给定一个连通图，请检查该图是否为二部图。如果可以使用两种颜色对图形进行着色，从而用一组相同的颜色对集合中的顶点进行着色，则二部图可能是可行的。请注意，可以使用两种颜色以均匀的周期为周期图着色。例如，请参见下图。
不可能用两种颜色的奇数周期为周期图着色。
在上一篇文章中，已经讨论了使用BFS的方法。在这篇文章中，已经实现了使用DFS的方法。
下面给出的是检查图的二部性的算法。
- 使用color []数组为每个表示相反颜色的节点存储0或1。
- 从任何节点调用函数DFS。
- 如果先前尚未访问过节点u，则将！color [v]分配给color [u]，然后再次调用DFS来访问连接到u的节点。
- 如果在任何时候color [u]等于color [v]，则该节点是二分的。
- 修改DFS函数，使其在最后返回一个布尔值。
下面是上述方法的实现：
C++
// C++ program to check if a connected
// graph is bipartite or not suing DFS
#include
using namespace std;
// function to store the connected nodes
void addEdge(vector adj[], int u, int v)
{
adj[u].push_back(v);
adj[v].push_back(u);
}
// function to check whether a graph is bipartite or not
bool isBipartite(vector adj[], int v,
vector& visited, vector& color)
{
for (int u : adj[v]) {
// if vertex u is not explored before
if (visited[u] == false) {
// mark present vertic as visited
visited[u] = true;
// mark its color opposite to its parent
color[u] = !color[v];
// if the subtree rooted at vertex v is not bipartite
if (!isBipartite(adj, u, visited, color))
return false;
}
// if two adjacent are colored with same color then
// the graph is not bipartite
else if (color[u] == color[v])
return false;
}
return true;
}
// Driver Code
int main()
{
// no of nodes
int N = 6;
// to maintain the adjacency list of graph
vector adj[N + 1];
// to keep a check on whether
// a node is discovered or not
vector visited(N + 1);
// to color the vertices
// of graph with 2 color
vector color(N + 1);
// adding edges to the graph
addEdge(adj, 1, 2);
addEdge(adj, 2, 3);
addEdge(adj, 3, 4);
addEdge(adj, 4, 5);
addEdge(adj, 5, 6);
addEdge(adj, 6, 1);
// marking the source node as visited
visited[1] = true;
// marking the source node with a color
color[1] = 0;
// Function to check if the graph
// is Bipartite or not
if (isBipartite(adj, 1, visited, color)) {
cout << "Graph is Bipartite";
}
else {
cout << "Graph is not Bipartite";
}
return 0;
} Java
// Java program to check if a connected
// graph is bipartite or not suing DFS
import java.util.*;
class GFG{
// Function to store the connected nodes
static void addEdge(ArrayList> adj,
int u, int v)
{
adj.get(u).add(v);
adj.get(v).add(u);
}
// Function to check whether a
// graph is bipartite or not
static boolean isBipartite(ArrayList> adj,
int v, boolean visited[],
int color[])
{
for(int u : adj.get(v))
{
// If vertex u is not explored before
if (visited[u] == false)
{
// Mark present vertic as visited
visited[u] = true;
// Mark its color opposite to its parent
color[u] = 1 - color[v];
// If the subtree rooted at vertex
// v is not bipartite
if (!isBipartite(adj, u, visited, color))
return false;
}
// If two adjacent are colored with
// same color then the graph is
// not bipartite
else if (color[u] == color[v])
return false;
}
return true;
}
// Driver Code
public static void main(String args[])
{
// No of nodes
int N = 6;
// To maintain the adjacency list of graph
ArrayList<
ArrayList> adj = new ArrayList<
ArrayList>(N + 1);
// Initialize all the vertex
for(int i = 0; i <= N; i++)
{
adj.add(new ArrayList());
}
// To keep a check on whether
// a node is discovered or not
boolean visited[] = new boolean[N + 1];
// To color the vertices
// of graph with 2 color
int color[] = new int[N + 1];
// The value '-1' of colorArr[i] is
// used to indicate that no color is
// assigned to vertex 'i'. The value
// 1 is used to indicate first color
// is assigned and value 0 indicates
// second color is assigned.
Arrays.fill(color, -1);
// Adding edges to the graph
addEdge(adj, 1, 2);
addEdge(adj, 2, 3);
addEdge(adj, 3, 4);
addEdge(adj, 4, 5);
addEdge(adj, 5, 6);
addEdge(adj, 6, 1);
// Marking the source node as visited
visited[1] = true;
// Marking the source node with a color
color[1] = 0;
// Function to check if the graph
// is Bipartite or not
if (isBipartite(adj, 1, visited, color))
{
System.out.println("Graph is Bipartite");
}
else
{
System.out.println("Graph is not Bipartite");
}
}
}
// This code is contributed by adityapande88 Python3
# Python3 program to check if a connected
# graph is bipartite or not suing DFS
# Function to store the connected nodes
def addEdge(adj, u, v):
adj[u].append(v)
adj[v].append(u)
# Function to check whether a graph is
# bipartite or not
def isBipartite(adj, v, visited, color):
for u in adj[v]:
# If vertex u is not explored before
if (visited[u] == False):
# Mark present vertic as visited
visited[u] = True
# Mark its color opposite to its parent
color[u] = not color[v]
# If the subtree rooted at vertex v
# is not bipartite
if (not isBipartite(adj, u,
visited, color)):
return false
# If two adjacent are colored with
# same color then the graph is not
# bipartite
elif (color[u] == color[v]):
return Talse
return True
# Driver Code
if __name__=='__main__':
# No of nodes
N = 6
# To maintain the adjacency list of graph
adj = [[] for i in range(N + 1)]
# To keep a check on whether
# a node is discovered or not
visited = [0 for i in range(N + 1)]
# To color the vertices
# of graph with 2 color
color = [0 for i in range(N + 1)]
# Adding edges to the graph
addEdge(adj, 1, 2)
addEdge(adj, 2, 3)
addEdge(adj, 3, 4)
addEdge(adj, 4, 5)
addEdge(adj, 5, 6)
addEdge(adj, 6, 1)
# Marking the source node as visited
visited[1] = True
# Marking the source node with a color
color[1] = 0
# Function to check if the graph
# is Bipartite or not
if (isBipartite(adj, 1, visited, color)):
print("Graph is Bipartite")
else:
print("Graph is not Bipartite")
# This code is contributed by rutvik_56C#
// C# program to check if a connected
// graph is bipartite or not suing DFS
using System;
using System.Collections.Generic;
class GFG{
// Function to store the connected nodes
static void addEdge(List> adj,
int u, int v)
{
adj[u].Add(v);
adj[v].Add(u);
}
// Function to check whether a
// graph is bipartite or not
static bool isBipartite(List> adj,
int v, bool []visited,
int []color)
{
foreach(int u in adj[v])
{
// If vertex u is not explored before
if (visited[u] == false)
{
// Mark present vertic as visited
visited[u] = true;
// Mark its color opposite to its parent
color[u] = 1 - color[v];
// If the subtree rooted at vertex
// v is not bipartite
if (!isBipartite(adj, u, visited, color))
return false;
}
// If two adjacent are colored with
// same color then the graph is
// not bipartite
else if (color[u] == color[v])
return false;
}
return true;
}
// Driver Code
public static void Main(String []args)
{
// No of nodes
int N = 6;
// To maintain the adjacency list of graph
List> adj = new List>(N + 1);
// Initialize all the vertex
for(int i = 0; i <= N; i++)
{
adj.Add(new List());
}
// To keep a check on whether
// a node is discovered or not
bool []visited = new bool[N + 1];
// To color the vertices
// of graph with 2 color
int []color = new int[N + 1];
// The value '-1' of colorArr[i] is
// used to indicate that no color is
// assigned to vertex 'i'. The value
// 1 is used to indicate first color
// is assigned and value 0 indicates
// second color is assigned.
for(int i = 0; i <= N; i++)
color[i] = -1;
// Adding edges to the graph
addEdge(adj, 1, 2);
addEdge(adj, 2, 3);
addEdge(adj, 3, 4);
addEdge(adj, 4, 5);
addEdge(adj, 5, 6);
addEdge(adj, 6, 1);
// Marking the source node as visited
visited[1] = true;
// Marking the source node with a color
color[1] = 0;
// Function to check if the graph
// is Bipartite or not
if (isBipartite(adj, 1, visited, color))
{
Console.WriteLine("Graph is Bipartite");
}
else
{
Console.WriteLine("Graph is not Bipartite");
}
}
}
// This code is contributed by Princi Singh 输出：
Graph is Bipartite时间复杂度： O(N)
辅助空间： O(N)
要从最佳影片策划和实践问题去学习，检查了C++基础课程为基础，以先进的C++和C++ STL课程基础加上STL。要完成从学习语言到DS Algo等的更多准备工作，请参阅“完整面试准备课程” 。