Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 22.3, Problem 1E
Program Plan Intro
To make chart of
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This assignment requires the extension of your graph code to apply it to movement through a “world”. The world will be a weighted, directed graph, with nodes for the start position and target(s), and other nodes containing blocks, diversions, boosts and portals. For example, in a cat world, a dog may block you, toys may take your attention, food may give you more energy and portals may prove that cats are pan-dimensional beings. This structure could also be used to implement Snakes and Ladders, or other games. Your task is to build a representation of the world and explore the possible routes through the world and rank them.
Sample input files will be available – with various scenarios in a cat world.
Your program should be called gameofcatz.py/java, and have three starting options:
* No command line arguments : provides usage information
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* "-s" : simulation mode (usage: gameofcatz –s infile savefile)
When the program starts in interactive mode,…
Consider the line from (5, 5) to (13, 9).Use the Bresenham’s line drawing algorithm to draw this line. You are expected to find out all the pixels of the line and draw it on a graph paper
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Chapter 22 Solutions
Introduction to Algorithms
Ch. 22.1 - Prob. 1ECh. 22.1 - Prob. 2ECh. 22.1 - Prob. 3ECh. 22.1 - Prob. 4ECh. 22.1 - Prob. 5ECh. 22.1 - Prob. 6ECh. 22.1 - Prob. 7ECh. 22.1 - Prob. 8ECh. 22.2 - Prob. 1ECh. 22.2 - Prob. 2E
Ch. 22.2 - Prob. 3ECh. 22.2 - Prob. 4ECh. 22.2 - Prob. 5ECh. 22.2 - Prob. 6ECh. 22.2 - Prob. 7ECh. 22.2 - Prob. 8ECh. 22.2 - Prob. 9ECh. 22.3 - Prob. 1ECh. 22.3 - Prob. 2ECh. 22.3 - Prob. 3ECh. 22.3 - Prob. 4ECh. 22.3 - Prob. 5ECh. 22.3 - Prob. 6ECh. 22.3 - Prob. 7ECh. 22.3 - Prob. 8ECh. 22.3 - Prob. 9ECh. 22.3 - Prob. 10ECh. 22.3 - Prob. 11ECh. 22.3 - Prob. 12ECh. 22.3 - Prob. 13ECh. 22.4 - Prob. 1ECh. 22.4 - Prob. 2ECh. 22.4 - Prob. 3ECh. 22.4 - Prob. 4ECh. 22.4 - Prob. 5ECh. 22.5 - Prob. 1ECh. 22.5 - Prob. 2ECh. 22.5 - Prob. 3ECh. 22.5 - Prob. 4ECh. 22.5 - Prob. 5ECh. 22.5 - Prob. 6ECh. 22.5 - Prob. 7ECh. 22 - Prob. 1PCh. 22 - Prob. 2PCh. 22 - Prob. 3PCh. 22 - Prob. 4P
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- Q- In order to plot a graph of f(x)=z and g(y)=z in the same graph, with t as a parameter. The function used is plot3(x,y,z) O plot(x,y,z) O surf(x,y,z) O mesh(z) Oarrow_forward"For the undirected graph shown below, give the number of vertices, the number of edges, and the degree of each vertex, and represent the graph with an adjacency matrix." This task is solved here, but it is only solved for task a, not b. could you help me with task b?arrow_forwardOne can manually count path lengths in a graph using adjacency matrices. Using the simple example below, produces the following adjacency matrix: A B A 1 1 B 1 0 This matrix means that given two vertices A and B in the graph above, there is a connection from A back to itself, and a two-way connection from A to B. To count the number of paths of length one, or direct connections in the graph, all one must do is count the number of 1s in the graph, three in this case, represented in letter notation as AA, AB, and BA. AA means that the connection starts and ends at A, AB means it starts at A and ends at B, and so on. However, counting the number of two-hop paths is a little more involved. The possibilities are AAA, ABA, and BAB, AAB, and BAA, making a total of five 2-hop paths. The 3-hop paths starting from A would be AAAA, AAAB, AABA, ABAA, and ABAB. Starting from B, the 3-hop paths are BAAA, BAAB, and BABA. Altogether, that would be eight 3-hop paths within this graph. Write a program…arrow_forward
- draw the graph that represents said matrix and find out, using Python, the number of 3-paths that connect the vertices v1 and v3 of the same.arrow_forwardCan we draw a planar graph with n= 7 and e = 12 such that each region is bounded by exactly 3-edges ?arrow_forwardAn edge is called a bridge if the removal of the edge increases the number of connected components in G by one. The removal of a bridge thus separates a component of G into two separate components. Let G be a graph on 6 vertices and 8 edges. How many bridges can G have at the most? (The answer is an integer)arrow_forward
- Given N cities represented as vertices V₁, V2, un on an undirected graph (i.e., each edge can be traversed in both directions). The graph is fully-connected where the edge eij connecting any two vertices vį and vj is the straight-line distance between these two cities. We want to search for the shortest path from v₁ (the source) to VN (the destination). ... Assume that all edges have different values, and €₁,7 has the largest value among the edges. That is, the source and destination have the largest straight-line distance. Compare the lists of explored vertices when we run the uniform-cost search and the A* search for this problem. Hint: The straight-line distance is the shortest path between any two cities. If you do not know how to start, try to run the algorithms by hand on some small cases first; but remember to make sure your graphs satisfy the conditions in the question.arrow_forwardSuppose you have a graph G with 6 vertices and 7 edges, and you are given the following information: The degree of vertex 1 is 3. The degree of vertex 2 is 4. The degree of vertex 3 is 2. The degree of vertex 4 is 3. The degree of vertex 5 is 2. The degree of vertex 6 is 2. What is the minimum possible number of cycles in the graph G?arrow_forwardCreate a graph containing the following edges and display the nodes of a graph in depth first traversal and breadth first traversal. V(G) = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} E(G) = {(0, 1), (0, 5), (1, 2), (1, 3), (1, 5), (2, 4), (4, 3), (5, 6), (6, 8), (7, 3), (7, 8), (8, 10), (9, 4), (9, 7), (9, 10)} The input file should consist of the number of vertices in the graph in the first line and the vertices that are adjacent to the vertex in the following lines. Header File #ifndef H_graph #define H_graph #include <iostream> #include <fstream> #include <iomanip> #include "linkedList.h" #include "unorderedLinkedList.h" #include "linkedQueue.h" using namespace std; class graphType { public: bool isEmpty() const; void createGraph(); void clearGraph(); void printGraph() const; void depthFirstTraversal(); void dftAtVertex(int vertex); void breadthFirstTraversal(); graphType(int size = 0); ~graphType(); protected: int maxSize; //maximum number of…arrow_forward
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