diff --git a/be-graphes-model/src/main/java/org/insa/graphs/model/Path.java b/be-graphes-model/src/main/java/org/insa/graphs/model/Path.java
index e654c12..73d364c 100644
--- a/be-graphes-model/src/main/java/org/insa/graphs/model/Path.java
+++ b/be-graphes-model/src/main/java/org/insa/graphs/model/Path.java
@@ -57,7 +57,41 @@ public class Path {
     public static Path createShortestPathFromNodes(Graph graph, List<Node> nodes)
             throws IllegalArgumentException {
         List<Arc> arcs = new ArrayList<Arc>();
-        // TODO:
+        
+        
+
+        if(nodes.size() == 1)
+        {
+            return new Path(graph, nodes.get(0));
+        }
+
+        for(int i = 0; i < nodes.size() - 1;i++)
+        {
+            Node origin = nodes.get(i);
+            Node destination = nodes.get(i+1);
+
+            List<Arc> successors = origin.getSuccessors();
+            Arc bestArc = null;
+            float lengthMin = Float.MAX_VALUE;
+            for(Arc successor : successors)
+            {
+                float legnthSuccessor = successor.getLength();
+                if(successor.getDestination().equals(destination))
+                {
+                    if (legnthSuccessor < lengthMin)
+                    {
+                        bestArc = successor;
+                        lengthMin = successor.getLength();
+                    }
+                }
+            }
+            if (bestArc == null)
+            {
+                throw new IllegalArgumentException("No arc from " + origin.getId()+ "to " + destination.getId());
+            }
+            arcs.add(bestArc);
+        }
+        
         return new Path(graph, arcs);
     }
 
@@ -196,7 +230,35 @@ public class Path {
      * @deprecated Need to be implemented.
      */
     public boolean isValid() {
-        // TODO:
+        //it is empty
+        if(this.isEmpty()) return true;
+        //it contains a single node (without arcs)
+        else if((this.getArcs().isEmpty())) return true;
+
+        else{
+        List<Arc> arcs = this.getArcs();
+        
+        //nombre d arcs dans une variable 
+        int sizeArcs = arcs.size();
+
+        if(arcs == null || arcs.size() < 1) return false;
+        
+        //the first arc has for origin the origin of the path 
+        if(arcs.get(0).getOrigin().equals(origin))
+            {
+            /*for two consecutive
+            * arcs, the destination of the first one is the origin of the second one */
+            for(int i = 0; i < sizeArcs-1; i++)
+            {
+
+                if(!(arcs.get(i).getDestination().equals(arcs.get(i+1).getOrigin()))) return false;
+            }
+
+            return true;
+            }
+        }
+
+
         return false;
     }
 
@@ -224,13 +286,8 @@ public class Path {
      * @deprecated Need to be implemented.
      */
     public double getTravelTime(double speed) {
-<<<<<<< HEAD
         return getLength() * 3600.0 / (speed * 1000.0);
        
-=======
-        // TODO:
-        return getLength() * 3600.0 / (speed * 1000.0);
->>>>>>> refs/remotes/origin/main
     }
 
     /**