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 33.1, Problem 7E
Program Plan Intro
To compute whether a point p0 is in the interior of an n-vertex polygon P in
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If n points are connected to fom a closed polygon as shown below, the area of the polygon
can be compuled as
n-2
Area = (%)E (*»1 + x ) (y»1 - y )
=0
Notice that although the ilustrated polygon has only 6 distinct comers, n for his polygon is 7
because the algorithmexpects that the last point (x.ya) will be repeat of the initial point, (Ko.yo).
Define a structure for a point. Each point contains x coordinate and y coordinate. The
represe ntation of a Polygon must be an array of structures in your program.
Write a C program that takes the number of actual points (n-1) from the user. After that, user
enters x and y coordinates of each point. (The last point will be repeat of the initial point). Writo
a compute Are a function which returns the area of the Polygon. Print he area of the Polygon
in main. Display the area with wo digts after the decimal point.
Note: The absolute value can be computed with fabs function.
Example:
double x.50: fabs(x) is 5.0
double x 0.0: fabs(x) is 0.0
double…
Example 9: Show that L= {0'\n is a perfect square } is not regular.
3. An
basically Rº above, has a 0 if there isn't an edge from one vertex
to another while a 1 indicates the presence of a directed edge. In a transitive closure, the ones and
zeroes correspond to
between vertices, not just edges.
4. Use Floyd's to get the All Pairs Shortest Distances. Show all 5 D matrices, including Dº:
Dº a
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D²
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D¹ a
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D³
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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
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- The edge-coloring problem is to color the edges of a graph with the fewest number of colors in such a way any two edges that share a vertex have different colors . You are given the algorithm that colors a graph with at most d+1 colors if the graph has a vertex with maximum degree d. You do not need to know how the algorithm works. Prove that this algorithm is a 2-approximation to the edge coloring problem. You may assume that d≥1. There are no decision problems in NP-hard class. True or Falsearrow_forwardLet V= {cities of Metro Manila} and E = {(x; y) | x and y are adjacent cities in Metro Manila.} (a) Draw the graph G defined by G = (V; E). You may use initials to name a vertex representing a city. (b) Apply the Four-Color Theorem to determine the chromatic number of the vertex coloring for G.arrow_forwardIs the following statement true or false? a. Performing one rotation always preserves the AVL property. b. For any two functions f and g, we always have either f = O(g) or g = O(f). c. We run the breadth-first search algorithm (BFS) on a undirected graph G such that all edges have the same weight. BFS returns the shortest path from a source vertex s to any other vertex.arrow_forward
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