def prim2(graph: GraphCore):
pq = Heap()
visited = set()
src = next(iter(graph.vertices))
visited.add(src)
edges = set()
for edge in graph.get_edges(src).items():
dst, edge_props = edge
weight = edge_props['weight']
pq.push((weight, src, dst))
while len(visited) != len(graph.vertices) and pq.size() > 0:
top = pq.pop()
while pq.size() > 0:
weight, src, dst = top
if dst not in visited:
break
top = pq.pop()
visited.add(dst)
edges.add(top)
if len(visited) == len(graph.vertices):
break
src = dst
for edge in graph.get_edges(src).items():
dst, edge_props = edge
weight = edge_props['weight']
if dst not in visited:
pq.push((weight, src, dst))
return edges
def get_cycle_nodes(graph: GraphCore):
'''
1. Append all the vertices whose degree is 1 to a queue.
2. Pop the queue front and mark it visited.
3. Then decrement neighbours degree by 1. If it becomes 1, add neigh to queue.
4. Repeat 2-3.
5. Whichever nodes are not visited, they are in the cycle.
'''
degrees = {}
que = deque()
for src in graph.vertices:
edges = graph.get_edges(src)
degrees[src] = len(edges.keys())
if degrees[src] == 1:
que.append(src)
visited = set()
while que:
front = que.popleft()
assert (front not in visited)
visited.add(front)
neighbours = graph.get_edges(front).keys()
for neigh in neighbours:
degrees[neigh] -= 1
if degrees[neigh] == 1:
que.append(neigh)
return graph.vertices - visited
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 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(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 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 get_connected_components(graph: GraphCore):
disjoint_set = DisjointSet()
for src in graph.vertices:
disjoint_set._add_node_if_absent(src)
for src, edges in graph.get_all_edges().items():
for dst in edges.keys():
disjoint_set.join(src, dst)
return disjoint_set.get_groups()
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(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()
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()
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(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)
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 compute_longest_path_starting_at(graph: GraphCore, src, longest_distances):
if src in longest_distances:
return longest_distances[src]
longest_path_distance = 1
for neigh, edge_weight in graph.get_edges(src).items():
longest_path_distance = max(
longest_path_distance,
compute_longest_path_starting_at(graph, neigh, longest_distances) +
edge_weight["weight"],
)
longest_distances[src] = longest_path_distance
return longest_path_distance
def get_strongly_connected_components(graph: GraphCore):
visit_order = []
visited = set()
for src in graph.vertices:
if src not in visited:
visit(src, graph, visited, visit_order)
graph_reverse = graph.get_transpose()
visit_order.reverse()
parent_mapping = {}
for src in visit_order:
assign_component(src, graph_reverse, parent_mapping, src)
return parent_mapping
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(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 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 longest_path_dag_negate(graph: GraphCore, src):
"""
Computes the single-source longest path from a source vertex src.
Works for negative edges also!
First negate all the edges (5 becomes -5).
Then find the shortest path from src to all nodes.
Multipy the distances with -1 to reverse negation.
"""
for _, edges in graph.get_all_edges().items():
for __, edge in edges.items():
edge["weight"] = -edge["weight"]
distances = shortest_path_dag_topo(graph, src)
for node in distances:
distances[node] = -distances[node]
return distances
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