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
Concept explainers
Question
Chapter 24, Problem 2P
(a)
Program Plan Intro
To prove that Nesting relation is transitive in nature.
(b)
Program Plan Intro
An efficient method to proof that a box B is nested inside another box.
(c)
Program Plan Intro
An efficient method to find out the longest sequence of nested boxes with an optimized time complexity.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Artificial Intelligence - Local Search
Starting from a randomly generated state of the 15-puzzle game (https://en.wikipedia.org/wiki/15_puzzle), steepest-ascent hill-climbing (the vanilla version of hill-climbing search) gets stuck 76% of the time, i.e., solving only 24% of problem instances. But it works very quickly, i.e., it takes just 6 steps on average when it succeeds and 5 steps when it gets stuck. In contrast, if sideways moves are allowed, this raises the percentage of problem instances solved by hill-climbing from 24% to 81%, with the success at a cost: the algorithm averages roughly 7 steps for each successful instance and 32 steps for each failure. Now suppose that we are implementing random-restart hill climbing (i.e., if a search fails, it keeps to try, and try, until it gets a success) by the following two versions:
one uses vanilla steepest-ascent hill climbing, and
the other one uses hill climbing with sideways moves.
Can you please tell which version of…
Correct answer will be upvoted else downvoted. Computer science.
Child Ehab has a piece of Cut and Stick with an exhibit an of length n composed on it. He intends to snatch some scissors and do the accompanying to it:
pick a reach (l,r) and cut out each component al, al+1, ..., ar in this reach;
stick a portion of the components together in a similar request they were in the exhibit;
end up with different pieces, where each piece contains a portion of the components and each component has a place with some piece.
All the more officially, he segments the arrangement al, al+1, ..., ar into aftereffects. He thinks a dividing is lovely if for each piece (aftereffect) it holds that, assuming it has length x, no worth happens rigorously more than ⌈x2⌉ times in it.
He didn't pick a reach yet, so he's pondering: for q ranges (l,r), what is the base number of pieces he really wants to parcel the components al, al+1, ..., ar into with the goal that the dividing is delightful.…
Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science.
Today the kindergarten has another gathering of n kids who should be situated during supper. The seats at the table are numbered from 1 to 4n. Two children can't sit on a similar seat. It is realized that two children who sit on seats with numbers an and b (a≠b) will enjoy if:
gcd(a,b)=1 or,
a partitions b or b separates a.
gcd(a,b) — the greatest number x with the end goal that an is distinct by x and b is detachable by x.
For instance, if n=3 and the children sit on seats with numbers 2, 3, 4, then, at that point, they will enjoy since 4 is isolated by 2 and gcd(2,3)=1. On the off chance that children sit on seats with numbers 4, 6, 10, they won't enjoy.
The educator truly doesn't need the wreck at the table, so she needs to situate the children so there are no 2 of the child that can enjoy. All the more officially, she needs no pair of seats an and b that the children…
Chapter 24 Solutions
Introduction to Algorithms
Ch. 24.1 - Prob. 1ECh. 24.1 - Prob. 2ECh. 24.1 - Prob. 3ECh. 24.1 - Prob. 4ECh. 24.1 - Prob. 5ECh. 24.1 - Prob. 6ECh. 24.2 - Prob. 1ECh. 24.2 - Prob. 2ECh. 24.2 - Prob. 3ECh. 24.2 - Prob. 4E
Ch. 24.3 - Prob. 1ECh. 24.3 - Prob. 2ECh. 24.3 - Prob. 3ECh. 24.3 - Prob. 4ECh. 24.3 - Prob. 5ECh. 24.3 - Prob. 6ECh. 24.3 - Prob. 7ECh. 24.3 - Prob. 8ECh. 24.3 - Prob. 9ECh. 24.3 - Prob. 10ECh. 24.4 - Prob. 1ECh. 24.4 - Prob. 2ECh. 24.4 - Prob. 3ECh. 24.4 - Prob. 4ECh. 24.4 - Prob. 5ECh. 24.4 - Prob. 6ECh. 24.4 - Prob. 7ECh. 24.4 - Prob. 8ECh. 24.4 - Prob. 9ECh. 24.4 - Prob. 10ECh. 24.4 - Prob. 11ECh. 24.4 - Prob. 12ECh. 24.5 - Prob. 1ECh. 24.5 - Prob. 2ECh. 24.5 - Prob. 3ECh. 24.5 - Prob. 4ECh. 24.5 - Prob. 5ECh. 24.5 - Prob. 6ECh. 24.5 - Prob. 7ECh. 24.5 - Prob. 8ECh. 24 - Prob. 1PCh. 24 - Prob. 2PCh. 24 - Prob. 3PCh. 24 - Prob. 4PCh. 24 - Prob. 5PCh. 24 - Prob. 6P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Similar questions
- “Rectangles” A rectangle can be specified in a 2-dimensional plane using the top left (north west) point and the bottom right (south east) point. Given n rectangles (using 2 points each), give an O(n log n) algorithm that tells if any two rectangles from the list overlap. Two rectangles are said to overlap, if there is a common point in both of them. [If a rectangle is entirely contained in another, they are still said to “overlap”, even though their lines don’t cross.]arrow_forwardCan you help me with this code because I am struggling. The Lights Out puzzle consists of an m x n grid of lights, each of which has two states: on and off. The goal of the puzzle is to turn all the lights off, with the caveat that whenever a light is toggled, its neighbors above, below, to the left, and to the right will be toggled as well. If a light along the edge of the board is toggled, then fewer than four other lights will be affected, as the missing neighbors will beignored. In this section, you will investigate the behavior of Lights Out puzzles of various sizes by implementing a LightsOutPuzzle class. Once you have completed the problems in this section, you can test your code in an interactive setting using the provided GUI. See the end of the section for more details. Task: A natural representation for this puzzle is a two-dimensional list of Boolean values, where True corresponds to the on state and False corresponds to the off state. In the LightsOutPuzzle class, write an…arrow_forwardCreating decagons There are 1000 points in the plane, no three of them on the same line. Devise an algorithm to construct 100 decagons with their vertices at these points. The decagons need not be convex, but each of them has to be simple, i.e., its boundary should not cross itself, and no two decagons may have a common point.arrow_forward
- (Graph Theory) In chess, a knight can move from a square to another square if one of their coordinates differs by 1, and the other differs by 2. A knight's tour is a traversal by knight moves starting at a square, visiting each square once, and returning to the start. Does a 7 × 7 chessboard admit a knight's tour? If so, show the tour.arrow_forwardChirality def is_left_handed(pips): Even though this has no effect on fairness, pips from one to six are not painted on dice just any which way, but so that pips on the opposite faces always add up to seven. (This convention makes it easier to tell when someone tries to use crooked dice with certain undesirable pip values replaced with values that are more desirable for the cheater.) In each of the 23 = 8 corners of the cube, exactly one value from each pair of forbidden opposites 1-6, 2-5 and 3-4 meets two values chosen from the other two pairs of opposites. You can twist and turn any corner of the die to face you, and yet two opposite sides never spread into simultaneous view. This discipline still allows for two distinct ways to paint the pips. If the numbers in the corner shared by the faces 1, 2, and 3 read out clockwise as 1-2-3, that die is left-handed, whereas if they read out as 1-3-2, that die is right-handed. Analogous to a pair of shoes made separately for the left and…arrow_forwardUnion-Find: Maze Write a program that generates mazes of arbitrary size using the union-find algorithm. A simple algorithm to generate the maze is to start by creating an N x M grid of cells separated by walls on all sides, except for entrance and exit. Then continually choose a wall randomly, and knock it down if the cells are not already connected to each other. If we repeat the process until the starting and ending cells are connected, we have a maze. It is better to continue knocking down the walls until every cell is reachable from every cell as this would generate more false leads in the maze. Test you algorithm by creating a 15 x 15 grid, and print all the walls that have been knocked down. Darrow_forward
- A weighted, directed graph is a suitable representation to represent the daily airline routes flown by a small airline. The airline have the following daily flights: - Three flights from Cape Town to Johannesburg, - Two flights from Johannesburg to Cape Town. - Four flights from Johannesburg to Durban. - Three flights from Durban to Johannesburg. - One flight from Johannesburg to George. - One flight from George to Johannesburg. Draw the graph and answer the questions that followarrow_forwardComputer Science There is an n × n grid of squares. Each square is either special, or has a positive integer costassigned to it. No square on the border of the grid is special.A set of squares S is said to be good if it does not contain any special squares and, starting fromany special square, you cannot reach a square on the border of the grid by performing up, down,left and right moves without entering a cell belonging to S. 5 3 4 9 4 X 3 6 1 9 X 4 1 2 3 5 - Design an algorithm which receives an arbitrary n × n grid, runs in time poly-nomial in n and determines a good set of squares with minimum total cost.arrow_forwardCorrect answer will upvoted else downvoted. You are given a coordinated chart G which can contain circles (edges from a vertex to itself). Multi-edges are missing in G which implies that for every single arranged pair (u,v) exists all things considered one edge from u to v. Vertices are numbered from 1 to n. A way from u to v is a grouping of edges to such an extent that: vertex u is the beginning of the principal edge in the way; vertex v is the finish of the last edge in the way; for all sets of neighboring edges next edge begins at the vertex that the past edge finishes on. We will expect that the unfilled succession of edges is a way from one u to another. For every vertex v output one of four qualities: 0, in case there are no ways from 1 to v; 1, in case there is just a single way from 1 to v; 2, in case there is more than one way from 1 to v and the number of ways is limited; −1, if the number of ways from 1 to v is endless. Input :The first…arrow_forward
- A.“Cat is on a mat, and it is happy” B. “If a cat is on a mat, then it is a happy pet’ C. “If a cat is on a mat, then it is happy’ D. Nonearrow_forwardCorrect answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. You have a knapsack with the limit of W. There are likewise n things, the I-th one has weight wi. You need to place a portion of these things into the knapsack so that their all out weight C is half of its size, however (clearly) doesn't surpass it. Officially, C ought to fulfill: ⌈W2⌉≤C≤W. Output the rundown of things you will place into the knapsack or establish that satisfying the conditions is unimaginable. In case there are a few potential arrangements of things fulfilling the conditions, you can output any. Note that you don't need to expand the amount of loads of things in the knapsack. Input Each test contains various experiments. The principal line contains the number of experiments t (1≤t≤104). Depiction of the experiments follows. The main line of each experiment contains integers n and W (1≤n≤200000, 1≤W≤1018). The second line of each experiment…arrow_forwardGiven a maze arena as shown below. Design a Position Identification algorithm so that the robot can find out which position in the maze above, with a robot size of 450mm x 420mm and a wall width of 45mm. a) Algorithms and methods used are free. b) Explain the reasons for choosing the algorithm. c) Algorithm is designed and explained using Structure English or Description Algorithm (with descriptive sentences).arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
Operations Research : Applications and Algorithms
Computer Science
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole