mirror of
https://github.com/TheAlgorithms/Python.git
synced 2025-02-22 17:22:04 +00:00
357 lines
9.5 KiB
Python
357 lines
9.5 KiB
Python
"""
|
|
Author : Yashwanth Adimulam
|
|
Date : 26th Oct 2024
|
|
|
|
Implement the class of Graphs with useful functions based on it.
|
|
|
|
Useful Links: https://www.geeksforgeeks.org/applications-advantages-and-disadvantages-of-weighted-graph/
|
|
https://www.tutorialspoint.com/applications-advantages-and-disadvantages-of-unweighted-graph
|
|
https://www.baeldung.com/cs/weighted-vs-unweighted-graphs
|
|
https://en.wikipedia.org/wiki/Graph_(discrete_mathematics)
|
|
"""
|
|
|
|
|
|
from collections import deque
|
|
from math import floor
|
|
from random import random
|
|
from time import time
|
|
|
|
class DirectedGraph:
|
|
def __init__(self):
|
|
self.graph = {}
|
|
|
|
def add_pair(self, u, v, w=1):
|
|
"""
|
|
Add a directed edge from u to v with weight w.
|
|
|
|
>>> g = DirectedGraph()
|
|
>>> g.add_pair(1, 2, 3)
|
|
>>> g.graph
|
|
{1: [[3, 2]], 2: []}
|
|
"""
|
|
if self.graph.get(u):
|
|
if self.graph[u].count([w, v]) == 0:
|
|
self.graph[u].append([w, v])
|
|
else:
|
|
self.graph[u] = [[w, v]]
|
|
if not self.graph.get(v):
|
|
self.graph[v] = []
|
|
|
|
def all_nodes(self):
|
|
"""
|
|
Return a list of all nodes in the graph.
|
|
|
|
>>> g = DirectedGraph()
|
|
>>> g.add_pair(1, 2)
|
|
>>> g.all_nodes()
|
|
[1, 2]
|
|
"""
|
|
return list(self.graph)
|
|
|
|
def remove_pair(self, u, v):
|
|
"""
|
|
Remove the directed edge from u to v.
|
|
|
|
>>> g = DirectedGraph()
|
|
>>> g.add_pair(1, 2)
|
|
>>> g.remove_pair(1, 2)
|
|
>>> g.graph
|
|
{1: [], 2: []}
|
|
"""
|
|
if self.graph.get(u):
|
|
for _ in self.graph[u]:
|
|
if _[1] == v:
|
|
self.graph[u].remove(_)
|
|
|
|
def dfs(self, s=-2, d=-1):
|
|
"""
|
|
Perform depth-first search from node s to d.
|
|
|
|
>>> g = DirectedGraph()
|
|
>>> g.add_pair(1, 2)
|
|
>>> g.add_pair(2, 3)
|
|
>>> g.dfs(1, 3)
|
|
[1, 2, 3]
|
|
>>> g.dfs(1, 2)
|
|
[1, 2]
|
|
"""
|
|
if s == d:
|
|
return []
|
|
stack = []
|
|
visited = []
|
|
if s == -2:
|
|
s = next(iter(self.graph))
|
|
stack.append(s)
|
|
visited.append(s)
|
|
while True:
|
|
if len(self.graph[s]) != 0:
|
|
ss = s
|
|
for node in self.graph[s]:
|
|
if visited.count(node[1]) < 1:
|
|
if node[1] == d:
|
|
visited.append(d)
|
|
return visited
|
|
else:
|
|
stack.append(node[1])
|
|
visited.append(node[1])
|
|
ss = node[1]
|
|
break
|
|
|
|
if s == ss:
|
|
stack.pop()
|
|
if len(stack) != 0:
|
|
s = stack[len(stack) - 1]
|
|
else:
|
|
s = ss
|
|
|
|
if len(stack) == 0:
|
|
return visited
|
|
|
|
def fill_graph_randomly(self, c=-1):
|
|
"""
|
|
Fill the graph with random edges.
|
|
|
|
>>> g = DirectedGraph()
|
|
>>> g.fill_graph_randomly(5)
|
|
>>> len(g.all_nodes()) > 0
|
|
True
|
|
"""
|
|
if c == -1:
|
|
c = floor(random() * 10000) + 10
|
|
for i in range(c):
|
|
for _ in range(floor(random() * 102) + 1):
|
|
n = floor(random() * c) + 1
|
|
if n != i:
|
|
self.add_pair(i, n, 1)
|
|
|
|
def bfs(self, s=-2):
|
|
"""
|
|
Perform breadth-first search starting from node s.
|
|
|
|
>>> g = DirectedGraph()
|
|
>>> g.add_pair(1, 2)
|
|
>>> g.add_pair(2, 3)
|
|
>>> g.bfs(1)
|
|
[1, 2, 3]
|
|
"""
|
|
d = deque()
|
|
visited = []
|
|
if s == -2:
|
|
s = next(iter(self.graph))
|
|
d.append(s)
|
|
visited.append(s)
|
|
while d:
|
|
s = d.popleft()
|
|
if len(self.graph[s]) != 0:
|
|
for node in self.graph[s]:
|
|
if visited.count(node[1]) < 1:
|
|
d.append(node[1])
|
|
visited.append(node[1])
|
|
return visited
|
|
|
|
def in_degree(self, u):
|
|
"""
|
|
Calculate in-degree of node u.
|
|
|
|
>>> g = DirectedGraph()
|
|
>>> g.add_pair(1, 2)
|
|
>>> g.in_degree(2)
|
|
1
|
|
"""
|
|
count = 0
|
|
for x in self.graph:
|
|
for y in self.graph[x]:
|
|
if y[1] == u:
|
|
count += 1
|
|
return count
|
|
|
|
def out_degree(self, u):
|
|
"""
|
|
Calculate out-degree of node u.
|
|
|
|
>>> g = DirectedGraph()
|
|
>>> g.add_pair(1, 2)
|
|
>>> g.out_degree(1)
|
|
1
|
|
"""
|
|
return len(self.graph[u])
|
|
|
|
def topological_sort(self, s=-2):
|
|
"""
|
|
Perform topological sort of the graph.
|
|
|
|
>>> g = DirectedGraph()
|
|
>>> g.add_pair(1, 2)
|
|
>>> g.add_pair(2, 3)
|
|
>>> g.topological_sort()
|
|
[1, 2, 3]
|
|
>>> g.add_pair(3, 1) # Introducing a cycle
|
|
>>> g.topological_sort()
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: Graph has cycles, cannot perform topological sort.
|
|
"""
|
|
stack = []
|
|
visited = []
|
|
if s == -2:
|
|
s = next(iter(self.graph))
|
|
stack.append(s)
|
|
visited.append(s)
|
|
sorted_nodes = []
|
|
|
|
while True:
|
|
if len(self.graph[s]) != 0:
|
|
ss = s
|
|
for node in self.graph[s]:
|
|
if visited.count(node[1]) < 1:
|
|
stack.append(node[1])
|
|
visited.append(node[1])
|
|
ss = node[1]
|
|
break
|
|
|
|
if s == ss:
|
|
sorted_nodes.append(stack.pop())
|
|
if len(stack) != 0:
|
|
s = stack[len(stack) - 1]
|
|
else:
|
|
s = ss
|
|
|
|
if len(stack) == 0:
|
|
return sorted_nodes
|
|
|
|
def cycle_nodes(self):
|
|
"""
|
|
Get nodes that are part of a cycle.
|
|
|
|
>>> g = DirectedGraph()
|
|
>>> g.add_pair(1, 2)
|
|
>>> g.add_pair(2, 1)
|
|
>>> g.cycle_nodes()
|
|
[1, 2]
|
|
>>> g.add_pair(2, 3)
|
|
>>> g.cycle_nodes() # No cycles now
|
|
[]
|
|
"""
|
|
stack = []
|
|
visited = []
|
|
s = next(iter(self.graph))
|
|
stack.append(s)
|
|
visited.append(s)
|
|
parent = -2
|
|
indirect_parents = []
|
|
ss = s
|
|
anticipating_nodes = set()
|
|
|
|
while True:
|
|
if len(self.graph[s]) != 0:
|
|
ss = s
|
|
for node in self.graph[s]:
|
|
if (
|
|
visited.count(node[1]) > 0
|
|
and node[1] != parent
|
|
and indirect_parents.count(node[1]) > 0
|
|
):
|
|
len_stack = len(stack) - 1
|
|
while len_stack >= 0:
|
|
if stack[len_stack] == node[1]:
|
|
anticipating_nodes.add(node[1])
|
|
break
|
|
else:
|
|
anticipating_nodes.add(stack[len_stack])
|
|
len_stack -= 1
|
|
if visited.count(node[1]) < 1:
|
|
stack.append(node[1])
|
|
visited.append(node[1])
|
|
ss = node[1]
|
|
break
|
|
|
|
if s == ss:
|
|
stack.pop()
|
|
if len(stack) != 0:
|
|
s = stack[len(stack) - 1]
|
|
else:
|
|
parent = s
|
|
s = ss
|
|
|
|
if len(stack) == 0:
|
|
return list(anticipating_nodes)
|
|
|
|
def has_cycle(self):
|
|
"""
|
|
Check if the graph has a cycle.
|
|
|
|
>>> g = DirectedGraph()
|
|
>>> g.add_pair(1, 2)
|
|
>>> g.add_pair(2, 1)
|
|
>>> g.has_cycle()
|
|
True
|
|
>>> g.add_pair(2, 3)
|
|
>>> g.has_cycle()
|
|
True # Still has a cycle
|
|
>>> g.remove_pair(1, 2) # Now no cycle
|
|
>>> g.has_cycle()
|
|
False
|
|
"""
|
|
stack = []
|
|
visited = []
|
|
s = next(iter(self.graph))
|
|
stack.append(s)
|
|
visited.append(s)
|
|
parent = -2
|
|
indirect_parents = []
|
|
ss = s
|
|
|
|
while True:
|
|
if len(self.graph[s]) != 0:
|
|
ss = s
|
|
for node in self.graph[s]:
|
|
if (
|
|
visited.count(node[1]) > 0
|
|
and node[1] != parent
|
|
and indirect_parents.count(node[1]) > 0
|
|
):
|
|
return True
|
|
if visited.count(node[1]) < 1:
|
|
stack.append(node[1])
|
|
visited.append(node[1])
|
|
ss = node[1]
|
|
break
|
|
|
|
if s == ss:
|
|
stack.pop()
|
|
if len(stack) != 0:
|
|
s = stack[len(stack) - 1]
|
|
else:
|
|
s = ss
|
|
|
|
if len(stack) == 0:
|
|
return False
|
|
|
|
def dfs_time(self, s=-2, e=-1):
|
|
"""
|
|
Measure the time taken for DFS.
|
|
|
|
>>> g = DirectedGraph()
|
|
>>> g.add_pair(1, 2)
|
|
>>> g.dfs_time(1, 2) >= 0
|
|
True
|
|
"""
|
|
begin = time()
|
|
self.dfs(s, e)
|
|
end = time()
|
|
return end - begin
|
|
|
|
def bfs_time(self, s=-2):
|
|
"""
|
|
Measure the time taken for BFS.
|
|
|
|
>>> g = DirectedGraph()
|
|
>>> g.add_pair(1, 2)
|
|
>>> g.bfs_time(1) >= 0
|
|
True
|
|
"""
|
|
begin = time()
|
|
self.bfs(s)
|
|
end = time()
|
|
return end - begin
|