Hexadecimal equivalents in Binary Valued Graph

Given a binary valued undirected graph with V vertices and E edges, the task is to find the hexadecimal equivalents of all the connected components of the graph. A binary valued graph can be considered as having only binary numbers (0 or 1) as the vertex values.

Examples:

Input: E = 4, V = 7

Output:
Chain = 0 1      Hexadecimal equivalent = 1
Chain = 0 0 0      Hexadecimal equivalent = 0
Chain = 1 1      Hexadecimal equivalent = 3
Explanation:
In case of the first connected component, the binary chain is [0, 1]
Hence, the binary string = “01” and binary number = 01
So, the hexadecimal equivalent = 1

Input: E = 6, V = 10

Output:
Chain = 1      Hexadecimal equivalent = 1
Chain = 0 0 1 0      Hexadecimal equivalent = 2
Chain = 1 1 0      Hexadecimal equivalent = 6
Chain = 1 0      Hexadecimal equivalent = 2

Approach: The idea is to use Depth First Search Traversal to keep track of the connected components in the undirected graph as explained in this article. For each connected component, the binary string is displayed and the equivalent hexadecimal value is calculated from the binary value as explained in this article and printed.



Below is the implementation of the above approach:

C++

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// C++ implementation to find 
// hexadecimal equivalents of 
// all connected components 
#include <bits/stdc++.h>
using namespace std;
  
// Function to traverse the undirected 
// graph using the Depth first traversal
void depthFirst(int v,
                vector<int> graph[],
                vector<bool>& visited,
                vector<int>& storeChain)
{
    // Marking the visited
    // vertex as true
    visited[v] = true;
  
    // Store the connected chain
    storeChain.push_back(v);
  
    for (auto i : graph[v]) {
        if (visited[i] == false) {
  
            // Recursive call to
            // the DFS algorithm
            depthFirst(i, graph,
                       visited,
                       storeChain);
        }
    }
}
  
// Function to create map between binary
// number and its equivalent hexadecimal
void createMap(unordered_map<string,
                             char>* um)
{
  
    (*um)["0000"] = '0';
    (*um)["0001"] = '1';
    (*um)["0010"] = '2';
    (*um)["0011"] = '3';
    (*um)["0100"] = '4';
    (*um)["0101"] = '5';
    (*um)["0110"] = '6';
    (*um)["0111"] = '7';
    (*um)["1000"] = '8';
    (*um)["1001"] = '9';
    (*um)["1010"] = 'A';
    (*um)["1011"] = 'B';
    (*um)["1100"] = 'C';
    (*um)["1101"] = 'D';
    (*um)["1110"] = 'E';
    (*um)["1111"] = 'F';
}
  
// Function to return hexadecimal
// equivalent of each connected
// component
string hexaDecimal(string bin)
{
    int l = bin.size();
    int t = bin.find_first_of('.');
  
    // Length of string before '.'
    int len_left = t != -1 ? t : l;
  
    // Add min 0's in the beginning
    // to make left substring length
    // divisible by 4
    for (int i = 1;
         i <= (4 - len_left % 4) % 4;
         i++)
  
        bin = '0' + bin;
  
    // If decimal point exists
    if (t != -1) {
  
        // Length of string after '.'
        int len_right = l - len_left - 1;
  
        // Add min 0's in the end to
        // make right substring length
        // divisible by 4
        for (int i = 1;
             i <= (4 - len_right % 4) % 4;
             i++)
  
            bin = bin + '0';
    }
  
    // Create map between binary
    // and its equivalent hex code
    unordered_map<string,
                  char>
        bin_hex_map;
    createMap(&bin_hex_map);
  
    int i = 0;
    string hex = "";
  
    while (1) {
  
        // Extract from left,
        // substring of size 4 and add
        // its hex code
        hex += bin_hex_map[bin.substr(i, 4)];
        i += 4;
  
        if (i == bin.size())
            break;
  
        // If '.' is encountered add it
        // to result
        if (bin.at(i) == '.') {
  
            hex += '.';
            i++;
        }
    }
  
    // Required hexadecimal number
    return hex;
}
  
// Function to find the hexadecimal
// equivalents of all connected
// components
void hexValue(
    vector<int> graph[],
    int vertices,
    vector<int> values)
{
  
    // Initializing boolean array
    // to mark visited vertices
    vector<bool> visited(10001,
                         false);
  
    // Following loop invokes
    // DFS algorithm
    for (int i = 1; i <= vertices;
         i++) {
  
        if (visited[i] == false) {
  
            // Variable to hold
            // temporary length
            int sizeChain;
  
            // Container to store
            // each chain
            vector<int> storeChain;
  
            // DFS algorithm
            depthFirst(i, graph,
                       visited,
                       storeChain);
  
            // Variable to hold each
            // chain size
            sizeChain = storeChain.size();
  
            // Container to store
            // values of vertices of
            // individual chains
            int chainValues[sizeChain + 1];
  
            // Storing the values of
            // each chain
            for (int i = 0;
                 i < sizeChain; i++) {
  
                int temp = values[storeChain[i] - 1];
                chainValues[i] = temp;
            }
  
            // Printing binary chain
            cout << "Chain = ";
  
            for (int i = 0;
                 i < sizeChain; i++) {
  
                cout << chainValues[i]
                     << " ";
            }
            cout << "\t";
  
            // Converting the array
            // with vertex
            // values to a binary string
            // using string stream
            stringstream ss;
            ss << chainValues[0];
            string s = ss.str();
  
            for (int i = 1;
                 i < sizeChain; i++) {
  
                stringstream ss1;
                ss1 << chainValues[i];
                string s1 = ss1.str();
                s.append(s1);
            }
  
            // Printing the hexadecimal
            // values
            cout << "Hexadecimal "
                 << "equivalent = ";
            cout << hexaDecimal(s)
                 << endl;
        }
    }
}
  
// Driver Program
int main()
{
    // Initializing graph in the
    // form of adjacency list
    vector<int> graph[1001];
  
    // Defining the number of
    // edges and vertices
    int E, V;
    E = 4;
    V = 7;
  
    // Assigning the values
    // for each vertex of the
    // undirected graph
    vector<int> values;
    values.push_back(0);
    values.push_back(1);
    values.push_back(1);
    values.push_back(1);
    values.push_back(0);
    values.push_back(1);
    values.push_back(1);
  
    // 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[4].push_back(5);
    graph[5].push_back(4);
    graph[6].push_back(5);
    graph[5].push_back(6);
    graph[6].push_back(7);
    graph[7].push_back(6);
  
    hexValue(graph, V, values);
    return 0;
}

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Output:

Chain = 0 1
     Hexadecimal equivalent = 1
Chain = 1 1 0 1 1
     Hexadecimal equivalent = 1B


Time Complexity: O(V2)
The DFS algorithm requires O(V + E) complexity, where V, E are the vertices and edges of the undirected graph. Further, the hexadecimal equivalent is obtained at each iteration which requires an additional O(V) complexity to compute. Hence, the overall complexity is O(V2).

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