Merge pull request TheAlgorithms#558 from rmakynen/master

Added an explanation to SkylineProblem

Others/Dijkstra.java

@@ -0,0 +1,171 @@
+package Others;
+
+
+/**
+ * Dijkstra's algorithm,is a graph search algorithm that solves the single-source
+ * shortest path problem for a graph with nonnegative edge path costs, producing
+ * a shortest path tree.
+ * 
+ * NOTE:  The inputs to Dijkstra's algorithm are a directed and weighted graph consisting
+ * of 2 or more nodes, generally represented by an adjacency matrix or list, and a start node.
+ * 
+ * Original source of code: https://rosettacode.org/wiki/Dijkstra%27s_algorithm#Java
+ * Also most of the comments are from RosettaCode.
+ *
+ */
+//import java.io.*;
+import java.util.*; 
+public class Dijkstra {
+   private static final Graph.Edge[] GRAPH = {
+      new Graph.Edge("a", "b", 7),	//Distance from node "a" to node "b" is 7. In the current Graph there is no way to move the other way (e,g, from "b" to "a"), a new edge would be needed for that
+      new Graph.Edge("a", "c", 9),
+      new Graph.Edge("a", "f", 14),
+      new Graph.Edge("b", "c", 10),
+      new Graph.Edge("b", "d", 15),
+      new Graph.Edge("c", "d", 11),
+      new Graph.Edge("c", "f", 2),
+      new Graph.Edge("d", "e", 6),
+      new Graph.Edge("e", "f", 9),
+   };
+   private static final String START = "a";
+   private static final String END = "e";
+
+	/**
+	 * main function
+	 * Will run the code with "GRAPH" that was defined above.
+	 */
+   public static void main(String[] args) {
+      Graph g = new Graph(GRAPH);
+      g.dijkstra(START);
+      g.printPath(END);
+      //g.printAllPaths();
+   }
+}
+
+class Graph {
+   private final Map<String, Vertex> graph; // mapping of vertex names to Vertex objects, built from a set of Edges
+
+   /** One edge of the graph (only used by Graph constructor) */
+   public static class Edge {
+      public final String v1, v2;
+      public final int dist;
+      public Edge(String v1, String v2, int dist) {
+         this.v1 = v1;
+         this.v2 = v2;
+         this.dist = dist;
+      }
+   }
+
+   /** One vertex of the graph, complete with mappings to neighbouring vertices */
+  public static class Vertex implements Comparable<Vertex> {
+	public final String name;
+	public int dist = Integer.MAX_VALUE; // MAX_VALUE assumed to be infinity
+	public Vertex previous = null;
+	public final Map<Vertex, Integer> neighbours = new HashMap<>();
+
+	public Vertex(String name) {
+		this.name = name;
+	}
+
+	private void printPath() {
+		if (this == this.previous) {
+			System.out.printf("%s", this.name);
+		}
+		else if (this.previous == null) {
+			System.out.printf("%s(unreached)", this.name);
+		}
+		else {
+			this.previous.printPath();
+			System.out.printf(" -> %s(%d)", this.name, this.dist);
+		}
+	}
+
+	public int compareTo(Vertex other) {
+		if (dist == other.dist)
+			return name.compareTo(other.name);
+
+		return Integer.compare(dist, other.dist);
+	}
+
+	@Override public String toString() {
+		return "(" + name + ", " + dist + ")";
+	}
+}
+
+   /** Builds a graph from a set of edges */
+   public Graph(Edge[] edges) {
+      graph = new HashMap<>(edges.length);
+
+      //one pass to find all vertices
+      for (Edge e : edges) {
+         if (!graph.containsKey(e.v1)) graph.put(e.v1, new Vertex(e.v1));
+         if (!graph.containsKey(e.v2)) graph.put(e.v2, new Vertex(e.v2));
+      }
+
+      //another pass to set neighbouring vertices
+      for (Edge e : edges) {
+         graph.get(e.v1).neighbours.put(graph.get(e.v2), e.dist);
+         //graph.get(e.v2).neighbours.put(graph.get(e.v1), e.dist); // also do this for an undirected graph
+      }
+   }
+
+   /** Runs dijkstra using a specified source vertex */ 
+   public void dijkstra(String startName) {
+      if (!graph.containsKey(startName)) {
+         System.err.printf("Graph doesn't contain start vertex \"%s\"\n", startName);
+         return;
+      }
+      final Vertex source = graph.get(startName);
+      NavigableSet<Vertex> q = new TreeSet<>();
+
+      // set-up vertices
+      for (Vertex v : graph.values()) {
+         v.previous = v == source ? source : null;
+         v.dist = v == source ? 0 : Integer.MAX_VALUE;
+         q.add(v);
+      }
+
+      dijkstra(q);
+   }
+
+   /** Implementation of dijkstra's algorithm using a binary heap. */
+   private void dijkstra(final NavigableSet<Vertex> q) {      
+      Vertex u, v;
+      while (!q.isEmpty()) {
+
+         u = q.pollFirst(); // vertex with shortest distance (first iteration will return source)
+         if (u.dist == Integer.MAX_VALUE) break; // we can ignore u (and any other remaining vertices) since they are unreachable
+
+         //look at distances to each neighbour
+         for (Map.Entry<Vertex, Integer> a : u.neighbours.entrySet()) {
+            v = a.getKey(); //the neighbour in this iteration
+
+            final int alternateDist = u.dist + a.getValue();
+            if (alternateDist < v.dist) { // shorter path to neighbour found
+               q.remove(v);
+               v.dist = alternateDist;
+               v.previous = u;
+               q.add(v);
+            } 
+         }
+      }
+   }
+
+   /** Prints a path from the source to the specified vertex */
+   public void printPath(String endName) {
+      if (!graph.containsKey(endName)) {
+         System.err.printf("Graph doesn't contain end vertex \"%s\"\n", endName);
+         return;
+      }
+
+      graph.get(endName).printPath();
+      System.out.println();
+   }
+   /** Prints the path from the source to every vertex (output order is not guaranteed) */
+   public void printAllPaths() {
+      for (Vertex v : graph.values()) {
+         v.printPath();
+         System.out.println();
+      }
+   }
+}

SkylineProblem/SkylineProblem.java

@@ -1,3 +1,9 @@
+/**
+ * Given n rectangular buildings in a 2-dimensional city, computes the skyline of these buildings,
+ * eliminating hidden lines. The main task is to view buildings from a side and remove all sections
+ * that are not visible.
+ * Source for explanation: https://www.geeksforgeeks.org/the-skyline-problem-using-divide-and-conquer-algorithm/
+ */
 import java.util.ArrayList;
 import java.util.Iterator;
 import java.util.Scanner;