Add docstring and comments per Issue #727

graphs/floyd_warshall.py

@@ -1,9 +1,16 @@
+# floyd_warshall.py
+"""
+    The problem is to find the shortest distance between all pairs of vertices in a weighted directed graph that can
+    have negative edge weights.
+"""
+
 from __future__ import print_function
 
-def printDist(dist, V):
+
+def _print_dist(dist, v):
 	print("\nThe shortest path matrix using Floyd Warshall algorithm\n")
-	for i in range(V):
-		for j in range(V):
+	for i in range(v):
+		for j in range(v):
 			if dist[i][j] != float('inf') :
 				print(int(dist[i][j]),end = "\t")
 			else:
@@ -12,37 +19,84 @@ def printDist(dist, V):
 
 
 
-def FloydWarshall(graph, V):
-	dist=[[float('inf') for i in range(V)] for j in range(V)]
+def floyd_warshall(graph, v):
+	"""
+    :param graph: 2D array calculated from weight[edge[i, j]]
+    :type graph: List[List[float]]
+    :param v: number of vertices
+    :type v: int
+    :return: shortest distance between all vertex pairs
+    distance[u][v] will contain the shortest distance from vertex u to v.
+
+    1. For all edges from v to n, distance[i][j] = weight(edge(i, j)).
+    3. The algorithm then performs distance[i][j] = min(distance[i][j], distance[i][k] + distance[k][j]) for each
+    possible pair i, j of vertices.
+    4. The above is repeated for each vertex k in the graph.
+    5. Whenever distance[i][j] is given a new minimum value, next vertex[i][j] is updated to the next vertex[i][k].
+    """
+
+	dist=[[float('inf') for _ in range(v)] for _ in range(v)]
 
-	for i in range(V):
-		for j in range(V):
+	for i in range(v):
+		for j in range(v):
 			dist[i][j] = graph[i][j]
 
-	for k in range(V):
-		for i in range(V):
-			for j in range(V):
+    # check vertex k against all other vertices (i, j)
+	for k in range(v):
+		# looping through rows of graph array
+		for i in range(v):
+			# looping through columns of graph array
+			for j in range(v):
 				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]
 
-	printDist(dist, V)	
+	_print_dist(dist, v)
+	return dist, v
 
 
 
-#MAIN
-V = int(input("Enter number of vertices: "))
-E = int(input("Enter number of edges: "))
+if __name__== '__main__':
+	v = int(input("Enter number of vertices: "))
+	e = int(input("Enter number of edges: "))
+
+	graph = [[float('inf') for i in range(v)] for j in range(v)]
+
+	for i in range(v):
+		graph[i][i] = 0.0
+
+    # src and dst are indices that must be within the array size graph[e][v]
+    # failure to follow this will result in an error
+	for i in range(e):
+		print("\nEdge ",i+1)
+		src = int(input("Enter source:"))
+		dst = int(input("Enter destination:"))
+		weight = float(input("Enter weight:"))
+		graph[src][dst] = weight
+
+	floyd_warshall(graph, v)
+
+
+	# Example Input
+	# Enter number of vertices: 3
+	# Enter number of edges: 2
 
-graph = [[float('inf') for i in range(V)] for j in range(V)]
+	# # generated graph from vertex and edge inputs
+	# [[inf, inf, inf], [inf, inf, inf], [inf, inf, inf]]
+	# [[0.0, inf, inf], [inf, 0.0, inf], [inf, inf, 0.0]]
 
-for i in range(V):
-	graph[i][i] = 0.0
+	# specify source, destination and weight for edge #1
+	# Edge  1
+	# Enter source:1
+	# Enter destination:2
+	# Enter weight:2
 
-for i in range(E):
-	print("\nEdge ",i+1)
-	src = int(input("Enter source:"))
-	dst = int(input("Enter destination:"))
-	weight = float(input("Enter weight:"))
-	graph[src][dst] = weight
+	# specify source, destination and weight for edge #2
+	# Edge  2
+	# Enter source:2
+	# Enter destination:1
+	# Enter weight:1
 
-FloydWarshall(graph, V)
+	# # Expected Output from the vertice, edge and src, dst, weight inputs!!
+	# 0		INF	INF
+	# INF	0	2
+	# INF	1	0