#### Basic Graphs

R
```from collections import deque

def _input(message):
return input(message).strip().split(" ")

def initialize_unweighted_directed_graph(
node_count: int, edge_count: int
) -> dict[int, list[int]]:
graph: dict[int, list[int]] = {}
for i in range(node_count):
graph[i + 1] = []

for e in range(edge_count):
x, y = (int(i) for i in _input(f"Edge {e + 1}: <node1> <node2> "))
graph[x].append(y)
return graph

def initialize_unweighted_undirected_graph(
node_count: int, edge_count: int
) -> dict[int, list[int]]:
graph: dict[int, list[int]] = {}
for i in range(node_count):
graph[i + 1] = []

for e in range(edge_count):
x, y = (int(i) for i in _input(f"Edge {e + 1}: <node1> <node2> "))
graph[x].append(y)
graph[y].append(x)
return graph

def initialize_weighted_undirected_graph(
node_count: int, edge_count: int
) -> dict[int, list[tuple[int, int]]]:
graph: dict[int, list[tuple[int, int]]] = {}
for i in range(node_count):
graph[i + 1] = []

for e in range(edge_count):
x, y, w = (int(i) for i in _input(f"Edge {e + 1}: <node1> <node2> <weight> "))
graph[x].append((y, w))
graph[y].append((x, w))
return graph

if __name__ == "__main__":
n, m = (int(i) for i in _input("Number of nodes and edges: "))

graph_choice = int(
_input(
"Press 1 or 2 or 3 \n"
"1. Unweighted directed \n"
"2. Unweighted undirected \n"
"3. Weighted undirected \n"
)[0]
)

g = {
1: initialize_unweighted_directed_graph,
2: initialize_unweighted_undirected_graph,
3: initialize_weighted_undirected_graph,
}[graph_choice](n, m)

"""
--------------------------------------------------------------------------------
Depth First Search.
Args :  G - Dictionary of edges
s - Starting Node
Vars :  vis - Set of visited nodes
S - Traversal Stack
--------------------------------------------------------------------------------
"""

def dfs(g, s):
vis, _s = {s}, [s]
print(s)
while _s:
flag = 0
for i in g[_s[-1]]:
if i not in vis:
_s.append(i)
vis.add(i)
flag = 1
print(i)
break
if not flag:
_s.pop()

"""
--------------------------------------------------------------------------------
Breadth First Search.
Args :  G - Dictionary of edges
s - Starting Node
Vars :  vis - Set of visited nodes
Q - Traversal Stack
--------------------------------------------------------------------------------
"""

def bfs(g, s):
vis, q = {s}, deque([s])
print(s)
while q:
u = q.popleft()
for v in g[u]:
if v not in vis:
vis.add(v)
q.append(v)
print(v)

"""
--------------------------------------------------------------------------------
Dijkstra's shortest path Algorithm
Args :  G - Dictionary of edges
s - Starting Node
Vars :  dist - Dictionary storing shortest distance from s to every other node
known - Set of knows nodes
path - Preceding node in path
--------------------------------------------------------------------------------
"""

def dijk(g, s):
dist, known, path = {s: 0}, set(), {s: 0}
while True:
if len(known) == len(g) - 1:
break
mini = 100000
for i in dist:
if i not in known and dist[i] < mini:
mini = dist[i]
u = i
known.add(u)
for v in g[u]:
if v[0] not in known and dist[u] + v[1] < dist.get(v[0], 100000):
dist[v[0]] = dist[u] + v[1]
path[v[0]] = u
for i in dist:
if i != s:
print(dist[i])

"""
--------------------------------------------------------------------------------
Topological Sort
--------------------------------------------------------------------------------
"""

def topo(g, ind=None, q=None):
if q is None:
q = [1]
if ind is None:
ind = [0] * (len(g) + 1)  # SInce oth Index is ignored
for u in g:
for v in g[u]:
ind[v] += 1
q = deque()
for i in g:
if ind[i] == 0:
q.append(i)
if len(q) == 0:
return
v = q.popleft()
print(v)
for w in g[v]:
ind[w] -= 1
if ind[w] == 0:
q.append(w)
topo(g, ind, q)

"""
--------------------------------------------------------------------------------
Reading an Adjacency matrix
--------------------------------------------------------------------------------
"""

def adjm():
r"""
Reading an Adjacency matrix

Parameters:
None

Returns:
tuple: A tuple containing a list of edges and number of edges

Example:
>>> # Simulate user input for 3 nodes
>>> input_data = "4\n0 1 0 1\n1 0 1 0\n0 1 0 1\n1 0 1 0\n"
>>> import sys,io
>>> original_input = sys.stdin
>>> sys.stdin = io.StringIO(input_data)  # Redirect stdin for testing
>>> adjm()
([(0, 1, 0, 1), (1, 0, 1, 0), (0, 1, 0, 1), (1, 0, 1, 0)], 4)
>>> sys.stdin = original_input  # Restore original stdin
"""
n = int(input().strip())
a = []
for _ in range(n):
a.append(tuple(map(int, input().strip().split())))
return a, n

"""
--------------------------------------------------------------------------------
Floyd Warshall's algorithm
Args :  G - Dictionary of edges
s - Starting Node
Vars :  dist - Dictionary storing shortest distance from s to every other node
known - Set of knows nodes
path - Preceding node in path

--------------------------------------------------------------------------------
"""

def floy(a_and_n):
(a, n) = a_and_n
dist = list(a)
path = [[0] * n for i in range(n)]
for k in range(n):
for i in range(n):
for j in range(n):
if dist[i][j] > dist[i][k] + dist[k][j]:
dist[i][j] = dist[i][k] + dist[k][j]
path[i][k] = k
print(dist)

"""
--------------------------------------------------------------------------------
Prim's MST Algorithm
Args :  G - Dictionary of edges
s - Starting Node
Vars :  dist - Dictionary storing shortest distance from s to nearest node
known - Set of knows nodes
path - Preceding node in path
--------------------------------------------------------------------------------
"""

def prim(g, s):
dist, known, path = {s: 0}, set(), {s: 0}
while True:
if len(known) == len(g) - 1:
break
mini = 100000
for i in dist:
if i not in known and dist[i] < mini:
mini = dist[i]
u = i
known.add(u)
for v in g[u]:
if v[0] not in known and v[1] < dist.get(v[0], 100000):
dist[v[0]] = v[1]
path[v[0]] = u
return dist

"""
--------------------------------------------------------------------------------
Accepting Edge list
Vars :  n - Number of nodes
m - Number of edges
Returns : l - Edge list
n - Number of Nodes
--------------------------------------------------------------------------------
"""

def edglist():
r"""
Get the edges and number of edges from the user

Parameters:
None

Returns:
tuple: A tuple containing a list of edges and number of edges

Example:
>>> # Simulate user input for 3 edges and 4 vertices: (1, 2), (2, 3), (3, 4)
>>> input_data = "4 3\n1 2\n2 3\n3 4\n"
>>> import sys,io
>>> original_input = sys.stdin
>>> sys.stdin = io.StringIO(input_data)  # Redirect stdin for testing
>>> edglist()
([(1, 2), (2, 3), (3, 4)], 4)
>>> sys.stdin = original_input  # Restore original stdin
"""
n, m = tuple(map(int, input().split(" ")))
edges = []
for _ in range(m):
edges.append(tuple(map(int, input().split(" "))))
return edges, n

"""
--------------------------------------------------------------------------------
Kruskal's MST Algorithm
Args :  E - Edge list
n - Number of Nodes
Vars :  s - Set of all nodes as unique disjoint sets (initially)
--------------------------------------------------------------------------------
"""

def krusk(e_and_n):
"""
Sort edges on the basis of distance
"""
(e, n) = e_and_n
e.sort(reverse=True, key=lambda x: x[2])
s = [{i} for i in range(1, n + 1)]
while True:
if len(s) == 1:
break
print(s)
x = e.pop()
for i in range(len(s)):
if x[0] in s[i]:
break
for j in range(len(s)):
if x[1] in s[j]:
if i == j:
break
s[j].update(s[i])
s.pop(i)
break

def find_isolated_nodes(graph):
"""
Find the isolated node in the graph

Parameters:
graph (dict): A dictionary representing a graph.

Returns:
list: A list of isolated nodes.

Examples:
>>> graph1 = {1: [2, 3], 2: [1, 3], 3: [1, 2], 4: []}
>>> find_isolated_nodes(graph1)
[4]

>>> graph2 = {'A': ['B', 'C'], 'B': ['A'], 'C': ['A'], 'D': []}
>>> find_isolated_nodes(graph2)
['D']

>>> graph3 = {'X': [], 'Y': [], 'Z': []}
>>> find_isolated_nodes(graph3)
['X', 'Y', 'Z']

>>> graph4 = {1: [2, 3], 2: [1, 3], 3: [1, 2]}
>>> find_isolated_nodes(graph4)
[]

>>> graph5 = {}
>>> find_isolated_nodes(graph5)
[]
"""
isolated = []
for node in graph:
if not graph[node]:
isolated.append(node)
return isolated
```