{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

final_702_07

final_702_07 - CAS 702 Data Structures and Algorithms Final...

This preview shows pages 1–2. Sign up to view the full content.

CAS 702 – Data Structures and Algorithms – Final Exam – 60p December 14, 2007 – duration of the exam: 3 hours Name: Student Number: Signature: Problem 1 a. Prove or disprove the following: f ( n ) = Θ( f ( n/ 2)). 5p b. Consider the following: An array of n numbers contains only 1 , 0 and 1 can be sorted in O ( n ) time in the worst case. If true , describe an O ( n ) time algorithm briefly (you are not required to prove its correctness), if false give the correct worst case running time. 5p c. Prove or disprove the following: If a node in a binary search tree has two children, then its successor has no left child and its predecessor has no right child. 5p Problem 2 Consider a positive flow f in a network G = ( V, E ). We wish to decompose f into positive simple path (or cycle) flows f i , i.e. f = f i , where the edges of f i form a simple path form s to t in G , or any cycle in G . (Recall: a simple path has no repeated vertices, and a simple cycle has no repeated vertices aside from the start/end vertex).

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}