3. You are given a rectangular grid, where each cell corresponds to a land or sea area. If twocells of land are adjacent to each other vertically, horizontally, or diagonally on theyou can walk from one to the other. Two land areas belong to the same island if and only ifmap,thenthere is a path from one to the other.Describe a graph algorithm that returns the number of islands in the map and analyze runtimein terms of the number of cells n.

Answered: 3. You are given a rectangular grid,…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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The maze is described as a graph with a start, goal, edge lengths, and two types of edges: regular paths in the maze, and hedges which one can crawl through. We are only allowed to crawl through edge once. (Some parts of the maze are too thick to crawl through.) Design an algorithm which finds the shortest path to the goal, as quickly as possible. Please do not use the modified version of Dijkstra. Instead modify the graph and use regular version of Dijkstra
Although the plot function is designed primarily for plotting standard xy graphs, it can be adapted for other kinds of plotting as well. b. Make a plot of the curve, which is defined parametrically by the equations x = 2cosθ + cos2θ, y = 2sinθ - sin2θ, where 0 < θ < 2π. Take a set of values of θ between zero and 2π and calculate x and y for each from the equations above, then plot y as a function of x. b. Taking this approach a step further, one can make a polar plot r = f(θ) for some function f by calculating r for a range of values of θ and then converting r and θ to Cartesian coordinates using the standard equations x = r cosθ, y = r sinθ. Use this method to make a plot of the function r = ecosθ – 2 cos(4θ) + sin5 (θ/12) in the range 0 <= θ <= 24π. use python code to answer the highlight one
Using Matplotlib (based on python), write a code that takes the input of two different functions. The first function should be displayed first on a graph. Program such that the graph gradually transforms into the second function.
A graph is given below. What is the return value to run the graph function first( 0 )? int first(int v); // Get v's first neighbor 1 2 3 4 1 1 1 1 1 3 1 4 (a) (b) 1 2 3 4 (c) а. 2 b. 1 O c. 4 O d. 3 е.
Consider an undirected graph G = (V,E), in which each node u 2 V may be colored with some color between 1 and C. Your task is to write a program that determine the colors for the uncolored nodes in the graph such that • For all edges (u, v) 2 E, u and v have different colors. • The number of additional colors needed is minimum. Input (Standard input): Includes multiples lines. The first line contains two integers 1 n 1000, 1 m 100000 that correspond to the number of nodes and edges, respectively. Each of the following m lines contain two integers u and v, separated by one space, to denote an edge from u to v. Nodes are numbered from 1 to n. The last line contains n integers that are the colors of the nodes. Uncolored nodes are indicated with color 0. Output (Standard output): The first line contains an integer 0 D n that is the number of additional colors needed to color all the uncolored nodes in the graph. The next line contains n positive integers that are colors of the nodes. Your…
When the smog season arrives, the Civil Aviation Authority (CAA) is forced to shut down airports where visibility becomes poor to avoid any air traffic accidents. Imagine the country’s flight network as an undirected graph where the airports are nodes and flight routes connecting these airports are the edges. Ideally, you want the rest of the air traffic to remain undisturbed if one of the airports is shut down. State an algorithm (in pseudocode) that tests whether the removal of a given node (airport) makes a connected graph unconnected or not?
When faced with a difficult problem in mathematics, it often helps to draw a picture. If the problem involves a discrete collection of interrelated objects, it is natural to sketch the objects and draw lines between them to indicate the relationships. A graph (composed of dots called vertices connected by lines or curves called edges) is the mathematical version of such a sketch. The edges of a graph may have arrows on them; in this case, the graph is called a directed graph. When we draw a graph, it doesn’t really matter where we put the vertices or whether we draw the edges as curved or straight; rather, what matters is whether or not two given vertices are connected by an edge (or edges). The degree of a vertex is the number of edges incident to it (i.e., the number of times an edge touches it). This is different than the number of edges touching it, because an edge my form a loop; for instance, vertex ? in graph ? (above) has degree 5. In a directed graph, we can speak of the…
When faced with a difficult problem in mathematics, it often helps to draw a picture. If the problem involves a discrete collection of interrelated objects, it is natural to sketch the objects and draw lines between them to indicate the relationships. A graph (composed of dots called vertices connected by lines or curves called edges) is the mathematical version of such a sketch. The edges of a graph may have arrows on them; in this case, the graph is called a directed graph. When we draw a graph, it doesn’t really matter where we put the vertices or whether we draw the edges as curved or straight; rather, what matters is whether or not two given vertices are connected by an edge (or edges). The degree of a vertex is the number of edges incident to it (i.e., the number of times an edge touches it). This is different than the number of edges touching it, because an edge my form a loop; for instance, vertex ? in graph ? (above) has degree 5. In a directed graph, we can speak of the…
When faced with a difficult problem in mathematics, it often helps to draw a picture. If the problem involves a discrete collection of interrelated objects, it is natural to sketch the objects and draw lines between them to indicate the relationships. A graph (composed of dots called vertices connected by lines or curves called edges) is the mathematical version of such a sketch. The edges of a graph may have arrows on them; in this case, the graph is called a directed graph. When we draw a graph, it doesn’t really matter where we put the vertices or whether we draw the edges as curved or straight; rather, what matters is whether or not two given vertices are connected by an edge (or edges). The degree of a vertex is the number of edges incident to it (i.e., the number of times an edge touches it). This is different than the number of edges touching it, because an edge my form a loop; for instance, vertex ? in graph ? (above) has degree 5. In a directed graph, we can speak of the…
When faced with a difficult problem in mathematics, it often helps to draw a picture. If the problem involves a discrete collection of interrelated objects, it is natural to sketch the objects and draw lines between them to indicate the relationships. A graph (composed of dots called vertices connected by lines or curves called edges) is the mathematical version of such a sketch. The edges of a graph may have arrows on them; in this case, the graph is called a directed graph. When we draw a graph, it doesn’t really matter where we put the vertices or whether we draw the edges as curved or straight; rather, what matters is whether or not two given vertices are connected by an edge (or edges). The degree of a vertex is the number of edges incident to it (i.e., the number of times an edge touches it). This is different than the number of edges touching it, because an edge my form a loop; for instance, vertex ? in graph ? (above) has degree 5. In a directed graph, we can speak of the…
Hi I need help writing a java program that implements Prim's algorithm. The imput of the program is given by the scanner with an undirected graph. First input line is the number of vertices, second input is the number of undirected edges. After that the input is a matrix of 3 by the number of undirected edges. The matrix firt 2 column contain the end points and the third column contains the weight . The output of the program is an integer representing the sum of all the edges that make up the minimum spanning tre. I have attach a picture for farther details. THANKS
Our main objective is to implement breadth-first-search (BFS) to print the vertices of a graph G. To get the full grade, you must annotate your code (i.e., write relevant comments throughout your program) and proceed as follows: Ask the user to enter the number of nodes of a graph G. Ask the user to enter the edges of G (e.g., if the user enters 3 and 5; it means that there is an edge between nodes 3 and 5). Store the graph G using an adjacency matrix. Run BFS on G, starting form node 1 (i.e., we assume here that the start node is 1). Use a queue to implement BFS. You may use the queue class from the library of the programming language you are using (so there is no need to implement your own class queue). Write a main function to test your program, and make sure BFS is visiting the vertices of G as expected.

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