Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Count ways to Change Direction of Edges such that Graph Becomes Acyclic
The goal of the "Count ways to change direction of edges such that graph becomes acyclic" issue is to count the number of configurations where the edges of a graph may be changed so that the graph becomes acyclic. No cycles or loops exist in an acyclic network.A set of edges, or a graph, is given to us as the starting point of this issue. The aim is to find out how many different ways there are to change the orientation of these edges while still producing an acyclic graph.
The code presented utilises a hybrid of backtracking and depth−first search (DFS) to arrive at a solution. Graph cycles may be found using DFS, and all conceivable configurations can be explored with backtracking by repeatedly switching the orientations of edges and testing the resultant graphs for acyclicity.
Methods Used
Backtracking
Backtracking
Backtracking progressively builds and explores all viable solutions. This code backtracks over all edge direction configurations. The programme exhaustively investigates all possible solutions by reversing each edge and counting valid acyclic graphs.
Algorithm
Add each edge's visited vertex to the recursion stack:
if the edge source is the current vertex:
if not visited:
recursively call dfs with the destination vertex if the recursive call returns true, indicating a cycle:
return true unless the destination vertex is in the recursion stack:
return true
Example
#include <iostream>
#include <vector>
struct Edge {
int source, destination;
};
// Function to check if the graph becomes acyclic
bool isAcyclic(const std::vector<Edge>& edges, std::vector<bool>& visited);
// Depth-first search to detect cycles
bool dfs(const std::vector<Edge>& edges, std::vector<bool>& visited, std::vector<bool>& recursionStack, int vertex) {
visited[vertex] = true;
recursionStack[vertex] = true;
for (const Edge& edge : edges) {
if (edge.source == vertex) {
int destination = edge.destination;
if (!visited[destination] && dfs(edges, visited, recursionStack, destination))
return true;
else if (recursionStack[destination])
return true;
}
}
recursionStack[vertex] = false;
return false;
}
// Function to check if the graph becomes acyclic
bool isAcyclic(const std::vector<Edge>& edges, std::vector<bool>& visited) {
int numVertices = visited.size();
std::vector<bool> recursionStack(numVertices, false);
for (int i = 0; i < numVertices; ++i) {
if (!visited[i] && dfs(edges, visited, recursionStack, i))
return false;
}
return true;
}
// Function to count the ways to change edge directions to make the graph acyclic
int countAcyclicConfigurations(std::vector<Edge>& edges, std::vector<bool>& directed, int index) {
int numWays = 0;
int numEdges = edges.size();
if (index == numEdges) {
if (isAcyclic(edges, directed))
return 1;
else
return 0;
}
// Change direction of edge and backtrack
directed[index] = true;
numWays += countAcyclicConfigurations(edges, directed, index + 1);
// Restore direction of edge and backtrack
directed[index] = false;
numWays += countAcyclicConfigurations(edges, directed, index + 1);
return numWays;
}
int main() {
// Example usage
int numVertices = 4;
std::vector<Edge> edges = {
{0, 1},
{1, 2},
{2, 3},
{3, 0}
};
int numEdges = edges.size();
// Initialize directed array with false values
std::vector<bool> directed(numEdges, false);
int numAcyclicConfigurations = countAcyclicConfigurations(edges, directed, 0);
std::cout << "Number of ways to change edge directions to make the graph acyclic: " << numAcyclicConfigurations << std::endl;
return 0;
}
Output
Number of ways to change edge directions to make the graph acyclic: 16
Conclusion
Finally, the supplied code provides a solid answer to the question of how many possible methods there are to reverse the orientation of edges in a graph so that it becomes acyclic. The programme efficiently investigates all potential edge configurations and counts the number of valid acyclic graph configurations using a mix of depth−first search (DFS) and backtracking methods.The DFS method can identify cycles in the graph, guaranteeing that the final setups are cycle−free. The backtracking method makes it easier to systematically test out alternative edge routes, ultimately leading to a more thorough analysis of all viable options.
65 Views
