Speed up DijkstraAlgorithm

Author: likespro

src/main/java/com/thealgorithms/datastructures/graphs/DijkstraAlgorithm.java

@@ -1,6 +1,9 @@
 package com.thealgorithms.datastructures.graphs;
 
 import java.util.Arrays;
+import java.util.Set;
+import java.util.TreeSet;
+import org.apache.commons.lang3.tuple.Pair;
 
 /**
  * Dijkstra's algorithm for finding the shortest path from a single source vertex to all other vertices in a graph.
@@ -36,18 +39,24 @@ public int[] run(int[][] graph, int source) {
 
         int[] distances = new int[vertexCount];
         boolean[] processed = new boolean[vertexCount];
+        Set<Pair<Integer, Integer>> unprocessed = new TreeSet<>();
 
         Arrays.fill(distances, Integer.MAX_VALUE);
         Arrays.fill(processed, false);
         distances[source] = 0;
+        unprocessed.add(Pair.of(0, source));
 
-        for (int count = 0; count < vertexCount - 1; count++) {
-            int u = getMinDistanceVertex(distances, processed);
+        while (!unprocessed.isEmpty()) {
+            Pair<Integer, Integer> distanceAndU = unprocessed.iterator().next();
+            unprocessed.remove(distanceAndU);
+            int u = distanceAndU.getRight();
             processed[u] = true;
 
             for (int v = 0; v < vertexCount; v++) {
                 if (!processed[v] && graph[u][v] != 0 && distances[u] != Integer.MAX_VALUE && distances[u] + graph[u][v] < distances[v]) {
+                    unprocessed.remove(Pair.of(distances[v], v));
                     distances[v] = distances[u] + graph[u][v];
+                    unprocessed.add(Pair.of(distances[v], v));
                 }
             }
         }
@@ -56,27 +65,6 @@ public int[] run(int[][] graph, int source) {
         return distances;
     }
 
-    /**
-     * Finds the vertex with the minimum distance value from the set of vertices that have not yet been processed.
-     *
-     * @param distances The array of current shortest distances from the source vertex.
-     * @param processed The array indicating whether each vertex has been processed.
-     * @return The index of the vertex with the minimum distance value.
-     */
-    private int getMinDistanceVertex(int[] distances, boolean[] processed) {
-        int min = Integer.MAX_VALUE;
-        int minIndex = -1;
-
-        for (int v = 0; v < vertexCount; v++) {
-            if (!processed[v] && distances[v] <= min) {
-                min = distances[v];
-                minIndex = v;
-            }
-        }
-
-        return minIndex;
-    }
-
     /**
      * Prints the shortest distances from the source vertex to all other vertices.
      *