By Mark A. Weiss
Facts constructions and set of rules research in Java is an “advanced algorithms” ebook that matches among conventional CS2 and Algorithms research classes. within the outdated ACM Curriculum directions, this path used to be often called CS7. this article is for readers who are looking to study strong programming and set of rules research abilities at the same time in order to improve such courses with the utmost volume of potency. Readers must have a few wisdom of intermediate programming, together with subject matters as object-based programming and recursion, and a few historical past in discrete math.
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Additional resources for Data Structures and Algorithm Analysis in Java (3rd Edition)
2010. C H A P T E R 2 Algorithm Analysis An algorithm is a clearly speciﬁed set of simple instructions to be followed to solve a problem. Once an algorithm is given for a problem and decided (somehow) to be correct, an important step is to determine how much in the way of resources, such as time or space, the algorithm will require. An algorithm that solves a problem but requires a year is hardly of any use. Likewise, an algorithm that requires hundreds of gigabytes of main memory is not (currently) useful on most machines.
Use recursion for the second routine. 7 Prove the following formulas: a. log X < X for all X > 0 b. 8 Evaluate the following sums: ∞ 1 a. i=0 4i i b. ∞ i=0 4i ∞ i2 i=0 4i ∞ iN i=0 4i c. d. 10 What is 2100 (mod 5)? 2. Prove the following: N−2 a. i=1 Fi = FN − 2 √ b. FN < φ N , with φ = (1 + 5)/2 c. Give a precise closed-form expression for FN . 12 Prove the following formulas: N 2 a. i=1 (2i − 1) = N b. 14 N 3 i=1 i = N i=1 i 2 Design a generic class, Collection, that stores a collection of Objects (in an array), along with the current size of the collection.
As an example, the following program fragment is O(N2 ): for( i = 0; i < n; i++ ) for( j = 0; j < n; j++ ) k++; Rule 3—Consecutive Statements.