 Homework Explanation by TA Shang-chieh J Wu - Prof. Samir Khuller, Assignments of Algorithms and Programming

Download CMSC 351 Homework Explanation by TA Shang-chieh J Wu - Prof. Samir Khuller and more Assignments Algorithms and Programming in PDF only on Docsity! CMSC 351 HW #1 TA’s Explanation Shang-chieh J Wu Problem 1 The answer can be got from inspection as in the following two tables. i j Printing # 1 1 to 4 4 2 2 to 7 6 3 3 to 10 8 … … … n i Printing # 1 1 to 1 4 2 1 to 2 10 3 1 to 3 18 … … … But you must offer some concrete “evidence” to say the answer is something. Inspection is not good enough for such a kind course. (Algorithm) The inner loop is only a print statement, so the constant execution time is needed. You can use a “c” or “k” to denote the constant, or just using 1 (unity). Either is O (1). Take a look at your textbook pp.1058-1060 for some concepts about summations, and don’t been fooled by the index term (k in the following example) and the summed term (b in the following example). ∑ + = +=+== =++= 2 11 3 a ak akakak bbbbb In the above example, the exact value of a is NOT important, as long as it won’t change during summation. The same idea applies to professors’ solution. When doing ∑ + = +=+== +=+−+=+++= 13 131 221)()13(1...111 i ij ijijij iii i won’t change during the summation, which can be known by inspecting the code. The second equal sign can be got from a simple counting. I (TA) learned it when I was 10 years old.