33345 # K Shortest Path Python Not Working

I'm having certain Issues with my K Shortest Path algorithm. The code is given as:

```def K_shortest_Paths(graph,S,T,K=4): '''Initialize Variables Accordingly''' B = {} P = set() count = {} for U in graph.keys(): count[U] = 0 B[S] = 0 '''Algorithm Starts''' while(len(B)>=1 and count[T]<K): PU = min(B,key=lambda x:B[x]) cost = B[PU] U = PU[len(PU)-1] del B[PU] count[U] += 1 if U==T: P.add(PU) if count[U]<=K: V = graph[U].keys() for v in V: if v not in PU: PV = PU+v B[PV] = cost+1 return P ```

This is equivalent to https://en.wikipedia.org/wiki/K_shortest_path_routing which provides the Pseudo Code for Implementation. The Graph is given as: Now, It works well if I have Starting Node S<10, and Terminating Node T<10, but with S and T>10, it returns an empty set, Whereas it should return the Path. Please Note that I can't Use Networkx libraries. I only have to Use basic libraries in Python

Furthermore, the Code to Generate Graph is this:

```def create_dictionary(graph): D = {} for item in graph.items(): temp = {} connected = list(item) key = item for V in connected: temp[str(V)] = 1 D[str(key)] = temp return D def gen_p_graph(nodes,prob): if prob>1: er='error' return er graph_matrix=np.zeros([nodes,nodes]) num_of_connections=int(((nodes * (nodes-1)) * prob )/2) num_list_row=list(range(nodes-1)) while(np.sum(np.triu(graph_matrix))!=num_of_connections): row_num=random.choice(num_list_row) num_list_col=(list(range(row_num+1,nodes))) col_num=random.choice(num_list_col) if graph_matrix[row_num,col_num]==0: graph_matrix[row_num,col_num]=1 graph_matrix[col_num,row_num]=1 #create dictionary df=pd.DataFrame(np.argwhere(graph_matrix==1)) arr=np.unique(df.iloc[:,0]) dct={} for i in range(graph_matrix.shape): dct[str(i)]=set() for val in arr: dct[str(val)].update(df.loc[df.iloc[:,0]==val].iloc[:,1].values) return pd.DataFrame(graph_matrix),dct ```

And I run it like this:

```graph= create_dictionary(gen_p_graph(100,0.8)) K_shortest_Paths(graph,'11','10') ```

return an empty set whereas it should return paths.

```def k_shortest_paths(graph, src_node, dest_node, k=4): result = [] pathes = [[src_node]] while len(pathes) > 0 and len(result) < k: path = pathes.pop() last_node = path[-1] if last_node == dest_node: result.append(path) else: for child_node in graph[last_node].keys(): if child_node not in path: pathes.append(path + [child_node]) return result ```
If you call `K_shortest_Pathes(graph, "11", "10")` you will never add an element to the set `P`. Read my inline comments.
```def K_shortest_Paths(graph,S,T,K=4): '''Initialize Variables Accordingly''' B = {} P = set() count = {} for U in graph.keys(): count[U] = 0 # currently the B has only one item, i.e. { S: 0 } => { "11": 0 } B[S] = 0 '''Algorithm Starts''' while(len(B)>=1 and count[T]<K): # results in the only key in B, i.e. PU = S => PU = "11" PU = min(B,key=lambda x:B[x]) cost = B[PU] # U = PU[len(PU) - 1], where PU = "11" => # U = "11"[len("11")-1] => # *** U = "1" U = PU[len(PU)-1] del B[PU] count[U] += 1 # *** U == T => "1" == T => "1" == "10" which is False # Thus nothing is ever added to set P if U==T: P.add(PU) if count[U]<=K: V = graph[U].keys() for v in V: if v not in PU: PV = PU+v B[PV] = cost+1 return P ```