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C-Plus-Plus-TheAlgorithms
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591c47ee
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C-Plus-Plus-TheAlgorithms
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体验新版 GitCode,发现更多精彩内容 >>
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591c47ee
编写于
8月 16, 2020
作者:
D
David Leal
提交者:
GitHub
8月 16, 2020
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Merge pull request #1018 from AkVaya/master
Added is_graph_bipartite.cpp
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graph/is_graph_bipartite.cpp
graph/is_graph_bipartite.cpp
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graph/is_graph_bipartite.cpp
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/**
* @file
*
* @brief Algorithm to check whether a graph is [bipartite](https://en.wikipedia.org/wiki/Bipartite_graph)
*
* @details
* A graph is a collection of nodes also called vertices and these vertices
* are connected by edges.A bipartite graph is a graph whose vertices can be
* divided into two disjoint and independent sets U and V such that every edge
* connects a vertex in U to one in V.
*
* The given Algorithm will determine whether the given graph is bipartite or not
*
* <pre>
* Example - Here is a graph g1 with 5 vertices and is bipartite
*
* 1 4
* / \ / \
* 2 3 5
*
* Example - Here is a graph G2 with 3 vertices and is not bipartite
*
* 1 --- 2
* \ /
* 3
*
* </pre>
*
* @author [Akshat Vaya](https://github.com/AkVaya)
*
*/
#include <iostream>
#include <vector>
#include <queue>
/**
* @namespace graph
* @brief Graph algorithms
*/
namespace
graph
{
/**
* @namespace is_graph_bipartite
* @brief Functions for checking whether a graph is bipartite or not
*/
namespace
is_graph_bipartite
{
/**
* @brief Class for representing graph as an adjacency list.
*/
class
Graph
{
private:
int
n
;
/// size of the graph
std
::
vector
<
std
::
vector
<
int
>
>
adj
;
/// adj stores the graph as an adjacency list
std
::
vector
<
int
>
side
;
///stores the side of the vertex
static
const
int
nax
=
5e5
+
1
;
public:
/**
* @brief Constructor that initializes the graph on creation
*/
explicit
Graph
(
int
size
=
nax
){
n
=
size
;
adj
.
resize
(
n
);
side
.
resize
(
n
,
-
1
);
}
void
addEdge
(
int
u
,
int
v
);
/// function to add edges to our graph
bool
is_bipartite
();
/// function to check whether the graph is bipartite or not
};
/**
* @brief Function that add an edge between two nodes or vertices of graph
*
* @param u is a node or vertex of graph
* @param v is a node or vertex of graph
*/
void
Graph
::
addEdge
(
int
u
,
int
v
)
{
adj
[
u
-
1
].
push_back
(
v
-
1
);
adj
[
v
-
1
].
push_back
(
u
-
1
);
}
/**
* @brief function that checks whether the graph is bipartite or not
* the function returns true if the graph is a bipartite graph
* the function returns false if the graph is not a bipartite graph
*
* @details
* Here, side refers to the two disjoint subsets of the bipartite graph.
* Initially, the values of side are set to -1 which is an unassigned state. A for loop is run for every vertex of the graph.
* If the current edge has no side assigned to it, then a Breadth First Search operation is performed.
* If two neighbours have the same side then the graph will not be bipartite and the value of check becomes false.
* If and only if each pair of neighbours have different sides, the value of check will be true and hence the graph bipartite.
*
*/
bool
Graph
::
is_bipartite
(){
bool
check
=
true
;
std
::
queue
<
int
>
q
;
for
(
int
current_edge
=
0
;
current_edge
<
n
;
++
current_edge
)
{
if
(
side
[
current_edge
]
==
-
1
){
q
.
push
(
current_edge
);
side
[
current_edge
]
=
0
;
while
(
q
.
size
()){
int
current
=
q
.
front
();
q
.
pop
();
for
(
auto
neighbour
:
adj
[
current
]){
if
(
side
[
neighbour
]
==
-
1
){
side
[
neighbour
]
=
(
1
^
side
[
current
]);
q
.
push
(
neighbour
);
}
else
{
check
&=
(
side
[
neighbour
]
!=
side
[
current
]);
}
}
}
}
}
return
check
;
}
}
/// namespace is_graph_bipartite
}
/// namespace graph
/**
* Function to test the above algorithm
* @returns none
*/
static
void
test
(){
graph
::
is_graph_bipartite
::
Graph
G1
(
5
);
/// creating graph G1 with 5 vertices
/// adding edges to the graphs as per the illustrated example
G1
.
addEdge
(
1
,
2
);
G1
.
addEdge
(
1
,
3
);
G1
.
addEdge
(
3
,
4
);
G1
.
addEdge
(
4
,
5
);
graph
::
is_graph_bipartite
::
Graph
G2
(
3
);
/// creating graph G2 with 3 vertices
/// adding edges to the graphs as per the illustrated example
G2
.
addEdge
(
1
,
2
);
G2
.
addEdge
(
1
,
3
);
G2
.
addEdge
(
2
,
3
);
/// checking whether the graphs are bipartite or not
if
(
G1
.
is_bipartite
()){
std
::
cout
<<
"The given graph G1 is a bipartite graph
\n
"
;
}
else
{
std
::
cout
<<
"The given graph G1 is not a bipartite graph
\n
"
;
}
if
(
G2
.
is_bipartite
()){
std
::
cout
<<
"The given graph G2 is a bipartite graph
\n
"
;
}
else
{
std
::
cout
<<
"The given graph G2 is not a bipartite graph
\n
"
;
}
}
/**
* Main function
*/
int
main
(){
test
();
///Testing
return
0
;
}
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