def get_condensation_graph(graph, parent_mapping):
cond_graph = GraphCore(False)
for src, edges in graph.get_all_edges().items():
parent_src = parent_mapping[src]
for dst in edges:
parent_dst = parent_mapping[dst]
if parent_src == parent_dst:
continue
else:
cond_graph.add_edge(parent_src, parent_dst)
# For all the vertices which are disconnected from the rest of the graph.
for src in graph.vertices:
if parent_mapping[src] == src:
cond_graph.add_vertex(src)
return cond_graph
def main():
graph = GraphCore(False)
num_vertices = 4
edges_input = []
edges_input.append((1, 2))
edges_input.append((3, 2))
edges_input.append((4, 3))
edges_input.append((2, 1))
for edge in edges_input:
# Reverse edges.
graph.add_edge(edge[1], edge[0])
for vert in range(num_vertices):
graph.add_vertex(vert + 1)
ans = get_first_component_nodes(graph)
print(ans)
def simplify_debt_graph(debt_graph: GraphCore):
credit_flow = {}
for vert in debt_graph.vertices:
credit_flow[vert] = 0
for src, edges in debt_graph.get_all_edges().items():
for neigh, edge in edges.items():
wt = edge["weight"]
credit_flow[src] -= wt
credit_flow[neigh] += wt
debtors = []
creditors = []
for vert, flow in credit_flow.items():
if flow < 0:
debtors.append([vert, -flow])
else:
creditors.append([vert, flow])
assert sum(map(lambda item: item[1],
debtors)) == sum(map(lambda item: item[1], creditors))
simplified_graph = GraphCore()
for vert in debt_graph.vertices:
simplified_graph.add_vertex(vert)
debtors_idx = 0
creditors_idx = 0
while debtors_idx < len(debtors) and creditors_idx < len(creditors):
debtor = debtors[debtors_idx]
creditor = creditors[creditors_idx]
min_flow = min(debtor[1], creditor[1])
simplified_graph.add_edge(debtor[0], creditor[0], min_flow)
debtor[1] -= min_flow
creditor[1] -= min_flow
if debtor[1] == 0:
debtors_idx += 1
if creditor[1] == 0:
creditors_idx += 1
assert debtors_idx == len(debtors)
assert creditors_idx == len(creditors)
return simplified_graph