diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..969d625
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,21 @@
+# OS specific files and folders
+.DS_Store
+
+# Java specific files and folders
+bin
+target
+doc
+*.jar
+.settings
+.classpath
+.vscode
+
+# Editor specific files and folders
+*~
+.project
+
+# Project specific files and folders
+*.mapfg
+*.mapgr
+*.path
+*.tgz
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 7580981..b9accf1 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
@@ -30,7 +30,22 @@ public class Path {
     public static Path createFastestPathFromNodes(Graph graph, List<Node> nodes)
             throws IllegalArgumentException {
         List<Arc> arcs = new ArrayList<Arc>();
-        // TODO:
+        if (nodes.size() <= 2){
+            throw new IllegalArgumentException(); 
+        }else{
+            for (int j = 0; j < nodes.size(); j++){
+                Node premier = nodes.get(j);
+                List<Arc> suc = premier.getSuccessors();
+                Arc elu = suc.get(0);
+                for (int i=0; i < suc.size(); i++){
+
+                    if ( suc.get(i).getMinimumTravelTime() <= elu.getMinimumTravelTime()){
+                        elu = suc.get(i);
+                    }
+                    arcs.add(elu);
+                }
+            }
+        } 
         return new Path(graph, arcs);
     }
 
@@ -48,7 +63,24 @@ public class Path {
     public static Path createShortestPathFromNodes(Graph graph, List<Node> nodes)
             throws IllegalArgumentException {
         List<Arc> arcs = new ArrayList<Arc>();
-        // TODO:
+        if (nodes.size() <= 2){
+            throw new IllegalArgumentException(); 
+        }else{
+            for (int j = 0; j < nodes.size(); j++){
+                Node premier = nodes.get(j);
+                List<Arc> suc = premier.getSuccessors();
+                Arc elu = suc.get(0);
+                for (int i=0; i < suc.size(); i++){
+
+                    if ( suc.get(i).getLength() <= elu.getLength()){
+                        elu = suc.get(i);
+                    }
+                    arcs.add(elu);
+                }
+            }
+        }
+        
+
         return new Path(graph, arcs);
     }
 
@@ -186,9 +218,33 @@ public class Path {
      * @return true if the path is valid, false otherwise.
      * @deprecated Need to be implemented.
      */
-    public boolean isValid() {
-        // TODO:
+     public boolean isValid() {
+        if(this.arcs.isEmpty()){
+            return true ; 
+        }
+        if ( this.graph.getNodes().size() <= 1 ){
+            return true ; 
+        }
+        
+        Node origin = this.graph.getNodes().getFirst(); // à revoir ( on prend deux arcs quelconque et compare )
+        List<Arc> firstSucs = origin.getSuccessors();
+        List<Node> destFirstArc = new ArrayList<>() ; 
+        for( Arc fSuc : firstSucs){
+            destFirstArc.add(fSuc.getDestination()) ;
+
+        } 
+        for (Node secondNode : destFirstArc){
+           List<Arc> secondSucs = secondNode.getSuccessors();
+            for (Arc sSuc : secondSucs){
+                if ( sSuc.getDestination() == origin){
+                    return true ; 
+                }
+            }
+        
+        }
+
         return false;
+    
     }
 
     /**
@@ -198,8 +254,12 @@ public class Path {
      * @deprecated Need to be implemented.
      */
     public float getLength() {
-        // TODO:
-        return 0;
+        float sum = 0; 
+        for(Arc a: this.arcs){
+            sum += a.getLength();
+
+        }
+        return sum;
     }
 
     /**
@@ -211,8 +271,12 @@ public class Path {
      * @deprecated Need to be implemented.
      */
     public double getTravelTime(double speed) {
-        // TODO:
-        return 0;
+       double sum = 0; 
+        for(Arc a: this.arcs){
+            sum += a.getTravelTime(speed);
+
+        }
+        return sum;
     }
 
     /**
@@ -223,8 +287,13 @@ public class Path {
      * @deprecated Need to be implemented.
      */
     public double getMinimumTravelTime() {
-        // TODO:
-        return 0;
+         double sum = 0; 
+        for(Arc a: this.arcs){
+            sum += a.getMinimumTravelTime();
+
+        }
+        return sum;
     }
 
+
 }