```
/**
* @file cycle_check_directed graph.cpp
*
* @brief BFS and DFS algorithms to check for cycle in a directed graph.
*
* @author [Anmol3299](mailto:mittalanmol22@gmail.com)
*
*/
#include <iostream> // for std::cout
#include <map> // for std::map
#include <queue> // for std::queue
#include <stdexcept> // for throwing errors
#include <type_traits> // for std::remove_reference
#include <utility> // for std::move
#include <vector> // for std::vector
/**
* Implementation of non-weighted directed edge of a graph.
*
* The source vertex of the edge is labelled "src" and destination vertex is
* labelled "dest".
*/
struct Edge {
unsigned int src;
unsigned int dest;
Edge() = delete;
~Edge() = default;
Edge(Edge&&) = default;
Edge& operator=(Edge&&) = default;
Edge(Edge const&) = default;
Edge& operator=(Edge const&) = default;
/** Set the source and destination of the vertex.
*
* @param source is the source vertex of the edge.
* @param destination is the destination vertex of the edge.
*/
Edge(unsigned int source, unsigned int destination)
: src(source), dest(destination) {}
};
using AdjList = std::map<unsigned int, std::vector<unsigned int>>;
/**
* Implementation of graph class.
*
* The graph will be represented using Adjacency List representation.
* This class contains 2 data members "m_vertices" & "m_adjList" used to
* represent the number of vertices and adjacency list of the graph
* respectively. The vertices are labelled 0 - (m_vertices - 1).
*/
class Graph {
public:
Graph() : m_adjList({}) {}
~Graph() = default;
Graph(Graph&&) = default;
Graph& operator=(Graph&&) = default;
Graph(Graph const&) = default;
Graph& operator=(Graph const&) = default;
/** Create a graph from vertices and adjacency list.
*
* @param vertices specify the number of vertices the graph would contain.
* @param adjList is the adjacency list representation of graph.
*/
Graph(unsigned int vertices, AdjList adjList)
: m_vertices(vertices), m_adjList(std::move(adjList)) {}
/** Create a graph from vertices and adjacency list.
*
* @param vertices specify the number of vertices the graph would contain.
* @param adjList is the adjacency list representation of graph.
*/
Graph(unsigned int vertices, AdjList&& adjList)
: m_vertices(vertices), m_adjList(std::move(adjList)) {}
/** Create a graph from vertices and a set of edges.
*
* Adjacency list of the graph would be created from the set of edges. If
* the source or destination of any edge has a value greater or equal to
* number of vertices, then it would throw a range_error.
*
* @param vertices specify the number of vertices the graph would contain.
* @param edges is a vector of edges.
*/
Graph(unsigned int vertices, std::vector<Edge> const& edges)
: m_vertices(vertices) {
for (auto const& edge : edges) {
if (edge.src >= vertices || edge.dest >= vertices) {
throw std::range_error(
"Either src or dest of edge out of range");
}
m_adjList[edge.src].emplace_back(edge.dest);
}
}
/** Return a const reference of the adjacency list.
*
* @return const reference to the adjacency list
*/
std::remove_reference<AdjList>::type const& getAdjList() const {
return m_adjList;
}
/**
* @return number of vertices in the graph.
*/
unsigned int getVertices() const { return m_vertices; }
/** Add vertices in the graph.
*
* @param num is the number of vertices to be added. It adds 1 vertex by
* default.
*
*/
void addVertices(unsigned int num = 1) { m_vertices += num; }
/** Add an edge in the graph.
*
* @param edge that needs to be added.
*/
void addEdge(Edge const& edge) {
if (edge.src >= m_vertices || edge.dest >= m_vertices) {
throw std::range_error("Either src or dest of edge out of range");
}
m_adjList[edge.src].emplace_back(edge.dest);
}
/** Add an Edge in the graph
*
* @param source is source vertex of the edge.
* @param destination is the destination vertex of the edge.
*/
void addEdge(unsigned int source, unsigned int destination) {
if (source >= m_vertices || destination >= m_vertices) {
throw std::range_error(
"Either source or destination of edge out of range");
}
m_adjList[source].emplace_back(destination);
}
private:
unsigned int m_vertices = 0;
AdjList m_adjList;
};
/**
* Check if a directed graph has a cycle or not.
*
* This class provides 2 methods to check for cycle in a directed graph:
* isCyclicDFS & isCyclicBFS.
*
* - isCyclicDFS uses DFS traversal method to check for cycle in a graph.
* - isCyclidBFS used BFS traversal method to check for cycle in a graph.
*/
class CycleCheck {
private:
enum nodeStates : uint8_t { not_visited = 0, in_stack, visited };
/** Helper function of "isCyclicDFS".
*
* @param adjList is the adjacency list representation of some graph.
* @param state is the state of the nodes of the graph.
* @param node is the node being evaluated.
*
* @return true if graph has a cycle, else false.
*/
static bool isCyclicDFSHelper(AdjList const& adjList,
std::vector<nodeStates>* state,
unsigned int node) {
// Add node "in_stack" state.
(*state)[node] = in_stack;
// If the node has children, then recursively visit all children of the
// node.
auto const it = adjList.find(node);
if (it != adjList.end()) {
for (auto child : it->second) {
// If state of child node is "not_visited", evaluate that child
// for presence of cycle.
auto state_of_child = (*state)[child];
if (state_of_child == not_visited) {
if (isCyclicDFSHelper(adjList, state, child)) {
return true;
}
} else if (state_of_child == in_stack) {
// If child node was "in_stack", then that means that there
// is a cycle in the graph. Return true for presence of the
// cycle.
return true;
}
}
}
// Current node has been evaluated for the presence of cycle and had no
// cycle. Mark current node as "visited".
(*state)[node] = visited;
// Return that current node didn't result in any cycles.
return false;
}
public:
/** Driver function to check if a graph has a cycle.
*
* This function uses DFS to check for cycle in the graph.
*
* @param graph which needs to be evaluated for the presence of cycle.
* @return true if a cycle is detected, else false.
*/
static bool isCyclicDFS(Graph const& graph) {
auto vertices = graph.getVertices();
/** State of the node.
*
* It is a vector of "nodeStates" which represents the state node is in.
* It can take only 3 values: "not_visited", "in_stack", and "visited".
*
* Initially, all nodes are in "not_visited" state.
*/
std::vector<nodeStates> state(vertices, not_visited);
// Start visiting each node.
for (unsigned int node = 0; node < vertices; node++) {
// If a node is not visited, only then check for presence of cycle.
// There is no need to check for presence of cycle for a visited
// node as it has already been checked for presence of cycle.
if (state[node] == not_visited) {
// Check for cycle.
if (isCyclicDFSHelper(graph.getAdjList(), &state, node)) {
return true;
}
}
}
// All nodes have been safely traversed, that means there is no cycle in
// the graph. Return false.
return false;
}
/** Check if a graph has cycle or not.
*
* This function uses BFS to check if a graph is cyclic or not.
*
* @param graph which needs to be evaluated for the presence of cycle.
* @return true if a cycle is detected, else false.
*/
static bool isCyclicBFS(Graph const& graph) {
auto graphAjdList = graph.getAdjList();
auto vertices = graph.getVertices();
std::vector<unsigned int> indegree(vertices, 0);
// Calculate the indegree i.e. the number of incident edges to the node.
for (auto const& list : graphAjdList) {
auto children = list.second;
for (auto const& child : children) {
indegree[child]++;
}
}
std::queue<unsigned int> can_be_solved;
for (unsigned int node = 0; node < vertices; node++) {
// If a node doesn't have any input edges, then that node will
// definately not result in a cycle and can be visited safely.
if (!indegree[node]) {
can_be_solved.emplace(node);
}
}
// Vertices that need to be traversed.
auto remain = vertices;
// While there are safe nodes that we can visit.
while (!can_be_solved.empty()) {
auto solved = can_be_solved.front();
// Visit the node.
can_be_solved.pop();
// Decrease number of nodes that need to be traversed.
remain--;
// Visit all the children of the visited node.
auto it = graphAjdList.find(solved);
if (it != graphAjdList.end()) {
for (auto child : it->second) {
// Check if we can visited the node safely.
if (--indegree[child] == 0) {
// if node can be visited safely, then add that node to
// the visit queue.
can_be_solved.emplace(child);
}
}
}
}
// If there are still nodes that we can't visit, then it means that
// there is a cycle and return true, else return false.
return !(remain == 0);
}
};
/**
* Main function.
*/
int main() {
// Instantiate the graph.
Graph g(7, std::vector<Edge>{{0, 1}, {1, 2}, {2, 0}, {2, 5}, {3, 5}});
// Check for cycle using BFS method.
std::cout << CycleCheck::isCyclicBFS(g) << '\n';
// Check for cycle using DFS method.
std::cout << CycleCheck::isCyclicDFS(g) << '\n';
return 0;
}
```