Q: What is the difference between a vertex and an edge?

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A cycle is a closed path such that the end vertex of the final edge is the start vertex of the first edge.

A cone has one vertex, one edge, and one base.

No but it has a circular edge

vertex

2

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A cone has one vertex and one edge.

import java.util.List; import java.util.ArrayList; import java.util.Collections; class Vertex implements Comparable<Vertex> { public final String name; public Edge[] adjacencies; public double minDistance = Double.POSITIVE_INFINITY; public Vertex previous; public Vertex(String argName) { name = argName; } public String toString() { return name; } public int compareTo(Vertex other) { return Double.compare(minDistance, other.minDistance); } } class Edge { public final Vertex target; public final double weight; public Edge(Vertex argTarget, double argWeight) { target = argTarget; weight = argWeight; } } public class Dijkstra { public static void computePaths(Vertex source) { source.minDistance = 0.; PriorityQueue<Vertex> vertexQueue = new PriorityQueue<Vertex>(); vertexQueue.add(source); while (!vertexQueue.isEmpty()) { Vertex u = vertexQueue.poll(); // Visit each edge exiting u for (Edge e : u.adjacencies) { Vertex v = e.target; double weight = e.weight; double distanceThroughU = u.minDistance + weight; if (distanceThroughU < v.minDistance) { vertexQueue.remove(v); v.minDistance = distanceThroughU ; v.previous = u; vertexQueue.add(v); } } } } public static List<Vertex> getShortestPathTo(Vertex target) { List<Vertex> path = new ArrayList<Vertex>(); for (Vertex vertex = target; vertex != null; vertex = vertex.previous) path.add(vertex); Collections.reverse(path); return path; } public static void main(String[] args) { Vertex v0 = new Vertex("Harrisburg"); Vertex v1 = new Vertex("Baltimore"); Vertex v2 = new Vertex("Washington"); Vertex v3 = new Vertex("Philadelphia"); Vertex v4 = new Vertex("Binghamton"); Vertex v5 = new Vertex("Allentown"); Vertex v6 = new Vertex("New York"); v0.adjacencies = new Edge[]{ new Edge(v1, 79.83), new Edge(v5, 81.15) }; v1.adjacencies = new Edge[]{ new Edge(v0, 79.75), new Edge(v2, 39.42), new Edge(v3, 103.00) }; v2.adjacencies = new Edge[]{ new Edge(v1, 38.65) }; v3.adjacencies = new Edge[]{ new Edge(v1, 102.53), new Edge(v5, 61.44), new Edge(v6, 96.79) }; v4.adjacencies = new Edge[]{ new Edge(v5, 133.04) }; v5.adjacencies = new Edge[]{ new Edge(v0, 81.77), new Edge(v3, 62.05), new Edge(v4, 134.47), new Edge(v6, 91.63) }; v6.adjacencies = new Edge[]{ new Edge(v3, 97.24), new Edge(v5, 87.94) }; Vertex[] vertices = { v0, v1, v2, v3, v4, v5, v6 }; computePaths(v0); for (Vertex v : vertices) { System.out.println("Distance to " + v + ": " + v.minDistance); List<Vertex> path = getShortestPathTo(v); System.out.println("Path: " + path); } } }

The difference between standard form and vertex form is the standard form gives the coefficients(a,b,c) of the different powers of x. The vertex form gives the vertex 9hk) of the parabola as part of the equation.

A cycle is a closed path such that the end vertex of the final edge is the start vertex of the first edge.

vertex vertex

A face is the flat surface of an object (2 or 3 dimensional). An edge is when two sides (faces) meet on an object. A vertex is the corner of an object, where an angle exists between two or more lines.

A cone has one vertex, one edge, and one base.

No but it has a circular edge

vertex

2

its a triangle

sphere has 1 face and no vertex and it rolls but cone has 2 faces and it can roll and it has 1 vertex