Dado un gráfico no dirigido de valor binario con V vértices y E aristas, la tarea es encontrar los equivalentes hexadecimales de todos los componentes conectados del gráfico. Se puede considerar que un gráfico con valores binarios tiene solo números binarios (0 o 1) como valores de vértice.
Ejemplos:
Entrada: E = 4, V = 7
Salida:
String = 0 1 Equivalente hexadecimal = 1
String = 0 0 0 Equivalente hexadecimal = 0
String = 1 1 Equivalente hexadecimal = 3
Explicación:
En el caso del primer componente conectado, la string binaria es [0, 1]
Por lo tanto, el string = «01» y número binario = 01
Entonces, el equivalente hexadecimal = 1Entrada: E = 6, V = 10
Salida:
String = 1 Equivalente hexadecimal = 1
String = 0 0 1 0 Equivalente hexadecimal = 2
String = 1 1 0 Equivalente hexadecimal = 6
String = 1 0 Equivalente hexadecimal = 2
Enfoque: la idea es utilizar el recorrido transversal de búsqueda en profundidad para realizar un seguimiento de los componentes conectados en el gráfico no dirigido, como se explica en este artículo. Para cada componente conectado, se muestra la string binaria y el valor hexadecimal equivalente se calcula a partir del valor binario como se explica en este artículo y se imprime.
A continuación se muestra la implementación del enfoque anterior:
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
Python3
# Python3 implementation to find
# hexadecimal equivalents of
# all connected components
# Function to traverse the undirected
# graph using the Depth first traversal
def depthFirst(v, graph, visited, storeChain):
# Marking the visited
# vertex as true
visited[v] = True
# Store the connected chain
storeChain.append(v)
for i in graph[v] :
if not visited[i] :
# Recursive call to
# the DFS algorithm
depthFirst(i, graph, visited, storeChain)
# Function to create map between binary
# number and its equivalent hexadecimal
def createMap(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
def hexaDecimal(bn):
l = len(bn)
t = bn.find('.')
# Length of string before '.'
len_left = t if t != -1 else l
# Add min 0's in the beginning
# to make left substring length
# divisible by 4
for i in range(1,((4 - len_left % 4) % 4)+1):
bn = '0' + bn
# If decimal point exists
if (t != -1) :
# Length of string after '.'
len_right = l - len_left - 1
# Add min 0's in the end to
# make right substring length
# divisible by 4
for i in range(1,((4 - len_right % 4) % 4)+1):
bn = bn + '0'
# Create map between binary
# and its equivalent hx code
bin_hex_map=dict()
createMap(bin_hex_map)
i = 0
hx = ""
while (True) :
# Extract from left,
# substring of size 4 and add
# its hx code
hx += bin_hex_map[bn[i: i+4]]
i += 4
if (i == len(bn)):
break
# If '.' is encountered add it
# to result
if (bn[i] == '.') :
hx += '.'
i+=1
# Required hexadecimal number
return hx
# Function to find the hexadecimal
# equivalents of all connected
# components
def hexValue(graph, vertices, values):
# Initializing boolean array
# to mark visited vertices
visited=[False]*10001
# Following loop invokes
# DFS algorithm
for i in range(1,vertices+1):
if not visited[i]:
# Variable to hold
# temporary length
sizeChain=0
# Container to store
# each chain
storeChain=[]
# DFS algorithm
depthFirst(i, graph,
visited,
storeChain)
# Variable to hold each
# chain size
sizeChain = len(storeChain)
# Container to store
# values of vertices of
# individual chains
chainValues=[-1]*(sizeChain + 1)
# Storing the values of
# each chain
for i in range(sizeChain):
temp = values[storeChain[i] - 1]
chainValues[i] = temp
# Printing binary chain
print("Chain =",end=" ")
for i in range(sizeChain) :
print(chainValues[i],end=" ")
print("\t",end="")
# Converting the array
# with vertex
# values to a binary string
s=[]
for i in range(sizeChain):
s.append(str(chainValues[i]))
s=''.join(s)
# Printing the hexadecimal
# values
print("Hexadecimal equivalent =",hexaDecimal(s))
# Driver Program
if __name__=='__main__':
# Initializing graph in the
# form of adjacency list
graph=[[] for _ in range(1001)]
# Defining the number of
# edges and vertices
E = 4
V = 7
# Assigning the values
# for each vertex of the
# undirected graph
values=[]
values.append(0)
values.append(1)
values.append(1)
values.append(1)
values.append(0)
values.append(1)
values.append(1)
# Constructing the
# undirected graph
graph[1].append(2)
graph[2].append(1)
graph[3].append(4)
graph[4].append(3)
graph[4].append(5)
graph[5].append(4)
graph[6].append(5)
graph[5].append(6)
graph[6].append(7)
graph[7].append(6)
hexValue(graph, V, values)
Javascript
// JavaScript implementation to find
// hexadecimal equivalents of
// all connected components
// Function to traverse the undirected
// graph using the Depth first traversal
function depthFirst(v, graph, visited, storeChain)
{
// Marking the visited
// vertex as true
visited[v] = true;
// Store the connected chain
storeChain.push(v);
for (const i of graph[v])
{
if (!visited[i])
{
// Recursive call to
// the DFS algorithm
depthFirst(i, graph, visited, storeChain);
}
}
}
// Function to create map between binary
// number and its equivalent hexadecimal
function createMap(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
function hexaDecimal(bn)
{
var l = bn.length;
var t = bn.indexOf('.');
// Length of string before '.'
if (t != -1)
len_left = t;
else
len_left = l;
// Add min 0's in the beginning
// to make left substring length
// divisible by 4
for (var i = 1; i < ((4 - len_left % 4) % 4)+1; i++)
bn = '0' + bn;
// If decimal point exists
if (t != -1)
{
// Length of string after '.'
len_right = l - len_left - 1;
// Add min 0's in the end to
// make right substring length
// divisible by 4
for (var i = 1; i < ((4 - len_right % 4) % 4)+1; i++)
bn = bn + '0';
}
// Create map between binary
// and its equivalent hx code
var bin_hex_map= {};
createMap(bin_hex_map);
i = 0;
hx = "";
while (true)
{
// Extract from left,
// substring of size 4 and add
// its hx code
hx += bin_hex_map[bn.substring(i, i+4)];
i += 4;
if (i == bn.length)
break;
// If '.' is encountered add it
// to result
if (bn[i] == '.')
{
hx += '.';
i+=1;
}
}
// Required hexadecimal number
return hx;
}
// Function to find the hexadecimal
// equivalents of all connected
// components
function hexValue(graph, vertices, values)
{
// Initializing boolean array
// to mark visited vertices
var visited= new Array(10001).fill(false);
// Following loop invokes
// DFS algorithm
for (var i = 1; i <= vertices; i++)
{
if (!visited[i])
{
//Variable to hold
// temporary length
var sizeChain=0;
//Container to store
// each chain
var storeChain=[];
//DFS algorithm
depthFirst(i, graph,
visited,
storeChain);
// Variable to hold each
// chain size
var sizeChain = storeChain.length;
// Container to store
// values of vertices of
// individual chains
var chainValues = new Array(sizeChain + 1).fill(-1);
// Storing the values of
// each chain
for (var i = 0; i < sizeChain; i++)
{
var temp = values[storeChain[i] - 1];
chainValues[i] = temp;
}
// Printing binary chain
process.stdout.write("Chain = ");
for (var i = 0; i < sizeChain; i++)
process.stdout.write(chainValues[i] + " ");
process.stdout.write("\t");
// Converting the array
// with vertex
// values to a binary string
var s=[];
for (var i = 0; i < sizeChain; i++)
s.push(chainValues[i].toString());
s = s.join('');
//Printing the hexadecimal
// values
console.log("Hexadecimal equivalent =",hexaDecimal(s));
}
}
}
// Driver Program
//Initializing graph in the
// form of adjacency
var graph = [];
for (var i = 0; i < 10001; i ++)
graph.push([]);
// Defining the number of
// edges and vertices
var E = 4;
var V = 7;
// Assigning the values
// for each vertex of the
// undirected graph
var values=[];
values.push(0);
values.push(1);
values.push(1);
values.push(1);
values.push(0);
values.push(1);
values.push(1);
// Constructing the
// undirected graph
graph[1].push(2);
graph[2].push(1);
graph[3].push(4);
graph[4].push(3);
graph[4].push(5);
graph[5].push(4);
graph[6].push(5);
graph[5].push(6);
graph[6].push(7);
graph[7].push(6);
hexValue(graph, V, values);
//this code is contributed by phasing17
Producción:
Chain = 0 1
Hexadecimal equivalent = 1
Chain = 1 1 0 1 1
Hexadecimal equivalent = 1B
Complejidad temporal: O(V 2 )
El algoritmo DFS requiere una complejidad O(V + E), donde V, E son los vértices y las aristas del gráfico no dirigido. Además, el equivalente hexadecimal se obtiene en cada iteración, lo que requiere una complejidad O(V) adicional para calcular. Por lo tanto, la complejidad general es O(V 2 ) .
Espacio Auxiliar: O(V)
Publicación traducida automáticamente
Artículo escrito por PratikBasu y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA