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 33, Problem 3P
(a)
Program Plan Intro
To describe the way to find a line in
(b)
Program Plan Intro
Toprovide an
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Bomberman lives in a rectangular grid. Each cell in the grid either contains a bomb or nothing at all.
Each bomb can be planted in any cell of the grid but once planted, it will detonate after exactly 3 seconds. Once a bomb detonates, it's destroyed — along with anything in its four neighboring cells. This means that if a bomb detonates in cell , any valid cells and are cleared. If there is a bomb in a neighboring cell, the neighboring bomb is destroyed without detonating, so there's no chain reaction.
Bomberman is immune to bombs, so he can move freely throughout the grid. Here's what he does:
Initially, Bomberman arbitrarily plants bombs in some of the cells, the initial state.
After one second, Bomberman does nothing.
After one more second, Bomberman plants bombs in all cells without bombs, thus filling the whole grid with bombs. No bombs detonate at this point.
After one more second, any bombs planted exactly three seconds ago will detonate. Here, Bomberman stands back and…
Bomberman lives in a rectangular grid. Each cell in the grid either contains a bomb or nothing at all.
Each bomb can be planted in any cell of the grid but once planted, it will detonate after exactly 3 seconds. Once a bomb detonates, it's destroyed — along with anything in its four neighboring cells. This means that if a bomb detonates in cell , any valid cells and are cleared. If there is a bomb in a neighboring cell, the neighboring bomb is destroyed without detonating, so there's no chain reaction.
Bomberman is immune to bombs, so he can move freely throughout the grid. Here's what he does:
Initially, Bomberman arbitrarily plants bombs in some of the cells, the initial state.
After one second, Bomberman does nothing.
After one more second, Bomberman plants bombs in all cells without bombs, thus filling the whole grid with bombs. No bombs detonate at this point.
After one more second, any bombs planted exactly three seconds ago will detonate. Here, Bomberman stands back and…
Kingdom of Trolls is celebrating their Kingdom Day and one of the activities that is taking place is a game
where a player rolls a magic ball down the hill on a path with spikes. As the ball rolls down, it strikes a spike
and bursts open to release a number of smaller balls (in our simulated game, the number of smaller balls is a
randomly generated integer between 2 and 6, inclusive). As the smaller balls further roll down, when one
strikes a spike, that ball and all its sibling balls burst and each generates another set of smaller balls (using the
same random number already generated for the first roll). The balls keep rolling downhill and striking spikes
and bursting into smaller balls until a golden ball is released by one of the bursts. At this time, the game is
over and the player is told how many balls were generated during the last burst (including the golden ball).
The game is played by two players at a time and the player who had the lowest number of balls generated on
the…
Chapter 33 Solutions
Introduction to Algorithms
Ch. 33.1 - Prob. 1ECh. 33.1 - Prob. 2ECh. 33.1 - Prob. 3ECh. 33.1 - Prob. 4ECh. 33.1 - Prob. 5ECh. 33.1 - Prob. 6ECh. 33.1 - Prob. 7ECh. 33.1 - Prob. 8ECh. 33.2 - Prob. 1ECh. 33.2 - Prob. 2E
Ch. 33.2 - Prob. 3ECh. 33.2 - Prob. 4ECh. 33.2 - Prob. 5ECh. 33.2 - Prob. 6ECh. 33.2 - Prob. 7ECh. 33.2 - Prob. 8ECh. 33.2 - Prob. 9ECh. 33.3 - Prob. 1ECh. 33.3 - Prob. 2ECh. 33.3 - Prob. 3ECh. 33.3 - Prob. 4ECh. 33.3 - Prob. 5ECh. 33.3 - Prob. 6ECh. 33.4 - Prob. 1ECh. 33.4 - Prob. 2ECh. 33.4 - Prob. 3ECh. 33.4 - Prob. 4ECh. 33.4 - Prob. 5ECh. 33.4 - Prob. 6ECh. 33 - Prob. 1PCh. 33 - Prob. 2PCh. 33 - Prob. 3PCh. 33 - Prob. 4PCh. 33 - Prob. 5P
Knowledge Booster
Similar questions
- The game of Chomp is played by two players. In this game, cookies are laid out on a rectangular grid. The cookie in the top-left position is poisoned. The two players take turns making moves; at each move, a player is required to eat a remaining cookie, together with all cookies to the right and/or below (that is all the remaining cookies in the rectangle, in which the first cookie eaten is the top left corner). The loser is the player who has no choice but to eat the poisoned cookie. Prove that if the board is square (and bigger than 1 × 1) then the first player has a winning strategy.arrow_forwardIn an astronomy board game, N planets in an imaginary universe do not follow the normal law of gravitation. All the planets are positioned in a row. The planetary system can be in a stable state only if the sum of the mass of all planets at even positions is equal to the sum of the mass of planets at the odd positions. Initially, the system is not stable, but a player can destroy one planet to make it stable. Find the planet that should be destroyed to make the system stable. If no such planet exists, then return -1. If there are multiple such planets, then destroy the planet with the smallest index and return the index of the destroyed planet. Example Let N-5 and planets = [2,4,6,3,4]. Destroying the fourth planet of mass 3 will result in planets = [2,4,6,4], and here, the sum of odd positioned planets is (2+6)=8, and the sum of even positioned planets is (4+4)=8, and both are equal now. Hence, we destroy the fourth planet. 11 MNBASK19922 13 14 15 16 17 18 20 * The function is…arrow_forwardIn a card game, your opponent places n monster cards onto the board, the i th of which has hi health points. You in turn have m ≥ n hero cards in your hand, the j th of which deals dj damage per turn. To begin the game, you will choose n heroes from your hand and assign each of them to a different enemy monster. Each turn, your heroes will deal damage equal to their damage power to the opposing enemy. If at any point an opponent’s monster reaches 0 health or less, then it is destroyed. You are given a limited number of turns k to destroy all enemy monsters. Design an algorithm which runs in O(m + n log n) time and determines whether it is possible to assign your heroes in such a way as to destroy all enemy monsters in k turns or fewer First develop a Θ(m log m) time algorithm, then improve it to Θ(m + n log n) Do not write the code, give steps and methods. Explain the steps of algorithm, and the logic behind these steps in plain English input is The number of monsters n, the health…arrow_forward
- In a card game, your opponent places n monster cards onto the board, the i th of which has hi health points. You in turn have m ≥ n hero cards in your hand, the j th of which deals dj damage per turn. To begin the game, you will choose n heroes from your hand and assign each of them to a different enemy monster. Each turn, your heroes will deal damage equal to their damage power to the opposing enemy. If at any point an opponent’s monster reaches 0 health or less, then it is destroyed. You are given a limited number of turns k to destroy all enemy monsters. Design an algorithm which runs in O(m + n log n) time and determines whether it is possible to assign your heroes in such a way as to destroy all enemy monsters in k turns or fewer First develop a Θ(m log m) time algorithm, then improve it to Θ(m + n log n) Do not write the code, give steps and methods. Explain the steps of algorithm, time complexity, and the logic behind these steps in plain English Input is the number of monsters…arrow_forwardEmail me the answers to the following questions. If you are not familiar with Peg Solitaire, then look it up online. Peg Solitaire is a game consisting of a playing board with 33 holes together with 32 pegs. In the picture above, the hole in the center is empty and the remaining holes contain pegs. The goal is to remove all the pieces except one, which should be in the center. A piece can be removed by jumping an adjacent piece over it into an empty hole. Jumps are permitted horizontally or vertically, but not diagonally. Your assignment consists of one required part, plus one extra credit part: 1. Explain (in words) why Breadth First Search and Iterative Deepening are not good methods for this problem.arrow_forwardagents: An agent is trying to eat all the food in a maze that contains obstacles, but he now has the help of his friends! An agent cannot occupy a square that has an obstacle. There are initially k pieces of food (represented by dots), at positions (f1,...,fk). There are also n agents at positions (p1,...,pn). Initially, all agents start at random locations in the maze. Consider a search problem in which all agents move simultaneously ;that is, in each step each agent moves into some adjacent position (N, S, E, or W, or STOP). Note that any number of agents may occupy the same position. Give a search formulation to the problem of looking for both gold and diamond in a Knowing that you have M squares in the maze that do not have an What is the maximum size of the state space. What is the maximum branching For each of the following heuristics, indicate (yes/no) whether or not it is h1: The number of dots (representing food) remaining. [ True, False ]. h2(s)=0, where s is a…arrow_forward
- agents: An agent is trying to eat all the food in a maze that contains obstacles, but he now has the help of his friends! An agent cannot occupy a square that has an obstacle. There are initially k pieces of food (represented by dots), at positions (f1,...,fk). There are also n agents at positions (p1,...,pn). Initially, all agents start at random locations in the maze. Consider a search problem in which all agents move simultaneously ;that is, in each step each agent moves into some adjacent position (N, S, E, or W, or STOP). Note that any number of agents may occupy the same position. Figure 1: A maze with 3 agents For each of the following heuristics, indicate (yes/no) whether or not it is h1: The number of dots (representing food) remaining. [ True, False ]. h2(s)=0, where s is a state node. [ True, False ]. h3(s)=1, where s is a state node. [ True, False ].arrow_forwardOn a chess board of r rows and c columns there is a lone white rook surrounded by a group of opponent's black knights. Each knight attacks 8 squares as in a typical chess game, which are shown in the figure - the knight on the red square attacks the 8 squares with a red dot. The rook can move horizontally and vertically by any number of squares. The rook can safely pass through an empty square that is attacked by a knight, but it must move to a square that is not attacked by any knight. The rook cannot jump over a knight while moving. If the rook moves to a square that contains a knight, it may capture it and remove it from the board. The black knights. never move. Can the rook eventually safely move to the designated target square? The figure illustrates how the white rook can move to the blue target square at the top-right corner in the first sample case. The rook captures one black knight at the bottom-right of the board on its way. Rok nd kight lcoes by Chunen Input The first line…arrow_forwardCorrect answer will be upvoted else Multiple Downvoted. Computer science. one maneuver, the robot should move one cell to the left or right, given that it doesn't move beyond the field of play. As such, if the robot was in the cell I, it should move to either the cell i−1 or the cell i+1, as long as it lies among 1 and n (endpoints comprehensive). The cells, in the request they are visited (counting the cell the robot is set), together make a decent way. Every cell I has a worth computer based intelligence related with it. Let c0,c1,… ,ck be the succession of cells in a decent way in the request they are visited (c0 is the cell robot is at first positioned, c1 is the cell where the robot is after its first move, etc; all the more officially, ci is the cell that the robot is at after I moves). Then, at that point, the worth of the way is determined as ac0+ac1+⋯+ack. Your errand is to work out the amount of qualities over all conceivable great ways. Since this number can be…arrow_forward
- A Marble Game is played with M marbles on a square board. The board is divided into NxN squares, andM of those squares contain holes. Marbles and holes are numbered from 1 to M. The goal of the Marblegame is to roll each marble into the hole that has the same number. A game board may contain walls.Each wall is one unit long and stands between two adjacent unit squares. Two squares are consideredadjacent if and only if they share a side.At the beginning of the game, all marbles are placed on the board, each in a different square. A “move”consists of slightly lifting a side of the game board. Then all marbles on the board roll downward towardthe opposite side, each one rolling until it meets a wall or drops into an empty hole, or until the nextsquare is already occupied by another marble. Marbles roll subject to the following restrictions: Marbles cannot jump over walls, other marbles, or empty holes Marbles cannot leave the board (The edge is a wall) A unit square can contain at most…arrow_forwardQuestion 18 The following question uses a robot in a grid of squares. The robot is represented as a triangle, which is initially facing toward the top of the grid. The following code segment moves the robot around the grid. Assume that n is a positive integer.arrow_forwardA deck of cards contains 52 cards with four suits: club, diamond, heart and spade ranging in values from 2, ... to 10, Jack, Queen, King and Ace. Ace has the highest value in the same suit. Cards can be compared using their face values. A card with higher face value is bigger than a card with lower face value. If two cards have the same face value, then the suit determines the order. Club is smaller than diamond which is smaller than heart which is smaller than spade. For example: club 2 < diamond 2 < heart 2 < spade 2 if compared.Write an interactive Java program that allows you play cards with a computer. For this project, we are going to focus on one suit of the deck of cards. There are only 13 cards (value: 2, ... to 10, Jack, Queen, King and Ace) in a suit. To play:(a). You first pick a suit at random from the four suits (club, diamond, heart and spade), and display the suit. (b) Then you randomly draw a card from the suit, and let computer draw a card from the same…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