def main():
graph1 = GraphCore(True)
graph1.add_edge(1, 2, 5)
graph1.add_edge(2, 3, 6)
graph1.add_edge(1, 3, 2)
mst = kruskal(graph1)
print(mst)
def main():
debt_graph = GraphCore()
debt_graph.add_edge(0, 1, 1000)
debt_graph.add_edge(1, 2, 5000)
debt_graph.add_edge(0, 2, 2000)
simplified = simplify_debt_graph(debt_graph)
print(simplified)
def main():
# Will give wrong result if the graph is not bi-directional !!!
graph1 = GraphCore(True)
graph1.add_edge(1, 2, 5)
graph1.add_edge(2, 3, 6)
graph1.add_edge(1, 3, 2)
mst = prim(graph1)
print(mst)
def main():
graph = GraphCore(False)
graph.add_edge(0, 1)
graph.add_edge(2, 3)
graph.add_edge(3, 4)
print(graph)
ans = get_topo_sort(graph)
print(ans)
def main():
graph = GraphCore(True)
graph.add_edge(1, 2)
graph.add_edge(2, 3)
graph.add_edge(3, 1)
graph.add_edge(5, 6)
print(graph)
ans = get_connected_components(graph)
print(ans)
def main():
graph = GraphCore(True)
graph.add_edge(0, 1)
graph.add_edge(2, 3)
graph.add_edge(3, 4)
graph.add_edge(4, 2)
print(graph)
ans = get_cycle_nodes(graph)
print(ans)
def main():
graph = GraphCore(False)
graph.add_edge(0, 1)
graph.add_edge(2, 3)
graph.add_edge(3, 4)
graph.add_edge(4, 2)
print(graph)
ans = is_cyclic(graph)
print(ans)
def compare_words(word1, word2, graph: GraphCore):
idx1 = 0
idx2 = 0
while idx1 < len(word1) and idx2 < len(word2):
char1 = word1[idx1]
char2 = word2[idx2]
if char1 == char2:
idx1 += 1
idx2 += 1
continue
graph.add_edge(char1, char2)
break
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 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()
graph.add_edge(0, 1, 4)
graph.add_edge(0, 2, 1)
graph.add_edge(1, 2, 2)
graph.add_edge(1, 4, 3)
graph.add_edge(2, 1, 2)
graph.add_edge(2, 3, 2)
graph.add_edge(3, 4, 3)
distances = dijkstra(graph, 0)
print(distances)
def main():
graph = GraphCore(True)
graph.add_edge(1, 2)
graph.add_edge(1, 3)
graph.add_edge(2, 3)
graph.add_edge(2, 5)
graph.add_edge(3, 2)
graph.add_edge(3, 4)
graph.add_edge(4, 5)
print(graph)
state = get_dfs_edges(graph)
print(state)
def main():
graph = GraphCore(False)
graph.add_edge(1, 2)
graph.add_edge(1, 3)
graph.add_edge(2, 3)
graph.add_edge(2, 5)
graph.add_edge(3, 2)
graph.add_edge(3, 4)
graph.add_edge(4, 5)
print(graph)
path = dfs_iterative(graph, 1)
print(path)
def main():
graph = GraphCore()
graph.add_edge(0, 1, 4)
graph.add_edge(0, 2, 1)
graph.add_edge(1, 2, 2)
graph.add_edge(1, 4, 3)
graph.add_edge(2, 1, 2)
graph.add_edge(2, 3, 2)
graph.add_edge(3, 4, 3)
distances, paths = floyd_warshall(graph)
print(distances)
print(paths)
def snake_ladder_dijkstra(shortcuts):
"""
Assuming the snake and ladder board is of size 30.
Create a graph such that every number 'num' has an outward edge
going to num+1, num+2, ... num+6 of cost 1.
Also, create a 0-cost edge for every shortcut.
Then apply dijkstra directly.
Total number of edges = 6*30 + num_shortcuts
Note: We do not need to apply Dijkstra at all. See the BFS solution!!
"""
graph = GraphCore(False)
for src in range(1, 31):
for i in range(1, 7):
dst = src + i
if dst <= 30:
graph.add_edge(src, dst, 1)
for src, dst in shortcuts.items():
if dst > src:
graph.add_edge(src, dst, 0)
return dijkstra(graph, 1)[30]
def main():
graph = GraphCore(False)
graph.add_edge(1, 2)
graph.add_edge(1, 3)
graph.add_edge(2, 3)
graph.add_edge(2, 5)
graph.add_edge(3, 2)
graph.add_edge(3, 4)
graph.add_edge(4, 5)
print(graph)
visited = set()
dfs(graph, 1, 4, visited)
print(visited)
def main():
graph = GraphCore(False)
graph.add_edge(1, 2)
graph.add_edge(2, 3)
graph.add_edge(3, 1)
graph.add_edge(5, 6)
graph.add_edge(6, 5)
graph.add_edge(1, 5)
graph.add_edge(7, 6)
print(graph)
parent_mapping = get_strongly_connected_components(graph)
print(parent_mapping)
cond_graph = get_condensation_graph(graph, parent_mapping)
print(cond_graph)
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
def main():
graph = GraphCore()
graph.add_edge(2, 3)
graph.add_edge(3, 1)
graph.add_edge(4, 0)
graph.add_edge(4, 1)
graph.add_edge(5, 0)
graph.add_edge(5, 2)
topo_order = topo_sort(graph)
print(topo_order)
def main():
graph = GraphCore(True)
graph.add_edge(1, 2)
graph.add_edge(1, 3)
graph.add_edge(2, 4)
graph.add_edge(3, 4)
graph.add_edge(4, 5)
print(graph)
dist = bfs(graph, 3, 1)
print(dist)
def main():
graph = GraphCore(True)
graph.add_edge(1, 2)
graph.add_edge(2, 3)
graph.add_edge(3, 4)
graph.add_edge(4, 3)
graph.add_edge(4, 2)
print(graph)
ans = get_bridges_cut_points(graph)
print(ans)
def main():
graph = GraphCore(True)
graph.add_edge(1, 2)
graph.add_edge(1, 3)
graph.add_edge(2, 4)
graph.add_edge(3, 4)
graph.add_edge(4, 5)
print(graph)
is_it_really = is_bipartite(graph)
print(is_it_really)
def main():
graph = GraphCore(False)
graph.add_edge(1, 2)
graph.add_edge(2, 1)
graph.add_edge(2, 3)
graph.add_edge(3, 4)
graph.add_edge(4, 2)
print(graph)
parent_mapping = get_strongly_connected_components(graph)
print(parent_mapping)
def main():
graph = GraphCore()
graph.add_edge(2, 3, 1)
graph.add_edge(3, 1, 1)
graph.add_edge(4, 0, 1)
graph.add_edge(4, 1, 1)
graph.add_edge(5, 0, 1)
graph.add_edge(5, 2, 1)
longest_path = longest_path_dag_topo(graph, 2)
print(graph)
print(longest_path)
def main():
graph = GraphCore()
graph.add_edge(2, 3, 1)
graph.add_edge(3, 1, 1)
graph.add_edge(4, 0, 1)
graph.add_edge(4, 1, 1)
graph.add_edge(5, 0, 1)
graph.add_edge(5, 2, 1)
distances = longest_path_dag_negate(graph, 2)
print(graph)
print(distances)
def main():
graph = GraphCore(True)
graph.add_edge(1, 2)
graph.add_edge(1, 3)
graph.add_edge(1, 4)
graph.add_edge(5, 2)
graph.add_edge(5, 3)
graph.add_edge(5, 4)
print(graph)
dist = bfs_bidirectional(graph, 1, 5)
print(dist)