Implementation of Johnson Graph Algorithm

graphs/johnson_graph.py

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+from collections import deque
+import heapq
+import sys
+
+#First implementation of johnson algorithm
+class JohnsonGraph:
+    def __init__(self):
+        self.edges = []
+        self.graph = {}
+    
+    #add vertices for a graph
+    def add_vertices(self, u):
+        self.graph[u] = []
+    
+    #assign weights for each edges formed of the directed graph
+    def add_edge(self, u, v, w):
+        self.edges.append((u, v, w))
+        self.graph[u].append((v,w))
+
+    #perform a dijkstra algorithm on a directed graph
+    def dijkstra(self, s):
+        no_v = len(self.graph)
+        distances = {vertex: sys.maxsize-1 for vertex in self.graph}
+        pq = [(0,s)]
+        
+        distances[s] = 0
+        while pq:
+            weight, v = heapq.heappop(pq)
+            
+            if weight > distances[v]:
+                continue
+                
+            for node, w in self.graph[v]:
+                if distances[v]+w < distances[node]:
+                    distances[node] = distances[v]+w
+                    heapq.heappush(pq, (distances[node], node)) 
+        return distances
+
+    #carry out the bellman ford algorithm for a node and estimate its distance vector
+    def bellman_ford(self, s): 
+        no_v = len(self.graph)
+        distances = {vertex: sys.maxsize-1 for vertex in self.graph}
+        distances[s] = 0
+        
+        for u in self.graph:
+            for u, v, w in self.edges:
+                if distances[u] != sys.maxsize-1 and distances[u]+w<distances[v]:
+                    distances[v] = distances[u]+w
+
+        return distances
+ 
+    #perform the johnson algorithm to handle the negative weights that could not be handled by either the dijkstra
+    #or the bellman ford algorithm efficiently
+    def johnson_algo(self):
+        
+        self.add_vertices("#")
+        for v in self.graph:
+            if v != "#":
+                self.add_edge("#", v, 0)
+            
+        n = self.bellman_ford("#")
+        
+        for i in range(len(self.edges)):
+            u, v, weight = self.edges[i]
+            self.edges[i] = (u, v, weight + n[u] - n[v])
+
+        self.graph.pop("#")
+        self.edges = [(u, v, w) for u, v, w in self.edges if u != "#"]
+        
+        for u in self.graph:
+            self.graph[u] = [(v, weight) for x, v, weight in self.edges if x == u]
+        
+        distances = []
+        for u in self.graph:
+            new_dist = self.dijkstra(u)
+            for v in self.graph:
+                if new_dist[v] < sys.maxsize-1:
+                    new_dist[v] += n[v] - n[u]
+            distances.append(new_dist)
+        return distances
+        
+g = JohnsonGraph()
+#this a complete connected graph
+g.add_vertices("A")
+g.add_vertices("B")
+g.add_vertices("C")
+g.add_vertices("D")
+g.add_vertices("E")
+
+g.add_edge("A", "B", 1)
+g.add_edge("A", "C", 3)
+g.add_edge("B", "D", 4)
+g.add_edge("D", "E", 2)
+g.add_edge("E", "C", -2)
+
+
+optimal_paths = g.johnson_algo()
+print("Print all optimal paths of a graph using Johnson Algorithm")
+for i, row in enumerate(optimal_paths):
+    print(f"{i}: {row}")