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Maximum sum of values of nodes among all connected components of an undirected graph

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Given an undirected graph with V vertices and E edges. Every node has been assigned a given value. The task is to find the connected chain with the maximum sum of values among all the connected components in the graph. 
Examples:

Input: V = 7, E = 4 
Values = {10, 25, 5, 15, 5, 20, 0} 
 


Output : Max Sum value = 35 
Explanation: 
Component {1, 2} – Value {10, 25}: sumValue = 10 + 25 = 35 
Component {3, 4, 5} – Value {5, 15, 5}: sumValue = 5 + 15 + 5 = 25 
Component {6, 7} – Value {20, 0}: sumValue = 20 + 0 = 20 
Max Sum value chain is {1, 2} with values {10, 25}, hence 35 is answer. 
Input: V = 10, E = 6 
Values = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50}


Output : Max Sum value = 105


Approach: The idea is to use the Depth First Search traversal method to keep a track of all the connected components. A temporary variable is used to sum up all the values of the individual values of the connected chains. At each traversal of a connected component, the heaviest value till now is compared with the current value and updated accordingly. After all connected components have been traversed, the maximum among all will be the answer. 
Below is the implementation of the above approach:

C++

// C++ program to find Maximum sum of values
// of nodes among all connected
// components of an undirected graph
#include <bits/stdc++.h>
using namespace std;
 
// Function to implement DFS
void depthFirst(int v, vector<int> graph[],
                vector<bool>& visited,
                int& sum,
                vector<int> values)
{
    // Marking the visited vertex as true
    visited[v] = true;
 
    // Updating the value of connection
    sum += values[v - 1];
 
    // Traverse for all adjacent nodes
    for (auto i : graph[v]) {
 
        if (visited[i] == false) {
 
            // Recursive call to the DFS algorithm
            depthFirst(i, graph, visited,
                       sum, values);
        }
    }
}
 
void maximumSumOfValues(vector<int> graph[],
                        int vertices, vector<int> values)
{
    // Initializing boolean array to mark visited vertices
    vector<bool> visited(values.size() + 1, false);
 
    // maxChain stores the maximum chain size
    int maxValueSum = INT_MIN;
 
    // Following loop invokes DFS algorithm
    for (int i = 1; i <= vertices; i++) {
        if (visited[i] == false) {
 
            // Variable to hold temporary values
            int sum = 0;
 
            // DFS algorithm
            depthFirst(i, graph, visited,
                       sum, values);
 
            // Conditional to update max value
            if (sum > maxValueSum) {
                maxValueSum = sum;
            }
        }
    }
 
    // Printing the heaviest chain value
    cout << "Max Sum value = ";
    cout << maxValueSum << "\n";
}
 
// Driver function to test above function
int main()
{
 
    // Defining the number of edges and vertices
    int E = 4, V = 7;
 
      // Initializing graph in the form of adjacency list
    vector<int> graph[V+1];
 
   
   
    // Assigning the values for each
    // vertex of the undirected graph
    vector<int> values;
    values.push_back(10);
    values.push_back(25);
    values.push_back(5);
    values.push_back(15);
    values.push_back(5);
    values.push_back(20);
    values.push_back(0);
 
    // Constructing the undirected graph
    graph[1].push_back(2);
    graph[2].push_back(1);
    graph[3].push_back(4);
    graph[4].push_back(3);
    graph[3].push_back(5);
    graph[5].push_back(3);
    graph[6].push_back(7);
    graph[7].push_back(6);
 
    maximumSumOfValues(graph, V, values);
    return 0;
}

                    

Java

// Java program to find Maximum sum of
// values of nodes among all connected
// components of an undirected graph
import java.util.*;
 
class GFG{
     
static int sum;
 
// Function to implement DFS
static void depthFirst(int v,
                       Vector<Integer> graph[],
                       boolean []visited,
                       Vector<Integer> values)
{
     
    // Marking the visited vertex as true
    visited[v] = true;
 
    // Updating the value of connection
    sum += values.get(v - 1);
 
    // Traverse for all adjacent nodes
    for(int i : graph[v])
    {
        if (visited[i] == false)
        {
             
            // Recursive call to the DFS algorithm
            depthFirst(i, graph, visited, values);
        }
    }
}
 
static void maximumSumOfValues(Vector<Integer> graph[],
                               int vertices,
                               Vector<Integer> values)
{
     
    // Initializing boolean array to
    // mark visited vertices
    boolean []visited = new boolean[values.size() + 1];
 
    // maxChain stores the maximum chain size
    int maxValueSum = Integer.MIN_VALUE;
 
    // Following loop invokes DFS algorithm
    for(int i = 1; i <= vertices; i++)
    {
        if (visited[i] == false)
        {
             
            // Variable to hold temporary values
            sum = 0;
 
            // DFS algorithm
            depthFirst(i, graph, visited, values);
 
            // Conditional to update max value
            if (sum > maxValueSum)
            {
                maxValueSum = sum;
            }
        }
    }
     
    // Printing the heaviest chain value
    System.out.print("Max Sum value = ");
    System.out.print(maxValueSum + "\n");
}
 
// Driver code
public static void main(String[] args)
{
     
    // Initializing graph in the form
    // of adjacency list
    @SuppressWarnings("unchecked")
    Vector<Integer> []graph = new Vector[1001];
     
    for(int i = 0; i < graph.length; i++)
        graph[i] = new Vector<Integer>();
         
    // Defining the number of edges and vertices
    int E = 4, V = 7;
 
    // Assigning the values for each
    // vertex of the undirected graph
    Vector<Integer> values = new Vector<Integer>();
    values.add(10);
    values.add(25);
    values.add(5);
    values.add(15);
    values.add(5);
    values.add(20);
    values.add(0);
 
    // Constructing the undirected graph
    graph[1].add(2);
    graph[2].add(1);
    graph[3].add(4);
    graph[4].add(3);
    graph[3].add(5);
    graph[5].add(3);
    graph[6].add(7);
    graph[7].add(6);
 
    maximumSumOfValues(graph, V, values);
}
}
 
// This code is contributed by Rajput-Ji

                    

Python3

# Python3 program to find Maximum sum
# of values of nodes among all connected
# components of an undirected graph
import sys
 
graph = [[] for i in range(1001)]
visited = [False] * (1001 + 1)
sum = 0
 
# Function to implement DFS
def depthFirst(v, values):
     
    global sum
     
    # Marking the visited vertex as true
    visited[v] = True
 
    # Updating the value of connection
    sum += values[v - 1]
 
    # Traverse for all adjacent nodes
    for i in graph[v]:
        if (visited[i] == False):
 
            # Recursive call to the
            # DFS algorithm
            depthFirst(i, values)
 
def maximumSumOfValues(vertices,values):
     
    global sum
     
    # Initializing boolean array to
    # mark visited vertices
 
    # maxChain stores the maximum chain size
    maxValueSum = -sys.maxsize - 1
 
    # Following loop invokes DFS algorithm
    for i in range(1, vertices + 1):
        if (visited[i] == False):
 
            # Variable to hold temporary values
            # sum = 0
 
            # DFS algorithm
            depthFirst(i, values)
 
            # Conditional to update max value
            if (sum > maxValueSum):
                maxValueSum = sum
                 
            sum = 0
             
    # Printing the heaviest chain value
    print("Max Sum value = ", end = "")
    print(maxValueSum)
 
# Driver code
if __name__ == '__main__':
     
    # Initializing graph in the
    # form of adjacency list
 
    # Defining the number of
    # edges and vertices
    E = 4
    V = 7
 
    # Assigning the values for each
    # vertex of the undirected graph
    values = []
    values.append(10)
    values.append(25)
    values.append(5)
    values.append(15)
    values.append(5)
    values.append(20)
    values.append(0)
 
    # Constructing the undirected graph
    graph[1].append(2)
    graph[2].append(1)
    graph[3].append(4)
    graph[4].append(3)
    graph[3].append(5)
    graph[5].append(3)
    graph[6].append(7)
    graph[7].append(6)
 
    maximumSumOfValues(V, values)
 
# This code is contributed by mohit kumar 29

                    

C#

// C# program to find Maximum sum of
// values of nodes among all connected
// components of an undirected graph
using System;
using System.Collections.Generic;
 
class GFG{
     
static int sum;
 
// Function to implement DFS
static void depthFirst(int v,
                       List<int> []graph,
                       bool []visited,
                       List<int> values)
{
     
    // Marking the visited vertex as true
    visited[v] = true;
 
    // Updating the value of connection
    sum += values[v - 1];
 
    // Traverse for all adjacent nodes
    foreach(int i in graph[v])
    {
        if (visited[i] == false)
        {
             
            // Recursive call to the DFS algorithm
            depthFirst(i, graph, visited, values);
        }
    }
}
 
static void maximumSumOfValues(List<int> []graph,
                               int vertices,
                               List<int> values)
{
     
    // Initializing bool array to
    // mark visited vertices
    bool []visited = new bool[values.Count + 1];
 
    // maxChain stores the maximum chain size
    int maxValueSum = int.MinValue;
 
    // Following loop invokes DFS algorithm
    for(int i = 1; i <= vertices; i++)
    {
        if (visited[i] == false)
        {
             
            // Variable to hold temporary values
            sum = 0;
 
            // DFS algorithm
            depthFirst(i, graph, visited, values);
 
            // Conditional to update max value
            if (sum > maxValueSum)
            {
                maxValueSum = sum;
            }
        }
    }
     
    // Printing the heaviest chain value
    Console.Write("Max Sum value = ");
    Console.Write(maxValueSum + "\n");
}
 
// Driver code
public static void Main(String[] args)
{
     
    // Initializing graph in the form
    // of adjacency list
    List<int> []graph = new List<int>[1001];
     
    for(int i = 0; i < graph.Length; i++)
        graph[i] = new List<int>();
         
    // Defining the number of edges and vertices
    int V = 7;
 
    // Assigning the values for each
    // vertex of the undirected graph
    List<int> values = new List<int>();
     
    values.Add(10);
    values.Add(25);
    values.Add(5);
    values.Add(15);
    values.Add(5);
    values.Add(20);
    values.Add(0);
 
    // Constructing the undirected graph
    graph[1].Add(2);
    graph[2].Add(1);
    graph[3].Add(4);
    graph[4].Add(3);
    graph[3].Add(5);
    graph[5].Add(3);
    graph[6].Add(7);
    graph[7].Add(6);
 
    maximumSumOfValues(graph, V, values);
}
}
 
// This code is contributed by Amit Katiyar

                    

Javascript

<script>
 
// JavaScript program to find Maximum sum
// of values of nodes among all connected
// components of an undirected graph
 
let graph = new Array(1001);
for(let i=0;i<1001;i++){
    graph[i] = new Array();
}
let visited = new Array(1001+1).fill(false);
let sum = 0
 
// Function to implement DFS
function depthFirst(v, values){
     
    // Marking the visited vertex as true
    visited[v] = true
 
    // Updating the value of connection
    sum += values[v - 1]
 
    // Traverse for all adjacent nodes
    for(let i of graph[v]){
        if (visited[i] == false){
 
            // Recursive call to the
            // DFS algorithm
            depthFirst(i, values)
        }
    }
}
 
function maximumSumOfValues(vertices,values){
     
     
    // Initializing boolean array to
    // mark visited vertices
 
    // maxChain stores the maximum chain size
    let maxValueSum = Number.MIN_VALUE
 
    // Following loop invokes DFS algorithm
    for(let i=1;i<vertices + 1;i++){
        if (visited[i] == false){
 
            // Variable to hold temporary values
            // sum = 0
 
            // DFS algorithm
            depthFirst(i, values)
 
            // Conditional to update max value
            if (sum > maxValueSum)
                maxValueSum = sum
                 
            sum = 0
        }
    }
             
    // Printing the heaviest chain value
    document.write("Max Sum value = ","")
    document.write(maxValueSum)
}
 
// Driver code
 
// Initializing graph in the
// form of adjacency list
 
// Defining the number of
// edges and vertices
let E = 4
let V = 7
 
// Assigning the values for each
// vertex of the undirected graph
let values = []
values.push(10)
values.push(25)
values.push(5)
values.push(15)
values.push(5)
values.push(20)
values.push(0)
 
// Constructing the undirected graph
graph[1].push(2)
graph[2].push(1)
graph[3].push(4)
graph[4].push(3)
graph[3].push(5)
graph[5].push(3)
graph[6].push(7)
graph[7].push(6)
 
maximumSumOfValues(V, values)
 
// This code is contributed by shinjanpatra
 
</script>

                    

Output
Max Sum value = 35











Time Complexity: O(E + V) 
Auxiliary Space: O(E + V) 
 

Approach 2 :- Using Breadth Frirst Search (BFS) Technique

  • First we create boolean array visited to keep track of visited vertices
  • Next , we will traverse through every vertex if it is not visted and we calculate the sum of the connected components of current vertex using BFS.
  • Next , we will update the max with currentcomponentsum of every vertex.
  • so ,Finally the max variable will be storing the maximum component sum .
  • In breadthFirstSearch function , we first mark the vertex as visited.
  • Then we will add that vertex in the Queue Datastructure.
  • Next , we will travers through its adjacent vertices and add them into the queue and marking every adjacent vertex as visited.
  • Next , we will calculate the total componet sum by adding the values of every visited vertex.
  • Finally, we will return the total component sum .


Below is the Implementation of the BFS Approach :-

C++

#include <iostream>
#include <vector>
#include <queue>
#include <climits> // Include the header for INT_MIN
using namespace std;
 
// Function to implement BFS
int breadthFirst(int v, vector<int> graph[], bool visited[], vector<int>& values)
{
    // Initially sum will be assigned to zero
    int sum = 0;
 
    // Marking the vertex as visited
    visited[v] = true;
 
    queue<int> q;
 
    // Adding the current vertex in the queue data structure
    q.push(v);
 
    while (!q.empty()) {
        // Polling the current vertex and adding its value to the sum
        int node = q.front();
        q.pop();
        sum += values[node - 1];
 
        // Traversing its adjacent vertices
        for (int it : graph[node]) {
            // If the vertex is not visited, we add it into the queue and mark the vertex as visited
            if (!visited[it]) {
                q.push(it);
                visited[it] = true;
            }
        }
    }
 
    // Return the sum
    return sum;
}
 
void maximumSumOfValues(vector<int> graph[], int vertices, vector<int>& values)
{
    // Creating a boolean array to mark the visited nodes
    bool visited[vertices + 1] = {false};
 
    // Initializing maxSum with INT_MIN
    int maxSum = INT_MIN;
 
    // Traversing through each vertex
    for (int i = 1; i <= vertices; i++) {
        // If the current vertex is not visited, apply BFS to find the component sum with its adjacent nodes
        if (!visited[i]) {
            int currentComponentSum = breadthFirst(i, graph, visited, values);
 
            // Updating maxSum with currentComponentSum
            maxSum = max(maxSum, currentComponentSum);
        }
    }
 
    // Finally, printing the max component sum
    cout << "Max Sum Value = " << maxSum << endl;
}
 
int main() {
    // Initializing the graph in the form of an adjacency list
    vector<int> graph[1001];
 
    // Defining the number of edges and vertices
    int E = 6, V = 10;
 
    // Assigning values for each vertex of the undirected graph
    vector<int> values = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50};
 
    // Constructing the undirected graph
    graph[2].push_back(3);
    graph[3].push_back(2);
    graph[3].push_back(4);
    graph[4].push_back(3);
    graph[4].push_back(5);
    graph[5].push_back(4);
    graph[6].push_back(7);
    graph[7].push_back(6);
    graph[7].push_back(8);
    graph[8].push_back(7);
    graph[9].push_back(10);
    graph[10].push_back(9);
 
    maximumSumOfValues(graph, V, values);
    return 0;
}
 
// This code is contributed by shivamgupta0987654321

                    

Java

// Java program to find Maximum sum of
// values of nodes among all connected
// components of an undirected graph
import java.util.*;
 
class Main {
 
    // Function to implement BFS
    static int breadthFirst(int v, Vector<Integer> graph[],
                            boolean[] visited,
                            Vector<Integer> values)
    {
        // Iniatially sum will be assigned to zero
 
        int sum = 0;
 
        // marking the vertex as visited
 
        visited[v] = true;
 
        Queue<Integer> q = new LinkedList<>();
 
        // Adding the current vertex in the queue
        // datastructure
 
        q.add(v);
 
        while (!q.isEmpty()) {
            // polling the current vertex  and adding its
            // value to the sum
 
            int node = q.poll();
            sum += values.get(node - 1);
 
            // Traversing its adjacent vertices
 
            for (int it : graph[node]) {
                // if the vertex is not visited
                // we add it into the queue and
                // mark the vertex as visited
 
                if (visited[it] == false) {
                    q.add(it);
                    visited[it] = true;
                }
            }
        }
 
        // return the sum
        return sum;
    }
 
    static void maximumSumOfValues(Vector<Integer> graph[],
                                   int vertices,
                                   Vector<Integer> values)
    {
        // creating boolean array to mark the visited nodes
        boolean visited[] = new boolean[vertices + 1];
 
        // Initailizing max with Integer_MINVALUE;
 
        int max = Integer.MIN_VALUE;
 
        // Traversing through each vertex
 
        for (int i = 1; i < vertices + 1; i++) {
            // if the current vertex is not visited
            // we will apply bfs to the vertex to find
            // the component sum with its adjacent nodes
 
            if (visited[i] == false) {
                int currentComponentSum = breadthFirst(
                    i, graph, visited, values);
 
                // updating max with currentComponentSum
 
                max = Math.max(max, currentComponentSum);
            }
        }
 
        // finally printing the max componentSum
 
        System.out.print("Max Sum Value = " + max);
    }
    // Driver code
    public static void main(String[] args)
    {
 
        // Initializing graph in the form
        // of adjacency list
        @SuppressWarnings("unchecked")
        Vector<Integer>[] graph = new Vector[1001];
 
        for (int i = 0; i < graph.length; i++)
            graph[i] = new Vector<Integer>();
 
        // Defining the number of edges and vertices
        int E = 6, V = 10;
 
        // Assigning the values for each
        // vertex of the undirected graph
        Vector<Integer> values = new Vector<Integer>();
        values.add(5);
        values.add(10);
        values.add(15);
        values.add(20);
        values.add(25);
        values.add(30);
        values.add(35);
        values.add(40);
        values.add(45);
        values.add(50);
 
        // Constructing the undirected graph
        graph[2].add(3);
        graph[3].add(2);
        graph[3].add(4);
        graph[4].add(3);
        graph[4].add(5);
        graph[5].add(4);
        graph[6].add(7);
        graph[7].add(6);
        graph[7].add(8);
        graph[8].add(7);
        graph[9].add(10);
        graph[10].add(9);
 
        maximumSumOfValues(graph, V, values);
    }
}
 
// This code is contributed by srimann7

                    

Python3

from queue import Queue
 
# Function to implement BFS
def breadth_first(v, graph, visited, values):
    # Initially sum will be assigned to zero
    sum_value = 0
 
    # Marking the vertex as visited
    visited[v] = True
 
    q = Queue()
 
    # Adding the current vertex in the queue data structure
    q.put(v)
 
    while not q.empty():
        # Polling the current vertex and adding its value to the sum
        node = q.get()
        sum_value += values[node - 1]
 
        # Traversing its adjacent vertices
        for neighbor in graph[node]:
            # If the vertex is not visited, we add it into the queue and mark the vertex as visited
            if not visited[neighbor]:
                q.put(neighbor)
                visited[neighbor] = True
 
    # Return the sum
    return sum_value
 
def maximum_sum_of_values(graph, vertices, values):
    # Creating a boolean array to mark the visited nodes
    visited = [False] * (vertices + 1)
 
    # Initializing max_sum with negative infinity
    max_sum = float('-inf')
 
    # Traversing through each vertex
    for i in range(1, vertices + 1):
        # If the current vertex is not visited, apply BFS to find the component
        # sum with its adjacent nodes
        if not visited[i]:
            current_component_sum = breadth_first(i, graph, visited, values)
 
            # Updating max_sum with current_component_sum
            max_sum = max(max_sum, current_component_sum)
 
    # Finally, printing the max component sum
    print("Max Sum Value =", max_sum)
 
# Driver Code
if __name__ == "__main__":
    # Initializing the graph in the form of an adjacency list
    graph = [[] for _ in range(1001)]
 
    # Defining the number of edges and vertices
    E, V = 6, 10
 
    # Assigning values for each vertex of the undirected graph
    values = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]
 
    # Constructing the undirected graph
    graph[2].extend([3])
    graph[3].extend([2, 4])
    graph[4].extend([3, 5])
    graph[5].extend([4])
    graph[6].extend([7])
    graph[7].extend([6, 8])
    graph[8].extend([7])
    graph[9].extend([10])
    graph[10].extend([9])
 
    maximum_sum_of_values(graph, V, values)
 
# This code is contributed by shivamgupta310570

                    

C#

using System;
using System.Collections.Generic;
 
class Program
{
    // Function to implement BFS
    static int BreadthFirst(int v, List<List<int>> graph, bool[] visited, int[] values)
    {
        // Initially sum will be assigned to zero
        int sumValue = 0;
 
        // Marking the vertex as visited
        visited[v] = true;
 
        Queue<int> q = new Queue<int>();
 
        // Adding the current vertex in the queue data structure
        q.Enqueue(v);
 
        while (q.Count > 0)
        {
            // Polling the current vertex and adding its value to the sum
            int node = q.Dequeue();
            sumValue += values[node - 1];
 
            // Traversing its adjacent vertices
            foreach (int neighbor in graph[node])
            {
                // If the vertex is not visited, we add it into the queue and mark the vertex as visited
                if (!visited[neighbor])
                {
                    q.Enqueue(neighbor);
                    visited[neighbor] = true;
                }
            }
        }
 
        // Return the sum
        return sumValue;
    }
 
    static void MaximumSumOfValues(List<List<int>> graph, int vertices, int[] values)
    {
        // Creating a boolean array to mark the visited nodes
        bool[] visited = new bool[vertices + 1];
 
        // Initializing maxSum with negative infinity
        int maxSum = int.MinValue;
 
        // Traversing through each vertex
        for (int i = 1; i <= vertices; i++)
        {
            // If the current vertex is not visited, apply BFS to find the component
            // sum with its adjacent nodes
            if (!visited[i])
            {
                int currentComponentSum = BreadthFirst(i, graph, visited, values);
 
                // Updating maxSum with currentComponentSum
                maxSum = Math.Max(maxSum, currentComponentSum);
            }
        }
 
        // Finally, printing the max component sum
        Console.WriteLine("Max Sum Value = " + maxSum);
    }
 
    // Driver Code
    static void Main()
    {
        // Initializing the graph in the form of an adjacency list
        List<List<int>> graph = new List<List<int>>(1001);
        for (int i = 0; i < 1001; i++)
        {
            graph.Add(new List<int>());
        }
 
        // Defining the number of vertices
        int V = 10;
 
        // Assigning values for each vertex of the undirected graph
        int[] values = { 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 };
 
        // Constructing the undirected graph
        graph[2].Add(3);
        graph[3].AddRange(new[] { 2, 4 });
        graph[4].AddRange(new[] { 3, 5 });
        graph[5].Add(4);
        graph[6].Add(7);
        graph[7].AddRange(new[] { 6, 8 });
        graph[8].Add(7);
        graph[9].Add(10);
        graph[10].Add(9);
 
        MaximumSumOfValues(graph, V, values);
    }
}

                    

Javascript

// JavaScript program for the above approach
 
// Function to implement BFS
function breadthFirst(v, graph, visited, values) {
    // Initially sum will be assigned to zero
    let sum = 0;
 
    // Marking the vertex as visited
    visited[v] = true;
 
    let queue = [];
 
    // Adding the current vertex in the queue data structure
    queue.push(v);
 
    while (queue.length !== 0) {
        // Polling the current vertex and adding its value to the sum
        let node = queue.shift();
        sum += values[node - 1];
 
        // Traversing its adjacent vertices
        for (let it of graph[node]) {
            // If the vertex is not visited, we add it into the
            // queue and mark the vertex as visited
            if (!visited[it]) {
                queue.push(it);
                visited[it] = true;
            }
        }
    }
 
    // Return the sum
    return sum;
}
 
function maximumSumOfValues(graph, vertices, values) {
    // Creating a boolean array to mark the visited nodes
    let visited = new Array(vertices + 1).fill(false);
 
    // Initializing maxSum with INT_MIN
    let maxSum = Number.MIN_SAFE_INTEGER;
 
    // Traversing through each vertex
    for (let i = 1; i <= vertices; i++) {
        // If the current vertex is not visited, apply BFS to find the
        // component sum with its adjacent nodes
        if (!visited[i]) {
            let currentComponentSum = breadthFirst(i, graph, visited, values);
 
            // Updating maxSum with currentComponentSum
            maxSum = Math.max(maxSum, currentComponentSum);
        }
    }
 
    // Finally, printing the max component sum
    console.log("Max Sum Value =", maxSum);
}
 
// Initializing the graph in the form of an adjacency list
let graph = new Array(1001).fill().map(() => []);
 
// Defining the number of edges and vertices
let E = 6, V = 10;
 
// Assigning values for each vertex of the undirected graph
let values = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50];
 
// Constructing the undirected graph
graph[2].push(3);
graph[3].push(2);
graph[3].push(4);
graph[4].push(3);
graph[4].push(5);
graph[5].push(4);
graph[6].push(7);
graph[7].push(6);
graph[7].push(8);
graph[8].push(7);
graph[9].push(10);
graph[10].push(9);
 
maximumSumOfValues(graph, V, values);
 
// This code is contributed by Susobhan Akhuli

                    

Output
Max Sum Value = 105






Time Complexity :- O(V + E) , where V is number of vertices and E is number of edges.

Space Complexity :- O(V + E) , where V is number of vertices and E is number of edges.




Last Updated : 13 Dec, 2023
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