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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
:
if
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
():
n
=
input
().
strip
()
a
=
[]
for
_
in
range
(
n
):
a
.
append
(
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
:
if
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
():
n
,
m
=
map
(
int
,
input
().
split
(
" "
))
edges
=
[]
for
_
in
range
(
m
):
edges
.
append
(
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
# find the isolated node in the graph
def
find_isolated_nodes
(
graph
):
isolated
=
[]
for
node
in
graph
:
if
not
graph
[
node
]:
isolated
.
append
(
node
)
return
isolated
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