Algorithm complexity The complexity of a computer algorithm is the number of operations or steps the algorithm needs to complete its task assuming there are n pieces of input (for example, the number of steps needed to put n numbers in ascending order). Four algorithms for doing the same task have complexities of A: n 3/2 , B: n log 2 n , C: n (log 2 n ) 2 , and D: n log 2 n . Rank the algorithms in order of increasing efficiency for large values of n . Graph the complexities as they vary with n and comment on your observations.
Algorithm complexity The complexity of a computer algorithm is the number of operations or steps the algorithm needs to complete its task assuming there are n pieces of input (for example, the number of steps needed to put n numbers in ascending order). Four algorithms for doing the same task have complexities of A: n 3/2 , B: n log 2 n , C: n (log 2 n ) 2 , and D: n log 2 n . Rank the algorithms in order of increasing efficiency for large values of n . Graph the complexities as they vary with n and comment on your observations.
Solution Summary: The author explains the ranking order of the algorithms from least to most efficient is A, C, B, D.
Algorithm complexity The complexity of a computer algorithm is the number of operations or steps the algorithm needs to complete its task assuming there are n pieces of input (for example, the number of steps needed to put n numbers in ascending order). Four algorithms for doing the same task have complexities of A: n3/2, B: n log2n, C: n(log2n)2, and D:
n
log
2
n
. Rank the algorithms in order of increasing efficiency for large values of n. Graph the complexities as they vary with n and comment on your observations.
Analysis Of Algorithm
Question No:
(a) Compute given sum by driving some formulae : i. 4+8+12+16+….+200 (b) Prove following Asymptotic notations true or false : i. 100n3/5n+ 25n+ 7 = O(n) ii. n lg n +1000 n + n2 = θ(n)
Discrete Structure
Question 1:
A runner targets herself to improve her time on a certain course by 3 seconds a day. If on day 0 she runs the course in 3 minutes, how fast must she run it on day 14 to stay on target?
A certain computer algorithm executes twice as many operations when it is run with an input of size k as when it is run with an input of size k − 1 (where k is an integer that is greater than 1). When the algorithm is run with an input of size 1, it executes seven operations. How many operations does it execute when it is run with an input of size 25?
Question 2:
Consider the letters in the word COMPUTER.
a) In how many ways can these letters be arranged in a row?
b) In how many ways can these letters be arranged if the letters CO must remain next to each other (in order) as a unit?
Question 3:
A multiple-choice test contains 10 questions. There are four possible answers for each question.
a) In how many ways can a student answer the questions on the…
p(n) is the number of ways to perfectly cover a 2 x n grid with tiles (a tile is a 1x2 rectangle).
(a): Find a recursive formula for p(n)
(b): prove formula combinatorially
Chapter 4 Solutions
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
University Calculus: Early Transcendentals (3rd Edition)
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