diff --git a/core/src/main/java/aima/core/search/basic/uninformed/GraphSearch.java b/core/src/main/java/aima/core/search/basic/uninformed/GraphSearch.java
index 4a42f267f0..3a81d56d99 100644
--- a/core/src/main/java/aima/core/search/basic/uninformed/GraphSearch.java
+++ b/core/src/main/java/aima/core/search/basic/uninformed/GraphSearch.java
@@ -1,19 +1,11 @@
 package aima.core.search.basic.uninformed;
 
-import java.util.HashSet;
-import java.util.LinkedList;
-import java.util.List;
-import java.util.Queue;
-import java.util.Set;
-
-import aima.core.search.api.Node;
-import aima.core.search.api.NodeFactory;
-import aima.core.search.api.Problem;
-import aima.core.search.api.SearchController;
-import aima.core.search.api.SearchForActionsFunction;
+import aima.core.search.api.*;
 import aima.core.search.basic.support.BasicNodeFactory;
 import aima.core.search.basic.support.BasicSearchController;
 
+import java.util.*;
+
 /**
  * Artificial Intelligence A Modern Approach (4th Edition): Figure ??, page ??.
  * <br>
@@ -31,84 +23,84 @@
  *     expand the chosen node, adding the resulting nodes to the frontier
  *       only if not in the frontier or explored set
  * </pre>
- *
+ * <p>
  * Figure ?? An informal description of the general graph-search algorithm.
  *
- *
  * @author Ciaran O'Reilly
  */
 public class GraphSearch<A, S> implements SearchForActionsFunction<A, S> {
-
+	
+	protected NodeFactory<A, S> nodeFactory = new BasicNodeFactory<>();
+	protected SearchController<A, S> searchController = new BasicSearchController<A, S>();
+	
+	public GraphSearch() {
+		//empty constructor
+	}
+	
 	// function GRAPH-SEARCH(problem) returns a solution, or failure
 	@Override
 	public List<A> apply(Problem<A, S> problem) {
 		// initialize the frontier using the initial state of problem
 		Queue<Node<A, S>> frontier = newFrontier(problem.initialState());
-		// initialize the explored set to be empty
-		Set<S> explored = newExploredSet();
+		// initialize the reached table to be empty
+		Map<S, Node<A, S>> reached = new HashMap<>();
+		// initialize the solution
+		List<A> solution = failure();
+		
+		// if the frontier is empty then return failure
+		if (frontier.isEmpty()) {
+			return failure();
+		}
 		// loop do
-		while (true) {
-			// if the frontier is empty then return failure
-			if (frontier.isEmpty()) {
-				return failure();
-			}
+		while (!frontier.isEmpty()) {
 			// choose a leaf node and remove it from the frontier
-			Node<A, S> node = frontier.remove();
-			// if the node contains a goal state then return the corresponding
-			// solution
-			if (isGoalState(node, problem)) {
-				return solution(node);
-			}
-			// add the node to the explored set
-			explored.add(node.state());
-			// expand the chosen node, adding the resulting nodes to the
-			// frontier
-			for (A action : problem.actions(node.state())) {
-				Node<A, S> child = newChildNode(problem, node, action);
-				// only if not in the frontier or explored set
-				if (!(containsState(frontier, child) || explored.contains(child.state()))) {
+			Node<A, S> parent = frontier.remove();
+			// expand the chosen node
+			for (Node<A, S> child : expand(problem, parent)) {
+				// only if the child is not in reached or child is a cheaper path than reached[child.state()]
+				if (!reached.containsKey(child.state()) || child.pathCost() < reached.get(child.state()).pathCost()) {
+					// add child in reached and frontier
+					reached.put(child.state(), child);
 					frontier.add(child);
+					// if child is a goal and is cheaper than the best solution found so far then update the solution
+					if (isGoalState(child, problem)) {
+						solution = getSolution(child);
+					}
 				}
 			}
 		}
+		return solution;
 	}
-
-	//
-	// Supporting Code
-	protected NodeFactory<A, S> nodeFactory = new BasicNodeFactory<>();
-	protected SearchController<A, S> searchController = new BasicSearchController<A, S>();
-
-	public GraphSearch() {
+	
+	public List<Node<A, S>> expand(Problem<A, S> problem, Node<A, S> parent) {
+		List<Node<A, S>> nodes = new ArrayList<>();
+		for (A action : problem.actions(parent.state())) {
+			Node<A, S> node = newChildNode(problem, parent, action);
+			nodes.add(node);
+		}
+		return nodes;
 	}
-
+	
 	public Node<A, S> newChildNode(Problem<A, S> problem, Node<A, S> node, A action) {
 		return nodeFactory.newChildNode(problem, node, action);
 	}
-
+	
 	public Queue<Node<A, S>> newFrontier(S initialState) {
 		Queue<Node<A, S>> frontier = new LinkedList<>();
 		frontier.add(nodeFactory.newRootNode(initialState));
 		return frontier;
 	}
-
-	public Set<S> newExploredSet() {
-		return new HashSet<>();
-	}
-
+	
 	public List<A> failure() {
 		return searchController.failure();
 	}
-
-	public List<A> solution(Node<A, S> node) {
+	
+	public List<A> getSolution(Node<A, S> node) {
 		return searchController.solution(node);
 	}
-
+	
 	public boolean isGoalState(Node<A, S> node, Problem<A, S> problem) {
 		return searchController.isGoalState(node, problem);
 	}
-
-	public boolean containsState(Queue<Node<A, S>> frontier, Node<A, S> child) {
-		// NOTE: Not very efficient (i.e. linear in the size of the frontier)
-		return frontier.stream().anyMatch(frontierNode -> frontierNode.state().equals(child.state()));
-	}
+	
 }