mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-23 21:11:08 +00:00
6987614067
*added docstring and doctest for edglist *added docstring and doctest for adjm Co-authored-by: Ketan <ketanbmahajan@gmail.com>
378 lines
9.9 KiB
Python
378 lines
9.9 KiB
Python
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
|