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Update object-graph example to add path finding between nodes using BFS 

+ Clean code, add overloaded functions and helper functions for common tasks
This commit is contained in:
Shaun Reed 2021-07-01 17:17:47 -04:00
parent 348586ec38
commit 4a8b607ff6
3 changed files with 199 additions and 40 deletions
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94
cpp/algorithms/graphs/object/graph.cpp
View File

@ -14,7 +14,7 @@
int main (const int argc, const char * argv[])
{
// We could initialize the graph with some localNodes...
std::map<int, std::vector<int>> localNodes{
std::vector<Node> localNodes{
{1, {2, 5}}, // Node 1
{2, {1, 6}}, // Node 2
{3, {4, 6, 7}},
@ -24,34 +24,50 @@ int main (const int argc, const char * argv[])
{7, {3, 4, 6, 8}},
{8, {4, 6}},
};
// Graph bfsGraph(localNodes);
Graph bfsGraphInit(localNodes);
std::cout << "\n\n##### Breadth First Search #####\n";
// Or we could use an initializer list...
// Initialize a example graph for Breadth First Search
Graph bfsGraph (
Graph bfsGraph(
{
{Node(1, {2, 5})}, // Node 1
{Node(2, {1, 6})}, // Node 2...
{Node(3, {4, 6, 7})},
{Node(4, {3, 7, 8})},
{Node(5, {1})},
{Node(6, {2, 3, 7})},
{Node(7, {3, 4, 6, 8})},
{Node(8, {4, 6})},
{1, {2, 5}}, // Node 1
{2, {1, 6}}, // Node 2...
{3, {4, 6, 7}},
{4, {3, 7, 8}},
{5, {1}},
{6, {2, 3, 7}},
{7, {3, 4, 6, 8}},
{8, {4, 6}},
}
);
// The graph traversed in this example is seen in MIT Intro to Algorithms
// + Chapter 22, Figure 22.3 on BFS
auto iter = bfsGraph.nodes_.begin();
std::advance(iter, 1);
bfsGraph.BFS(*iter);
bfsGraph.BFS(bfsGraph.GetNodeCopy(2));
Node test = bfsGraph.GetNodeCopy(3);
std::cout << "\nTesting finding a path between two nodes using BFS...\n";
// Test finding a path between two nodes using BFS
auto path = bfsGraph.PathBFS(
bfsGraph.GetNodeCopy(1), bfsGraph.GetNodeCopy(7)
);
// If we were returned an empty path, it doesn't exist
if (path.empty()) std::cout << "No valid path found!\n";
else {
// If we were returned a path, print it
std::cout << "\nValid path from " << path.front()->number
<< " to " << path.back()->number << ": ";
for (const auto &node : path) {
std::cout << node->number << " ";
}
std::cout << std::endl;
}
std::cout << "\n\n##### Depth First Search #####\n";
// Initialize an example graph for Depth First Search
Graph dfsGraph (
Graph dfsGraph(
{
{1, {2, 4}},
{2, {5}},
@ -68,7 +84,41 @@ int main (const int argc, const char * argv[])
std::cout << "\n\n##### Topological Sort #####\n";
// Initialize an example graph for Depth First Search
// + The order of initialization is important
// + To produce the same result as seen in the book
// ++ If the order is changed, other valid topological orders will be found
// The book starts on the 'shirt' node (with the number 6, in this example)
Graph topologicalGraph (
{
{1, {4, 5}}, // undershorts
{2, {5}}, // socks
{3, {}}, // watch
{4, {5, 7}}, // pants
{5, {}}, // shoes
{6, {8, 7}}, // shirt
{7, {9}}, // belt
{8, {9}}, // tie
{9, {}}, // jacket
}
);
// The graph traversed in this example is seen in MIT Intro to Algorithms
// + Chapter 22, Figure 22.4 on DFS
// Unlike the simple-graph example, this final result matches MIT Algorithms
// + Aside from the placement of the watch node, which is not connected
// + This is because the node is visited after all other nodes are finished
std::vector<Node> order =
topologicalGraph.TopologicalSort(topologicalGraph.GetNodeCopy(6));
std::cout << "\n\nTopological order: ";
while (!order.empty()) {
std::cout << order.back().number << " ";
order.pop_back();
}
std::cout << std::endl;
// If we want the topological order to match what is seen in the book
// + We have to initialize the graph carefully to get this result -
Graph topologicalGraph2 (
{
{6, {8, 7}}, // shirt
{8, {9}}, // tie
@ -81,15 +131,11 @@ int main (const int argc, const char * argv[])
{2, {5}}, // socks
}
);
// The graph traversed in this example is seen in MIT Intro to Algorithms
// + Chapter 22, Figure 22.4 on DFS
// Unlike the simple-graph example, this final result matches MIT Algorithms
std::vector<Node> order = topologicalGraph.TopologicalSort();
auto order2 = topologicalGraph2.TopologicalSort(*topologicalGraph2.NodeBegin());
std::cout << "\n\nTopological order: ";
while (!order.empty()) {
std::cout << order.back().number << " ";
order.pop_back();
while (!order2.empty()) {
std::cout << order2.back().number << " ";
order2.pop_back();
}
std::cout << std::endl;
}
}

87
cpp/algorithms/graphs/object/lib-graph.cpp
View File

@ -14,13 +14,19 @@ void Graph::BFS(const Node& startNode) const
{
// Track the nodes we have discovered
// TODO: Do this at the end to maintain the state instead of at beginning?
for (const auto &node : nodes_) node.color = White;
for (const auto &node : nodes_) {
node.color = White;
node.distance = 0;
node.predecessor = nullptr;
}
// Create a queue to visit discovered nodes in FIFO order
std::queue<Node> visitQueue;
// Mark the startNode as in progress until we finish checking adjacent nodes
startNode.color = Gray;
// startNode.distance = 0;
// startNode.predecessor = nullptr;
// Visit the startNode
visitQueue.push(startNode);
@ -34,18 +40,47 @@ void Graph::BFS(const Node& startNode) const
// Check if we have already discovered all the adjacentNodes to thisNode
for (const auto &adjacent : thisNode.adjacent) {
if (nodes_[adjacent - 1].color == White) {
if (GetNode(adjacent).color == White) {
std::cout << "Found undiscovered adjacentNode: " << adjacent << "\n";
// Mark the adjacent node as in progress
nodes_[adjacent - 1].color = Gray;
GetNode(adjacent).color = Gray;
GetNode(adjacent).distance = thisNode.distance + 1;
GetNode(adjacent).predecessor =
const_cast<Node *>(&GetNode(thisNode.number));
// Add the discovered node the the visitQueue
visitQueue.push(nodes_[adjacent - 1]);
visitQueue.push(GetNode(adjacent));
}
}
// We are finished with this node and the adjacent nodes; Mark it discovered
thisNode.color = Black;
GetNode(thisNode.number).color = Black;
}
}
std::deque<const Node *> Graph::PathBFS(const Node &start, const Node &finish) const
{
std::deque<const Node *> path;
BFS(start);
const Node * next = finish.predecessor;
bool isValid = false;
do {
// If we have reached the start node, we have found a valid path
if (*next == Node(start)) isValid = true;
// Add the node to the path as we check each node
path.push_front(next);
// Move to the next node
next = next->predecessor;
} while (next != nullptr);
path.push_back(new Node(finish));
// If we never found a valid path, erase all contents of the path
if (!isValid) path.erase(path.begin(), path.end());
// Return the path, the caller should handle empty paths accordingly
return path;
}
void Graph::DFS() const
@ -67,6 +102,42 @@ void Graph::DFS() const
}
void Graph::DFS(const Node &startNode) const
{
// Track the nodes we have discovered
for (const auto &node : nodes_) node.color = White;
int time = 0;
Node begin = startNode;
auto startIter = std::find(nodes_.begin(), nodes_.end(),
Node(startNode.number, {})
);
// Visit each node in the graph
while (startIter != nodes_.end()) {
std::cout << "Visiting node " << startIter->number << std::endl;
// If the startIter is undiscovered, visit it
if (startIter->color == White) {
std::cout << "Found undiscovered node: " << startIter->number << std::endl;
// Visiting the undiscovered node will check it's adjacent nodes
DFSVisit(time, *startIter);
}
startIter++;
}
startIter = nodes_.begin();
while (! (*startIter == startNode)) {
std::cout << "Visiting node " << startIter->number << std::endl;
// If the startIter is undiscovered, visit it
if (startIter->color == White) {
std::cout << "Found undiscovered node: " << startIter->number << std::endl;
// Visiting the undiscovered node will check it's adjacent nodes
DFSVisit(time, *startIter);
}
startIter++;
}
}
void Graph::DFSVisit(int &time, const Node& startNode) const
{
startNode.color = Gray;
@ -80,7 +151,7 @@ void Graph::DFSVisit(int &time, const Node& startNode) const
// + Offset by 1 to account for 0 index of discovered vector
if (iter->color == White) {
std::cout << "Found undiscovered adjacentNode: "
<< nodes_[adjacent - 1].number << std::endl;
<< GetNode(adjacent).number << std::endl;
// Visiting the undiscovered node will check it's adjacent nodes
DFSVisit(time, *iter);
}
@ -90,9 +161,9 @@ void Graph::DFSVisit(int &time, const Node& startNode) const
startNode.discoveryFinish.second = time;
}
std::vector<Node> Graph::TopologicalSort() const
std::vector<Node> Graph::TopologicalSort(const Node &startNode) const
{
DFS();
DFS(GetNode(startNode.number));
std::vector<Node> topological(nodes_);
std::sort(topological.begin(), topological.end(), Node::FinishedSort);

58
cpp/algorithms/graphs/object/lib-graph.hpp
View File

@ -18,16 +18,23 @@
#include <queue>
#include <unordered_set>
// Color represents the discovery status of any given node
// + White is undiscovered, Gray is in progress, Black is fully discovered
enum Color {White, Gray, Black};
/******************************************************************************/
// Node structure for representing a graph
struct Node {
public:
// Constructors
Node(const Node &rhs) = default;
Node & operator=(Node rhs) {
if (this == &rhs) return *this;
swap(*this, rhs);
return *this;
}
Node(int num, std::vector<int> adj) : number(num), adjacent(std::move(adj)) {}
friend void swap(Node &a, Node &b) {
std::swap(a.number, b.number);
std::swap(a.adjacent, b.adjacent);
@ -35,13 +42,23 @@ public:
std::swap(a.discoveryFinish, b.discoveryFinish);
}
Node(int num, std::vector<int> adj) :
number(num), adjacent(std::move(adj)) {}
// Don't allow anyone to change these values when using a const reference
int number;
std::vector<int> adjacent;
// Mutable so we can update the color of the nodes during traversal
// Mutable members so we can update these values when using a const reference
// + Since they need to be modified during traversals
// Coloring of the nodes are used in both DFS and BFS
mutable Color color = White;
// Create a pair to track discovery / finish time
// Used in BFS to represent distance from start node
mutable int distance = 0;
// Used in BFS to represent the parent node that discovered this node
// + If we use this node as the starting point, this will remain a nullptr
mutable Node *predecessor = nullptr;
// Create a pair to track discovery / finish time when using DFS
// + Discovery time is the iteration the node is first discovered
// + Finish time is the iteration the node has been checked completely
// ++ A finished node has considered all adjacent nodes
@ -51,21 +68,46 @@ public:
// + This will help to sort nodes by finished time after traversal
static bool FinishedSort(const Node &node1, const Node &node2)
{ return node1.discoveryFinish.second < node2.discoveryFinish.second;}
// Define operator== for std::find
bool operator==(const Node &b) const { return this->number == b.number;}
};
/******************************************************************************/
// Graph class declaration
class Graph {
public:
// Constructor
explicit Graph(std::vector<Node> nodes) : nodes_(std::move(nodes)) {}
std::vector<Node> nodes_;
// Breadth First Search
void BFS(const Node& startNode) const;
std::deque<const Node *> PathBFS(const Node &start, const Node &finish) const;
// Depth First Search
void DFS() const;
void DFS(const Node &startNode) const;
void DFSVisit(int &time, const Node& startNode) const;
std::vector<Node> TopologicalSort() const;
// Topological sort, using DFS
std::vector<Node> TopologicalSort(const Node &startNode) const;
// Returns a copy of a node with the number i within the graph
inline Node GetNodeCopy(int i) { return GetNode(i);}
// Return a constant iterator for reading node values
inline std::vector<Node>::const_iterator NodeBegin() { return nodes_.begin();}
private:
// A non-const accessor for direct access to a node with the number value i
inline Node & GetNode(int i)
{ return *std::find(nodes_.begin(), nodes_.end(), Node(i, {}));}
// For use with const member functions to access mutable values
inline const Node & GetNode(int i) const
{ return *std::find(nodes_.begin(), nodes_.end(), Node(i, {}));}
std::vector<Node> nodes_;
};
#endif // LIB_GRAPH_HPP