diff --git a/programmation_dynamique/bellman/main.py b/programmation_dynamique/bellman/main.py
index f2a0dca..b0a26e8 100644
--- a/programmation_dynamique/bellman/main.py
+++ b/programmation_dynamique/bellman/main.py
@@ -1,28 +1,44 @@
-def bellman_ford(graphe, sommet):
+def bellman(graphe, sommet):
+    """Une fonction qui prend en parametre un graphe et renvoie un dictionnaire contenant le cout des chemins de tous les points du graphe
+
+    Args:
+        graphe (dict): dictionnaire
+        sommet (str): le point de depart
+
+    Raises:
+        ValueError: boucle infini (quand la comme des cout est negative)
+
+    Returns:
+        dict: un dictionnaire contenant les couts
+    >>> bellman({"A":[("B",3),("C",4)],"B":[("C",0)],"C":[]},"A")
+    {'A': 0, 'B': 3, 'C': 3}
+    """
     distance = {sommet: float("inf") for sommet in graphe}
     distance[sommet] = 0
 
     for i in range(len(graphe) - 1):
-        for u in graphe:
-            for v, coef in graphe[u]:
-                if distance[u] + coef < distance[v]:
-                    distance[v] = distance[u] + coef
+        for j in graphe:
+            for k, coef in graphe[j]:
+                if distance[j] + coef < distance[k]:
+                    distance[k] = distance[j] + coef
 
-    for u in graphe:
-        for v, coef in graphe[u]:
-            if distance[u] + coef < distance[v]:
-                raise ValueError("Cycle négatif détecté")
+    for j in graphe:
+        for k, coef in graphe[j]:
+            if distance[j] + coef < distance[k]:
+                raise ValueError("Cycle infini (le valeurs deviennent de plus en plus petite vers -inf)")
 
     return distance
 
 
 if __name__ == "__main__":
+    import doctest
+    doctest.testmod()
     graphe = {
         "A": [("G", 8), ("H", 4)],
         "G": [("H", 1), ("L", 2)],
         "H": [("L", 5), ("E", 7)],
-        "L": [("E", -2)],
+        "L": [("E", 2)],
         "E": [],
     }
-    distances = bellman_ford(graphe, "A")
+    distances = bellman(graphe, "A")
     print(distances)