midterm2007-fall - Data Structures and Algorithms (I)...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Data Structures and Algorithms (I) close-book midterm exam November 30, 2007 You may answer the questions in any order. Dishonest behaviors and attempts will be punished most seriously. When you are asked to justify, prove, or disprove your answers, you may directly use anything that we have shown in class in a “black-box” manner. Problem 1 (20 points) Let f ( n ) and g ( n ) be two positive functions. We say that f ( n ) = O ( g ( n )) if there exist two positive constants c and n such that f ( n ) ≤ c · g ( n ) holds for any n ≥ n . Let us define a “new” asymptotic notation ξ by saying that f ( n ) = ξ ( g ( n )) if f ( n ) = O ( g ( n )) and g ( n ) = O ( f ( n )) . Prove or disprove the statement that f ( n ) = ξ ( g ( n )) implies f ( n ) log 2 g ( n ) f ( n ) = ξ ( g ( n )) . Problem 2 (15 points) Prove the following theorem. Let a ≥ 1 and b > 1 be constants. Let f ( n ) be a positive function....
View Full Document

Page1 / 2

midterm2007-fall - Data Structures and Algorithms (I)...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online