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 = 1Input: 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++
// 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; } |
Java
// Java implementation to find // hexadecimal equivalents of // all connected components import java.io.*; import java.util.*; class GFG{ // Function to traverse the undirected // graph using the Depth first traversal static void depthFirst( int v, List<List<Integer>> graph, boolean [] visited, List<Integer> storeChain) { // Marking the visited // vertex as true visited[v] = true ; // Store the connected chain storeChain.add(v); for ( int i : graph.get(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 static void createMap(Map<String, Character> um) { um.put( "0000" , '0' ); um.put( "0001" , '1' ); um.put( "0010" , '2' ); um.put( "0011" , '3' ); um.put( "0100" , '4' ); um.put( "0101" , '5' ); um.put( "0110" , '6' ); um.put( "0111" , '7' ); um.put( "1000" , '8' ); um.put( "1001" , '9' ); um.put( "1010" , 'A' ); um.put( "1011" , 'B' ); um.put( "1100" , 'C' ); um.put( "1101" , 'D' ); um.put( "1110" , 'E' ); um.put( "1111" , 'F' ); } // Function to return hexadecimal // equivalent of each connected // component static String hexaDecimal(String bin) { int l = bin.length(); int t = bin.indexOf( '.' ); // 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 Map<String, Character> bin_hex_map = new HashMap<String, Character>(); createMap(bin_hex_map); int i = 0 ; String hex = "" ; while ( true ) { // One by one extract from left, substring // of size 4 and add its hex code hex += bin_hex_map.get(bin.substring(i, i + 4 )); i += 4 ; if (i == bin.length()) break ; // If '.' is encountered add it // to result if (bin.charAt(i) == '.' ) { hex += '.' ; i++; } } // Required hexadecimal number return hex; } // Function to find the hexadecimal // equivalents of all connected // components static void hexValue(List<List<Integer>> graph, int vertices, List<Integer> values) { // Initializing boolean array // to mark visited vertices boolean [] visited = new boolean [ 1001 ]; // 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 List<Integer> storeChain = new ArrayList<Integer>(); // 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 = new int [sizeChain + 1 ]; // Storing the values of each chain for ( int j = 0 ; j < sizeChain; j++) { int temp = values.get( storeChain.get(j) - 1 ); chainValues[j] = temp; } // Printing binary chain System.out.print( "Chain = " ); for ( int j = 0 ; j < sizeChain; j++) { System.out.print(chainValues[j] + " " ); } System.out.println(); System.out.print( "\t" ); // Converting the array with // vertex values to a binary // string String s = "" ; for ( int j = 0 ; j < sizeChain; j++) { String s1 = String.valueOf( chainValues[j]); s += s1; } // Printing the hexadecimal // values System.out.println( "Hexadecimal " + "equivalent = " + hexaDecimal(s)); } } } // Driver code public static void main(String[] args) { // Initializing graph in the // form of adjacency list @SuppressWarnings ( "unchecked" ) List<List<Integer>> graph = new ArrayList(); for ( int i = 0 ; i < 1001 ; i++) graph.add( new ArrayList<Integer>()); // Defining the number // of edges and vertices int E = 4 , V = 7 ; // Assigning the values for each // vertex of the undirected graph List<Integer> values = new ArrayList<Integer>(); values.add( 0 ); values.add( 1 ); values.add( 1 ); values.add( 1 ); values.add( 0 ); values.add( 1 ); values.add( 1 ); // Constructing the undirected graph graph.get( 1 ).add( 2 ); graph.get( 2 ).add( 1 ); graph.get( 3 ).add( 4 ); graph.get( 4 ).add( 3 ); graph.get( 4 ).add( 5 ); graph.get( 5 ).add( 4 ); graph.get( 6 ).add( 5 ); graph.get( 5 ).add( 6 ); graph.get( 6 ).add( 7 ); graph.get( 7 ).add( 6 ); hexValue(graph, V, values); } } // This code is contributed by jithin |
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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