Homework 4 Solutions

# Homework 4 Solutions - Solutions to Homework Four CS 191...

This preview shows pages 1–4. Sign up to view the full content.

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

View Full Document

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.

Unformatted text preview: Solutions to Homework Four CS 191 : Discrete Structures I Mar. 6 , Winter 2007 Due Date: Mar. 20, 2007, Tuesday, before the class meeting. Section 4.2, p155 Exercise (15) Write an algorithm whose input is a sequence s 1 , …, s n sorted in nondecreasing order and a value x . (Assume that all the values are real numbers.) The algorithm inserts x into the sequence so that the resulting sequence is sorted in nondecreqsing order. Example: If the sequence is 2, 6, 12, 14, and x = 5, the resulting sequence is 2, 5, 6, 12, 14. Answer : insert ( s , n , x ){ i :=1 while ( i ≤ n ) and x > s i do i := i + 1 // x should be inserted in front of the i th location. We need to right shift s i , …, s n one place. j := n while ( j ≥ i ) { do { s i +1 := s i j := j – 1 } //Insert x s i := x } Exercise (18) Describe the worst case input for algorithm 4.2.1. Answer : The worst case occurs when the for loop and the while loop run as long as possible. This situation is achieved when t consists of n 0’s and p consists of m-1 0’s followed by one 1. 1 Section 4.3, p168 Select a theta notation from Table 4.3.3 for each expression in exercises 1-12. Exercise (6) 4 6 6 + + n n Answer: 4 6 6 + + n n = Θ ( n 6 ) Exercise (9) (6 n + 4)(1+lg n ) Answer : (6 n + 4)(1+lg n ) = Θ ( n lg n ) Exercise (11) n n n n n 2 2 ) 1 )( lg ( + + + Answer : n n n n n 2 2 ) 1 )( lg ( + + + = Θ ( n ) Exercise (12) 2+4+8+16+…+ 2 n Answer: 2+4+8+16+…+ 2 n = 2 n +1 – 2 = Θ (2 n ) In Exercises 13-15, select a theta notation for f(n) + g(n). 2 Exercise (15) f ( n ) = Θ ( n 3/2 ), g ( n ) = Θ ( n 5/2 ), Answer : f(n) + g(n) = Θ ( n 3/2 ) + Θ ( n 5/2 ) = Θ ( n 5/2 ), In exercises 16-26, select a theta notation from among Θ (1), Θ (lg n ), Θ ( n ), Θ ( n lg n ), Θ ( n 2 ), Θ ( n 3 ),...
View Full Document

## This note was uploaded on 04/12/2008 for the course CS 191 taught by Professor Shen during the Winter '06 term at University of Missouri-Kansas City .

### Page1 / 9

Homework 4 Solutions - Solutions to Homework Four CS 191...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online