AlgFall06Comps

AlgFall06Comps - Algorithms Fall 2006 Graduate...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Algorithms Fall 2006 Graduate Comprehensive Exam 1. For two positive integers a , and n , naively computing a n takes multiplying a with itself n- times, i.e., Θ (n) time. Write a divide-and-conquer algorithm for the same purpose. Show your algorithm’s asymptotic time-complexity by setting up the corresponding recurrence equation and solving it. 2a. Explain in a line or two how can one detect in O( n ) time whether an input directed graph is a tree or not, where n is the number of vertices of the graph. 2b. What is the asymptotic time-complexity of the following algorithm-fragment in terms of n. ? (1) For i = 3 through n do (2) For p = 5 through 10 do (3) For k = 3 through i do (4) -constant or O (1) number of steps- end for loops; 2c. What will be the output value of count from line 6 after the following loops are executed? (0) int count := 0; (1) For i =1 through 5 do (2) For p = 1 through i*i do (3) if ( i divides p ) then (4) For k = 1 through i do (5) count++; end for loops; (6) print count ;
Background image of page 1

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

View Full DocumentRight Arrow Icon
3. For a weighted undirected graph
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/10/2012 for the course CSE 5211 taught by Professor Dmitra during the Spring '12 term at FIT.

Page1 / 3

AlgFall06Comps - Algorithms Fall 2006 Graduate...

This preview shows document pages 1 - 3. Sign up to view the full document.

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