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Detect Cycle in a an Undirected Graph
To detect if there is any cycle in the undirected graph or not, we will use the DFS traversal for the given graph. For every visited vertex v, when we have found any adjacent vertex u, such that u is already visited, and u is not the parent of vertex v. Then one cycle is detected.
We will assume that there are no parallel edges for any pair of vertices.
Input and Output: Adjacency matrix 0 1 0 0 0 1 0 1 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 Output: The graph has cycle.
Algorithm
dfs(vertex, visited, parent)
Input: The start vertex, the visited set, and the parent node of the vertex.
Output: True a cycle is found.Begin add vertex in the visited set for all vertex v which is adjacent with vertex, do if v = parent, then return true if v is not in the visited set, then return true if dfs(v, visited, vertex) is true, then return true done return false End hasCycle(graph) Input: The given graph. Output: True when a cycle has found.Begin for all vertex v in the graph, do if v is not in the visited set, then go for next iteration if dfs(v, visited, φ) is true, then //parent of v is null return true return false done End
Example
#include<iostream>
#include<set>
#define NODE 5
using namespace std;
int graph[NODE][NODE] = {
{0, 1, 0, 0, 0},
{1, 0, 1, 1, 0},
{0, 1, 0, 0, 1},
{0, 1, 0, 0, 1},
{0, 0, 1, 1, 0}
};
bool dfs(int vertex, set<int>&visited, int parent) {
visited.insert(vertex);
for(int v = 0; v<NODE; v++) {
if(graph[vertex][v]) {
if(v == parent) //if v is the parent not move that direction
continue;
if(visited.find(v) != visited.end()) //if v is already visited
return true;
if(dfs(v, visited, vertex))
return true;
}
}
return false;
}
bool hasCycle() {
set<int> visited; //visited set
for(int v = 0; v<NODE; v++) {
if(visited.find(v) != visited.end()) //when visited holds v, jump to next iteration
continue;
if(dfs(v, visited, -1)) { //-1 as no parent of starting vertex
return true;
}
}
return false;
}
int main() {
bool res;
res = hasCycle();
if(res)
cout << "The graph has cycle." << endl;
else
cout << "The graph has no cycle." << endl;
}Output
The graph has cycle.
Updated on: 16-Jun-2020
7K+ Views
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