Update graphs_floyd_warshall.py

Author: asmitannu

graphs/graphs_floyd_warshall.py

@@ -1,77 +1,79 @@
 # floyd_warshall.py
 """
-The problem is to find and return the shortest distance between all pairs of vertices in a
-weighted directed graph that can have negative edge weights.
+The problem is to find and return the shortest distance between all pairs of vertices 
+in a weighted directed graph that can have negative edge weights.
 
 https://docs.python.org/3/library/doctest.html
 
 """
 
-
-def floyd_warshall(graph: list[list[float]], vertex: int) -> tuple:
-    # 1. For all edges from v to n, distance[i][j] = weight(edge(i, j)).
-
-    # 3. distance[i][j] = min(distance[i][j], distance[i][k] +distance[k][j]) for each possible pair i, j of vertices.
-
-    # 4. Step 3 repeated for k vertex in the graph.
-
-    # 5. Whenever distance[i][j] is given a new minimum value, next vertex[i][j] = next vertex[i][k].
-
+def floyd_warshall(graph:list[list[float]], vertex:int) -> tuple:
+    #1. For all edges from v to n, distance[i][j] = weight(edge(i, j)).
+    
+    #2. distance[i][j] = min(distance[i][j], distance[i][k] + distance[k][j]).
+        
+    #3. Step 2 is true for each pair of vertices.Repeat for k vertex in the graph.
+    
+    #4. Whenever distance[i][j] is given a new minimum value, 
+    #   next vertex[i][j] = next vertex[i][k].
+        
     """
     :param graph: 2D array calculated from weight[edge[i, j]]
-
+    
     :param v: number of vertices
-
+    
     :return: shortest distance between all vertex pairs
-
+    
     distance[u][v] will contain the shortest distance from vertex u to v.
-
+    
     # doctests:
-
+     
     >>> graph = [[0, 3, float('inf')], [2, 0, float('inf')],[float('inf'), 7, 0]]
     >>> floyd_warshall(graph, 3)[0]
     [[0, 3, inf], [2, 0, inf], [9, 7, 0]]
-
+    
     >>> graph = [[0, 1, 4],[float('inf'), 0, 2],[float('inf'), float('inf'), 0]]
     >>> floyd_warshall(graph, 3)[0]
     [[0, 1, 3], [inf, 0, 2], [inf, inf, 0]]
-
+    
     >>> graph = [[0, 0, 0],[0, 0, 0],[0, 0, 0]]
     >>> floyd_warshall(graph, 3)[0]
     [[0, 0, 0], [0, 0, 0], [0, 0, 0]]
-
+    
     #Graph with all edge weights = infinity
-
-    >>> graph = [[float('inf'), float('inf'), float('inf')],[float('inf'), float('inf'), float('inf')],[float('inf'), float('inf'), float('inf')]]
+    
+    >>> graph = [[float('inf'), float('inf'), float('inf')],
+    ... [float('inf'), float('inf'), float('inf')],
+    ... [float('inf'), float('inf'), float('inf')]]
     >>> floyd_warshall(graph, 3)[0]
     [[inf, inf, inf], [inf, inf, inf], [inf, inf, inf]]
-
-
+    
+    
     #Handling negetive weighted graph:
-
+    
     >>> graph = [[0, -2, float('inf')],[float('inf'), 0, 3],[4, float('inf'), 0]]
     >>> floyd_warshall(graph, 3)[0]
     [[0, -2, 1], [7, 0, 3], [4, 2, 0]]
-
-
+    
+    
     #Handling negetive weighted cycle:
-
+    
     >>> graph = [[0, -1, float('inf')],[float('inf'), 0, -2],[-3, float('inf'), 0]]
     >>> floyd_warshall(graph, 3)[0]
     [[-6, -7, -9], [-5, -6, -8], [-9, -10, -12]]
-
-
+    
+    
     #Number of vertex in function arguement should match number of vertex in graph:
-
+    
     >>> graph = [[0, -1, float('inf')],[float('inf'), 0, -2]]
     >>> floyd_warshall(graph, 3)[0]
     Traceback (most recent call last):
         ...
     IndexError: list index out of range
-
-
+    
+    
     #Graph data type should be a 2D list:
-
+    
     >>> graph = "strings not allowed"
     >>> floyd_warshall(graph, 3)[0]
     Traceback (most recent call last):
@@ -85,25 +87,22 @@ def floyd_warshall(graph: list[list[float]], vertex: int) -> tuple:
         for j in range(vertex):
             dist[i][j] = graph[i][j]
             # check vertex k against all other vertices (i, j)
-
+            
     for k in range(vertex):
         # looping through rows of graph array
-
+        
         for i in range(vertex):
             # looping through columns of graph array
-
+            
             for j in range(vertex):
                 if (
                     dist[i][k] != float("inf")
                     and dist[k][j] != float("inf")
                     and dist[i][k] + dist[k][j] < dist[i][j]
-                ):
+                    ):
                     dist[i][j] = dist[i][k] + dist[k][j]
-
     return dist, vertex
 
-
-if __name__ == "__main__":
+if __name__== "__main__":
     import doctest
-
     doctest.testmod()