@@ -7,6 +7,7 @@
 ////////////////////////////////////////////////////////////////////////////////////////////////////////////////
 
 #include <iostream>
+#include <sstream>
 #include <stdio.h>
 #include <assert.h>
 #include <new>
@@ -115,6 +116,7 @@ class PuzzleState
 	bool GetSuccessors( AStarSearch<PuzzleState> *astarsearch, PuzzleState *parent_node );
 	float GetCost( PuzzleState &successor );
 	bool IsSameState( PuzzleState &rhs );
+	size_t Hash();
 
 	void PrintNodeInfo(); 
 
@@ -335,6 +337,19 @@ bool PuzzleState::IsSameState( PuzzleState &rhs )
 
 }
 
+// The 9 tiles positions can be encoded as digits
+size_t PuzzleState::Hash()
+{
+	stringstream stream;
+	for( size_t i = 0; i < (BOARD_HEIGHT * BOARD_WIDTH); i++ )
+	{
+		stream << tiles[i];
+	}
+	size_t state_digits;
+	stream >> state_digits;
+	return hash<size_t>{}(state_digits);
+}
+
 void PuzzleState::PrintNodeInfo()
 {
 	char str[100];
 
@@ -87,6 +87,7 @@ class MapSearchNode
 	bool GetSuccessors( AStarSearch<MapSearchNode> *astarsearch, MapSearchNode *parent_node );
 	float GetCost( MapSearchNode &successor );
 	bool IsSameState( MapSearchNode &rhs );
+	size_t Hash();
 
 	void PrintNodeInfo(); 
 
@@ -109,6 +110,13 @@ bool MapSearchNode::IsSameState( MapSearchNode &rhs )
 
 }
 
+size_t MapSearchNode::Hash()
+{
+	size_t h1 = hash<float>{}(x);
+	size_t h2 = hash<float>{}(y);
+	return h1 ^ (h2 << 1);
+}
+
 void MapSearchNode::PrintNodeInfo()
 {
 	char str[100];
 
@@ -49,6 +49,7 @@ class PathSearchNode
 	bool GetSuccessors( AStarSearch<PathSearchNode> *astarsearch, PathSearchNode *parent_node );
 	float GetCost( PathSearchNode &successor );
 	bool IsSameState( PathSearchNode &rhs );
+  size_t Hash();
 
 	void PrintNodeInfo();
 };
@@ -60,6 +61,11 @@ bool PathSearchNode::IsSameState( PathSearchNode &rhs )
   return(false);
 }
 
+size_t PathSearchNode::Hash()
+{
+  return hash<int>{}(city);
+}
+
 // Euclidean distance between "this" node city and Bucharest
 // Note: Numbers are taken from the book
 float PathSearchNode::GoalDistanceEstimate( PathSearchNode &nodeGoal )
 
@@ -73,6 +73,7 @@ class MapSearchNode
 	bool GetSuccessors( AStarSearch<MapSearchNode> *astarsearch, MapSearchNode *parent_node );
 	float GetCost( MapSearchNode &successor );
 	bool IsSameState( MapSearchNode &rhs );
+	size_t Hash();
 
 	void PrintNodeInfo(); 
 
@@ -190,6 +191,13 @@ float MapSearchNode::GetCost( MapSearchNode &successor )
 
 }
 
+size_t MapSearchNode::Hash()
+{
+	size_t h1 = hash<float>{}(x);
+	size_t h2 = hash<float>{}(y);
+	return h1 ^ (h2 << 1);
+}
+
 int main(int argc, char *argv[]) {
 
 	AStarSearch<MapSearchNode> astarsearch;