无向图中奇数和偶数度节点的度数之和之间的差异

给定具有N个顶点和M个边的无向图，任务是找到无向图中奇数度节点和偶数度节点的度之和之间的绝对差。
例子：

Input: N = 4, edges[][] = { { 1, 2 }, { 1, 3 }, { 1, 4 }, { 2, 3 }, { 2, 4 }, { 3, 4 } } 
Output: 12 
Explanation: 
Below is the graph for the above information: 
 

Node -> Degree 
1 -> 3 
2 -> 3 
3 -> 3 
4 -> 3
Sum of odd degree node = 3 + 3 + 3 + 3 = 12 
Sum of even degree node = 0 
Difference = 12
Input: N = 5, edges[][] = { { 1, 2 }, { 1, 3 }, { 2, 4 }, { 2, 5 } } 
Output: 4 
 

方法：

1. 对于每个顶点，度可以通过给定图在相应顶点处的邻接表的长度来计算。
2. 计算奇数度节点和偶数度节点的度数之和，然后打印出差异。

下面是上述方法的实现：

C++

// C++ implementation to print the
// Difference Between sum of degrees
// of odd degree nodes and even
// degree nodes.
#include 
using namespace std;
 
// Function to print the difference
// Between sum of degrees of odd
// degree nodes and even degree nodes.
int OddEvenDegree(int N, int M,
                    int edges[][2])
{
    // To store Adjacency List of
    // a Graph
    vector Adj[N + 1];
     
    int EvenSum = 0;
    int OddSum = 0;
 
    // Make Adjacency List
    for (int i = 0 ; i < M ; i++) {
        int x = edges[i][0];
        int y = edges[i][1];
 
        Adj[x].push_back(y);
        Adj[y].push_back(x);
    }
 
    // Traverse each vertex
    for (int i = 1; i <= N; i++) {
 
        // Find size of Adjacency List
        int x = Adj[i].size();
 
        // If length of Adj[i] is
        // an odd number, add
        // length in OddSum
        if (x % 2 != 0)
        {
            OddSum += x;
        }
        else
        {
            // If length of Adj[i] is
            // an even number, add
            // length in EvenSum
            EvenSum += x;
        }
             
    }
     
    return abs(OddSum - EvenSum);
}
 
// Driver code
int main()
{
    // Vertices and Edges
    int N = 4, M = 6;
 
    // Edges
    int edges[M][2] = { { 1, 2 }, { 1, 3 }, { 1, 4 },
                       { 2, 3 }, { 2, 4 }, { 3, 4 } };
 
    // Function Call
    cout<< OddEvenDegree(N, M, edges);
 
    return 0;
}

Java

// Java implementation to print the
// difference between sum of degrees
// of odd degree nodes and even
// degree nodes.
import java.util.*;
 
class GFG{
 
// Function to print the difference
// between sum of degrees of odd
// degree nodes and even degree nodes.
static int OddEvenDegree(int N, int M,
                         int edges[][])
{
     
    // To store adjacency list
    // of a graph
    @SuppressWarnings("unchecked")
    Vector []Adj = new Vector[N + 1];
     
    for(int i = 0; i < N + 1; i++)
    {
       Adj[i] = new Vector();
    }
     
    int EvenSum = 0;
    int OddSum = 0;
 
    // Make adjacency list
    for(int i = 0; i < M; i++)
    {
       int x = edges[i][0];
       int y = edges[i][1];
        
       Adj[x].add(y);
       Adj[y].add(x);
    }
 
    // Traverse each vertex
    for(int i = 1; i <= N; i++)
    {
         
       // Find size of adjacency list
       int x = Adj[i].size();
        
       // If length of Adj[i] is
       // an odd number, add
       // length in OddSum
       if (x % 2 != 0)
       {
           OddSum += x;
       }
       else
       {
            
           // If length of Adj[i] is
           // an even number, add
           // length in EvenSum
           EvenSum += x;
       }
    }
    return Math.abs(OddSum - EvenSum);
}
 
// Driver code
public static void main(String[] args)
{
     
    // Vertices and edges
    int N = 4, M = 6;
 
    // Edges
    int edges[][] = { { 1, 2 }, { 1, 3 }, { 1, 4 },
                      { 2, 3 }, { 2, 4 }, { 3, 4 } };
 
    // Function call
    System.out.print(OddEvenDegree(N, M, edges));
}
}
 
// This code is contributed by PrinciRaj1992

Python3

# Python3 implementation to print the
# Difference Between sum of degrees
# of odd degree nodes and even
# degree nodes.
 
# Function to print the difference
# Between sum of degrees of odd
# degree nodes and even degree nodes.
def OddEvenDegree(N, M, edges):
 
    # To store Adjacency
    # List of a Graph
    Adj = [[] for i in range(N + 1)]
      
    EvenSum = 0;
    OddSum = 0;
  
    # Make Adjacency List
    for i in range(M):
        x = edges[i][0];
        y = edges[i][1];
  
        Adj[x].append(y);
        Adj[y].append(x);
  
    # Traverse each vertex
    for i in range(1, N + 1):
  
        # Find size of
        # Adjacency List
        x = len(Adj[i])
  
        # If length of Adj[i] is
        # an odd number, add
        # length in OddSum
        if (x % 2 != 0):
            OddSum += x;       
        else:
             
            # If length of Adj[i] is
            # an even number, add
            # length in EvenSum
            EvenSum += x;       
      
    return abs(OddSum - EvenSum);
 
# Driver code
if __name__ == "__main__":
     
    # Vertices and Edges
    N = 4
    M = 6
  
    # Edges
    edges = [[1, 2], [1, 3],
             [1, 4], [2, 3],
             [2, 4], [3, 4]]
  
    # Function Call
    print(OddEvenDegree(N, M,
                        edges));
 
# This code is contributed by rutvik_56

C#

// C# implementation to print the
// difference between sum of degrees
// of odd degree nodes and even
// degree nodes.
using System;
using System.Collections.Generic;
class GFG{
 
// Function to print the difference
// between sum of degrees of odd
// degree nodes and even degree nodes.
static int OddEvenDegree(int N, int M,
                         int [,]edges)
{
  // To store adjacency list
  // of a graph
  List []Adj = new List[N + 1];
 
  for(int i = 0; i < N + 1; i++)
  {
    Adj[i] = new List();
  }
 
  int EvenSum = 0;
  int OddSum = 0;
 
  // Make adjacency list
  for(int i = 0; i < M; i++)
  {
    int x = edges[i, 0];
    int y = edges[i, 1];
 
    Adj[x].Add(y);
    Adj[y].Add(x);
  }
 
  // Traverse each vertex
  for(int i = 1; i <= N; i++)
  {
    // Find size of adjacency list
    int x = Adj[i].Count;
 
    // If length of Adj[i] is
    // an odd number, add
    // length in OddSum
    if (x % 2 != 0)
    {
      OddSum += x;
    }
    else
    {
      // If length of Adj[i] is
      // an even number, add
      // length in EvenSum
      EvenSum += x;
    }
  }
  return Math.Abs(OddSum - EvenSum);
}
 
// Driver code
public static void Main(String[] args)
{
  // Vertices and edges
  int N = 4, M = 6;
 
  // Edges
  int [,]edges = {{1, 2}, {1, 3}, {1, 4},
                  {2, 3}, {2, 4}, {3, 4}};
 
  // Function call
  Console.Write(OddEvenDegree(N, M, edges));
}
}
 
// This code is contributed by Princi Singh

输出：

12

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