diff --git a/graphs/directed_and_undirected_weighted_graph.py b/graphs/directed_and_undirected_weighted_graph.py
index 8ca645fdace8..5375ce73931c 100644
--- a/graphs/directed_and_undirected_weighted_graph.py
+++ b/graphs/directed_and_undirected_weighted_graph.py
@@ -268,7 +268,34 @@ def __init__(self):
# adding vertices and edges
# adding the weight is optional
# handles repetition
- def add_pair(self, u, v, w=1):
+ def add_pair(self, u, v, w=1) -> None:
+ """
+ Adds an edge between u and v with an optional weight w to an undirected graph
+
+ >>> g = Graph()
+ >>> g.add_pair(1,2)
+ >>> g.graph[1]
+ [[1, 2]]
+ >>> g.graph[2]
+ [[1, 1]]
+ >>> g.add_pair(1,2) # testing for duplicates
+ >>> g.graph[1]
+ [[1, 2]]
+ >>> g.add_pair(2,1) # reverse order, should not add a duplicate
+ >>> g.graph[2]
+ [[1, 1]]
+ >>> g.add_pair(1,3,5)
+ >>> g.graph[1]
+ [[1, 2], [5, 3]]
+ >>> g.graph[3]
+ [[5, 1]]
+ >>> g.add_pair(4,4) # test for self loop
+ >>> g.graph[4]
+ [[1, 4]]
+ >>> g.add_pair(1,2,3) # previously added nodes, different weight
+ >>> g.graph[1]
+ [[1, 2], [5, 3], [3, 2]]
+ """
# check if the u exists
if self.graph.get(u):
# if there already is a edge
@@ -287,7 +314,36 @@ def add_pair(self, u, v, w=1):
self.graph[v] = [[w, u]]
# handles if the input does not exist
- def remove_pair(self, u, v):
+ def remove_pair(self, u, v) -> None:
+ """
+ Removes the edge between u and v in an undirected graph, if it exists
+
+ >>> g = Graph()
+ >>> g.add_pair(1,2)
+ >>> g.add_pair(1,3,5)
+ >>> g.graph[1]
+ [[1, 2], [5, 3]]
+ >>> g.remove_pair(1, 2)
+ >>> g.graph[1]
+ [[5, 3]]
+ >>> g.graph[2]
+ []
+ >>> g.remove_pair(1,4) # node 4 does not exist
+ >>> g.remove_pair(10, 11) # neither exists
+ >>> g.add_pair(5,5)
+ >>> g.graph[5]
+ [[1, 5]]
+ >>> g.remove_pair(5,5)
+ >>> g.graph[5]
+ []
+ >>> g.add_pair(6,7,2)
+ >>> g.add_pair(6,7,3)
+ >>> g.graph[6]
+ [[2, 7], [3, 7]]
+ >>> g.remove_pair(6,7)
+ >>> g.graph[6]
+ [[3, 7]]
+ """
if self.graph.get(u):
for _ in self.graph[u]:
if _[1] == v:
@@ -299,7 +355,32 @@ def remove_pair(self, u, v):
self.graph[v].remove(_)
# if no destination is meant the default value is -1
- def dfs(self, s=-2, d=-1):
+ def dfs(self, s=-2, d=-1) -> list[int]:
+ """
+ Performs a depth-first search starting from node s.
+ If destination d is given, stops when d is found
+
+ >>> g = Graph()
+ >>> g.add_pair(1,2)
+ >>> g.add_pair(2,3)
+ >>> g.dfs(1)
+ [1, 2, 3]
+ >>> g.dfs(1,3)
+ [1, 2, 3]
+ >>> g.dfs(1,4) # 4 not in graph
+ [1, 2, 3]
+ >>> g.dfs(1,1) # start equals dest
+ []
+ >>> g2 = Graph()
+ >>> g2.add_pair(10,20)
+ >>> g2.add_pair(20,30)
+ >>> g2.dfs() # default start
+ [10, 20, 30]
+ >>> g2.add_pair(30,40)
+ >>> g2.add_pair(40, 50)
+ >>> g2.dfs(d=40) # checking if destination works properly
+ [10, 20, 30, 40]
+ """
if s == d:
return []
stack = []
@@ -349,8 +430,36 @@ def fill_graph_randomly(self, c=-1):
if n != i:
self.add_pair(i, n, 1)
- def bfs(self, s=-2):
- d = deque()
+ def bfs(self, s=-2) -> list[int]:
+ """
+ Performs breadth-first search starting from node s.
+ If s is not given, starts from the first node in the graph
+
+ Returns:
+ list of nodes found after performing breadth-first search
+
+ >>> g = Graph()
+ >>> g.add_pair(1,2)
+ >>> g.add_pair(1,3)
+ >>> g.add_pair(2,4)
+ >>> g.add_pair(3,5)
+ >>> g.bfs(1)
+ [1, 2, 3, 4, 5]
+ >>> g.bfs(2)
+ [2, 1, 4, 3, 5]
+ >>> g.bfs(4) # leaf node test
+ [4, 2, 1, 3, 5]
+ >>> g.bfs(10) # nonexistent node
+ Traceback (most recent call last):
+ ...
+ KeyError: 10
+ >>> g2 = Graph()
+ >>> g2.add_pair(10,20)
+ >>> g2.add_pair(20,30)
+ >>> g2.bfs()
+ [10, 20, 30]
+ """
+ d: deque = deque()
visited = []
if s == -2:
s = next(iter(self.graph))
@@ -421,14 +530,52 @@ def cycle_nodes(self):
if len(stack) == 0:
return list(anticipating_nodes)
- def has_cycle(self):
+ def has_cycle(self) -> bool:
+ """
+ Detects whether the undirected graph contains a cycle.
+
+ Note:
+ - This function assumes the graph is connected and only traverses from the
+ first node found in the graph.
+ - It does not detect cycles that exist in disconnected components.
+ - It also does not detect self-loops
+ (e.g., an edge from a node to itself like 1-1).
+
+ Returns:
+ bool: True if a cycle is detected in the connected component starting
+ from the first node; False otherwise.
+
+ >>> g = Graph()
+ >>> g.add_pair(1, 2)
+ >>> g.add_pair(2, 3)
+ >>> g.has_cycle()
+ False
+ >>> g2 = Graph()
+ >>> g2.add_pair(1, 2)
+ >>> g2.add_pair(2, 3)
+ >>> g2.add_pair(3, 1) # creates a cycle
+ >>> g2.has_cycle()
+ True
+ >>> g3 = Graph()
+ >>> g3.add_pair(1, 1) # self-loop
+ >>> g3.has_cycle() # Self-loops are not detected by this method
+ False
+ >>> g4 = Graph()
+ >>> g4.add_pair(1, 2)
+ >>> g4.add_pair(3, 4)
+ >>> g4.add_pair(4, 5)
+ >>> g4.add_pair(5, 3) # cycle in disconnected component
+ >>> g4.has_cycle() # Only checks the component reachable from the first node 1
+ False
+ """
+
stack = []
visited = []
s = next(iter(self.graph))
stack.append(s)
visited.append(s)
parent = -2
- indirect_parents = []
+ indirect_parents: list[int] = []
ss = s
on_the_way_back = False
anticipating_nodes = set()
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