Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
expand_more
expand_more
format_list_bulleted
Question
Chapter 16, Problem 4P
(a)
Program Plan Intro
To show that whether scheduling
(b)
Program Plan Intro
To analyze the running time complexity of disjoint forest tree algorithm.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
The search algorithm developed will be used for users to search the catalog for all items matching the search keyword(s), and there are a
total of 15000 items in the catalog. During development, three different algorithms were created.
• Algorithm A runs in constant time, with a maximum runtime of 1.10 seconds and returns all matching results.
●
Algorithm B runs in logarithmic time, with a maximum runtime of 0.3 seconds, and returns only the first result.
●
Algorithm C runs in linear time, with a maximum runtime of 1.50 seconds and returns all matching results.
Which algorithm would be the least suitable for the requirements stated? In your answer, justify your choice by explaining why you picked that
algorithm, and why you did not pick the other two algorithms.OND OND OND DAD
Job scheduling Consider the problem of scheduling n jobs of known durations t1,t2,. . .,tn for execution by a single processor.
The jobs can be executed in any order, one job at a time.
You want to find a schedule that minimizes the total time spent by all the jobs in the system. (The time spent by one job in the system is the sum of the time spent by this job in waiting plus the time spent on its execution.)
Design a greedy algorithm for this problem. Does the greedy algorithm always yield an optimal solution?
The least solution to Eq 1, whenever it exists, is anupper bound on the WCRT of task τi.
Chapter 16 Solutions
Introduction to Algorithms
Ch. 16.1 - Prob. 1ECh. 16.1 - Prob. 2ECh. 16.1 - Prob. 3ECh. 16.1 - Prob. 4ECh. 16.1 - Prob. 5ECh. 16.2 - Prob. 1ECh. 16.2 - Prob. 2ECh. 16.2 - Prob. 3ECh. 16.2 - Prob. 4ECh. 16.2 - Prob. 5E
Ch. 16.2 - Prob. 6ECh. 16.2 - Prob. 7ECh. 16.3 - Prob. 1ECh. 16.3 - Prob. 2ECh. 16.3 - Prob. 3ECh. 16.3 - Prob. 4ECh. 16.3 - Prob. 5ECh. 16.3 - Prob. 6ECh. 16.3 - Prob. 7ECh. 16.3 - Prob. 8ECh. 16.3 - Prob. 9ECh. 16.4 - Prob. 1ECh. 16.4 - Prob. 2ECh. 16.4 - Prob. 3ECh. 16.4 - Prob. 4ECh. 16.4 - Prob. 5ECh. 16.5 - Prob. 1ECh. 16.5 - Prob. 2ECh. 16 - Prob. 1PCh. 16 - Prob. 2PCh. 16 - Prob. 3PCh. 16 - Prob. 4PCh. 16 - Prob. 5P
Knowledge Booster
Similar questions
- There are ? tasks assigned to ? workers, and each worker can be assigned only one task. Each worker can complete any one of the tasks, but the time spent varies. Use the ant colony algorithm to find the best allocation scheme that minimizes the total time spent. Please write a program to solve the problem (with python/C/C++)arrow_forwardConsider the following functions: • log₂ x • x.log₂ x • (3/2)* ● x/log₂ x • 2x ● • x² ● (log₂ x)² (1/3)* You are told that, functions above represent the number of operations carried out by a set of algorithms that do the same job, albeit in different ways. Order the functions from slowest growth rate to the fastest growth rate (i.e., sort the algorithms from fastest to slowest). Explain your reasoning for consecutively ordered functions, possibly by using the limit method, to get credit.arrow_forwardA deadlock is the very unpleasant situation that may occur in very dynamic world of running processes, a situation that must be avoided at all costs. One famous algorithm for deadlock avoidance is the Banker's algorithm for deadlock avoidance. The version of this algorithm presented in this module's commentary gives just one solution (the Greedy approach). Consider the Greedy approach to the Banker's algorithm. Give an example of application of this algorithm for 7 processes (named P1, ... , P7) and 5 resource types (named R1, ... , R5). Start by listing the matrices involved in this algorithm, that constitute its input data; also, do not forget to mention the overall resources of each type available in this fictional system. Proceed by describing the algorithm, step by step; for each step, mention the test performed, which process was chosen, what is the old and new status of the Work array, etc. In the end, list the solution, that is the safe sequence of processes resulting from this…arrow_forward
- Wireless sensor networks (WSNs) refer to a domain of communication networks. In a WSN, small devices called sensor nodes are used for data transfer among each other and a base station. One limitation of a sensor node is that it has a very limited processing capability and very small memory. Consider a scenario in which you have an algorithm that can be subdivided into smaller problems. If you have to run these sub-problems in different sensor nodes, would you prefer to use divide & conquer approach or dynamic programming approach? Write briefly and precisely.arrow_forwardConsider the following part of a function (assume n>=1 and m>=1 and n and m are inputs to the function) for (i = 1 to n) for (j - 1 to m) for (k = 1 through 1000) { Task A Task B If Task A requires t time units and Task B requires s time units, then the algorithm requires _in the worst case, assuming that t and s are constants. time units to be executed, and therefore it is 1000 * t* s* n units, O(1000 * t* s ) 1000 + n + m +t + s units, O(1000 + n+ m +t+ s) n*m* t*s units, O(n*m*t*s) 1000*n*m* (t +s) units, O(n*m) O (1000 +m + n) * (t +s) units, O(m + n) O m'n units, O(mn)arrow_forwardAs a teaching administrator of the department, your responsibility is to schedule the classes for a particular classroom. Suppose there are n classes, each class i is represented by its start time and finishing time [Si, fi], and we say that two classes i and j are non-conflicting if they do not overlap in time (i.e., sizfj or szfi). You want to schedule as many classes for the classroom as possible, but the scheduled classes should be non-conflicting. Develop an algorithm so that you can select the maximum number of classes for the classroom. (We are expecting either pseudocode or language description of your algorithm)arrow_forward
- Consider array A of n numbers. We want to design a dynamic programming algorithm to find the maximum sum of consecutive numbers with at least one number. Clearly, if all numbers are positive, the maximum will be the sum of all the numbers. On the other hand, if all of them are negative, the maximum will be the largest negative number. The complexity of your dynamic programming algorithm must be O(n2). However, the running time of the most efficient algorithm is O(n). Design the most efficient algorithm you can and answer the following questions based on it. To get the full points you should design the O(n) algorithm. However, if you cannot do that, still answer the following questions based on your algorithm and you will get partial credit. Write the recursion that computes the optimal solution recursively based on the solu- (a) tion(s) to subproblem(s). Briefly explain how it computes the solution. Do not forget the base case(s) of your recursion.arrow_forwardBus timetables specify to the second the exact arrival and departure time of each bus on each stop. You need to pay for the full fare of every bus you ride and different bus lines charge different fees , but they are flat fees (independent of distance travelled on the line) A travel plan is a sequence of stop-time pairs where stop is a location of a bus stop and time is when we arrive at that stop. The plan is feasible if for any two consecutive pairs (a, t) and (b, t′) in the plan there exists a bus that departs after t and arrives at b at exactly t′. That is, a travel plan does not allow us to walk between stops. Assuming that no two buses arrive at the same time at the same stop, a feasible plan uniquely identifies the bus lines that we need to take to realize the plan. The cost of the plan is the sum of the fares we need to pay. Your task is to design an efficient algorithm that given a departure time t, an arrival time t′, an origin stop a and a destination stop b, finds the…arrow_forwardConsider the following problem: You have a large collection of music files (e.g., MP3 files), and for each file you know the artist name (as a string) and the song title (also as a string). You wish to find the name of the artist who has the largest number of songs featured in the collection. Describe an algorithm for this problem.the algorithm should be as efficient as possible. State the running time of your algorithm, assuming that there are in total n songs, across t different artistsarrow_forward
- Problem Alice was given a number line containing every positive integer, x, where 1<=x<=n. She was also given m line segments, each having a left endpoint, l (1<=l<=n), a right endpoint, r (1<=r<=n), and an integer weight, w. Her task is to cover all numbers on the given number line using a subset of the line segments, such that the maximum weight among all the line segments in the chosen subset is minimal. In other words, let S=(l1,r1,w1),(l2,r2,w2),....,(lk,rk,wk), represent a set of k line segments chosen by Alice, max(w1,w2,...,wk) should be minimized. All numbers 1,2,....n should be covered by at least one of k the chosen line segments. It is okay for the chosen line segments to overlap. You program should output the minimized maximum weight in the chosen subset that covers all the numbers on the number line, or -1 if it is not possible to cover the number line. Input format The first line of the input contains an integer, n - denoting the range of numbers…arrow_forwardToday is Max's birthday. He has ordered a rectangular fruit cake which is divided into N x M pieces. Each piece of the cake contains a different fruit numbered from 1 to N*M. He has invited K friends, each of whom have brought a list of their favorite fruit choices. A friend goes home happy if the piece he receives is of his favorite fruit. Note that each friend can receive only one piece of cake. Design a way for Max to find the maximum number of friends he can make happy. Input The first line of the input consists of an integer - numOfFriends, representing the number of friends(k). The next Klines consist of X+1 space-separated integers, where the first integer represents the count of choices of the th friend followed by X space-separated integers representing the fruits he likes. The next line of the input consists of an integer - numN, representing the number of rows. The next line of the input consists of an integer - numM, representing the number of columns. Output Print an…arrow_forwardWrite a code to decide if Gram-Schmidt Algorithm can be applied to columns of a given matrix A through calculation of rank. The code should print appropriate messages indicating whether Gram-Schmidt is applicable on columns of the matrix or not. Deliverable(s) : The code that performs the test.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- C++ Programming: From Problem Analysis to Program...Computer ScienceISBN:9781337102087Author:D. S. MalikPublisher:Cengage Learning
C++ Programming: From Problem Analysis to Program...
Computer Science
ISBN:9781337102087
Author:D. S. Malik
Publisher:Cengage Learning