a cone * * * * * That cannot be correct. The apex of the cone is a vertex. I do not believe that such a shape is possible. Wherever the two faces meet, there will be an edge.
The shape you're looking for that has 2 faces, 0 edges, and 0 vertices would be a cylinder.
No such shape exists. The closest contenders would be: a cylinder - 3 faces, 2 edges, 0 verticies or a cone - 2 faces, 1 edge, 1 vertex
a sphere
No vertices (0). a heart shape is not a polygon shape, only polygon shapes have vertices.
One possible answer is an infinite cone. Spheres have one face but no vertex. No physical 3-D shape can have a vertex without having more than one face (a real cone typically has two: side and bottom).
An infinite cone.
one face one vertex and two circle edges * * * * * What kind of cone is that? It has 1 edge, 2 faces (one curved and one plane), and 1 vertex.
There is no such shape. If anyone can prove otherwise, I'd be grateful if they'd let me know.
a cone * * * * * That cannot be correct. The apex of the cone is a vertex. I do not believe that such a shape is possible. Wherever the two faces meet, there will be an edge.
cone
Faces-2 (1 flat face and 1 curved face), 1 curved edge, and 1 vertex.
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 shape you're looking for that has 2 faces, 0 edges, and 0 vertices would be a cylinder.
No such shape exists. The closest contenders would be: a cylinder - 3 faces, 2 edges, 0 verticies or a cone - 2 faces, 1 edge, 1 vertex
No such shape exists. The closest contenders would be: a cylinder - 3 faces, 2 edges, 0 verticies or a cone - 2 faces, 1 edge, 1 vertex
No such shape exists. the closest contenders would be: a cylinder - 3 faces, 2 edges, 0 verticies or a cone - 2 faces, 1 edge, 1 vertex