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[cpp] Update weighted graph 

+ totalWeight is now tracked for BFS & DFS traversals
+ Refactor graph search info structs
This commit is contained in:
Shaun Reed 2022-04-14 14:20:59 -04:00
parent 4b47630548
commit ca11b7b58c
5 changed files with 105 additions and 92 deletions
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14
cpp/algorithms/graphs/object/lib-graph.hpp
View File

@ -63,8 +63,8 @@ enum Color {
Black
};
// Information used in all searches
struct SearchInfo {
// Information used in all searches tracked for each node
struct NodeInfo {
// Coloring of the nodes is used in both DFS and BFS
Color discovered = White;
};
@ -73,8 +73,8 @@ struct SearchInfo {
/******************************************************************************/
// BFS search information struct
// Information that is only used in BFS
struct BFS : SearchInfo {
// Node information that is only used in BFS
struct BFS : NodeInfo {
// Used to represent distance from start node
int distance = 0;
// Used to represent the parent node that discovered this node
@ -90,8 +90,8 @@ using InfoBFS = std::unordered_map<int, struct BFS>;
/******************************************************************************/
// DFS search information struct
// Information that is only used in DFS
struct DFS : SearchInfo {
// Node information that is only used in DFS
struct DFS : NodeInfo {
// Create a pair to track discovery / finish time
// + Discovery time is the iteration the node is first discovered
// + Finish time is the iteration the node has been checked completely
@ -119,7 +119,7 @@ public:
// An alternate DFS that checks each node of the graph beginning at startNode
InfoDFS DFS(const Node &startNode) const;
// Visit function is used in both versions of DFS
void DFSVisit(int &time, const Node& startNode, InfoDFS &searchInfo) const;
void DFSVisit(int &time, const Node& startNode, InfoDFS &dfs) const;
// Topological sort, using DFS
std::vector<Node> TopologicalSort(const Node &startNode) const;

14
cpp/algorithms/graphs/templated/lib-graph.hpp
View File

@ -79,8 +79,8 @@ enum Color {
Black
};
// Information used in all searches
struct SearchInfo {
// Information used in all searches tracked for each node
struct NodeInfo {
// Coloring of the nodes is used in both DFS and BFS
Color discovered = White;
};
@ -89,9 +89,9 @@ struct SearchInfo {
/******************************************************************************/
// BFS search information struct
// Information that is only used in BFS
// Node information that is only used in BFS
template <typename T>
struct BFS : SearchInfo {
struct BFS : NodeInfo {
// Used to represent distance from start node
int distance = 0;
// Used to represent the parent node that discovered this node
@ -107,8 +107,8 @@ template <typename T> using InfoBFS = std::unordered_map<T, struct BFS<T>>;
/******************************************************************************/
// DFS search information struct
// Information that is only used in DFS
struct DFS : SearchInfo {
// Node information that is only used in DFS
struct DFS : NodeInfo {
// Create a pair to track discovery / finish time
// + Discovery time is the iteration the node is first discovered
// + Finish time is the iteration the node has been checked completely
@ -125,7 +125,7 @@ template <typename T> using InfoDFS = std::unordered_map<T, struct DFS>;
// Edges stored as multimap<weight, pair<nodeA.data_, nodeB.data_>>
template <typename T> using Edges = std::multimap<int, std::pair<T, T>>;
struct MST : SearchInfo {
struct MST : NodeInfo {
int32_t parent = INT32_MIN;
int rank = 0;
};

12
cpp/algorithms/graphs/weighted/graph.cpp
View File

@ -156,11 +156,19 @@ int main (const int argc, const char * argv[])
{9, {{3, 2}, {7, 6}}}
}
);
std::cout << "\nChecking weight traversing graph from node 1 using DFS...\n";
InfoDFS resultDFS = graphMST.DFS(graphMST.GetNodeCopy(1));
std::cout << "DFS total weight traversed: " << resultDFS.totalWeight << std::endl;
std::cout << "\nChecking weight traversing graph from node 1 using BFS...\n";
InfoBFS resultBFS = graphMST.BFS(graphMST.GetNodeCopy(1));
std::cout << "BFS total weight traversed: " << resultBFS.totalWeight << std::endl;
InfoMST resultMST = graphMST.KruskalMST();
std::cout << "Finding MST using Kruskal's...\n\nMST result: \n";
std::cout << "\n\nFinding MST using Kruskal's...\n\nMST result: \n";
for (const auto &edge : resultMST.edgesMST) {
std::cout << "Connected nodes: " << edge.second.first << "->"
<< edge.second.second << " with weight of " << edge.first << "\n";
}
std::cout << "Total MST weight: " << resultMST.weightMST << std::endl;
std::cout << "Total MST weight: " << resultMST.totalWeight << std::endl;
}

100
cpp/algorithms/graphs/weighted/lib-graph.cpp
View File

@ -14,13 +14,13 @@
InfoBFS Graph::BFS(const Node& startNode) const
{
// Create local object to track the information gathered during traversal
InfoBFS searchInfo;
InfoBFS bfs;
// Create a queue to visit discovered nodes in FIFO order
std::queue<const Node *> visitQueue;
// Mark the startNode as in progress until we finish checking adjacent nodes
searchInfo[startNode.number].discovered = Gray;
bfs.nodeInfo[startNode.number].discovered = Gray;
// Visit the startNode
visitQueue.push(&startNode);
@ -31,17 +31,17 @@ InfoBFS Graph::BFS(const Node& startNode) const
const Node * thisNode = visitQueue.front();
visitQueue.pop();
std::cout << "Visiting node " << thisNode->number << std::endl;
// Check if we have already discovered all the adjacentNodes to thisNode
for (const auto &adjacent : thisNode->adjacent) {
if (searchInfo[adjacent.first].discovered == White) {
if (bfs.nodeInfo[adjacent.first].discovered == White) {
std::cout << "Found undiscovered adjacentNode: " << adjacent.first
<< "\n";
bfs.totalWeight += adjacent.second;
// Mark the adjacent node as in progress
searchInfo[adjacent.first].discovered = Gray;
searchInfo[adjacent.first].distance =
searchInfo[thisNode->number].distance + 1;
searchInfo[adjacent.first].predecessor =
bfs.nodeInfo[adjacent.first].discovered = Gray;
bfs.nodeInfo[adjacent.first].distance =
bfs.nodeInfo[thisNode->number].distance + 1;
bfs.nodeInfo[adjacent.first].predecessor =
&GetNode(thisNode->number);
// Add the discovered node the the visitQueue
@ -49,11 +49,11 @@ InfoBFS Graph::BFS(const Node& startNode) const
}
}
// We are finished with this node and the adjacent nodes; Mark it discovered
searchInfo[thisNode->number].discovered = Black;
bfs.nodeInfo[thisNode->number].discovered = Black;
}
// Return the information gathered from this search, JIC caller needs it
return searchInfo;
return bfs;
}
std::deque<Node> Graph::PathBFS(const Node &start, const Node &finish) const
@ -62,8 +62,8 @@ std::deque<Node> Graph::PathBFS(const Node &start, const Node &finish) const
// + If the caller modifies these, it will not impact the graph's data
std::deque<Node> path;
InfoBFS searchInfo = BFS(start);
const Node * next = searchInfo[finish.number].predecessor;
InfoBFS bfs = BFS(start);
const Node * next = bfs.nodeInfo[finish.number].predecessor;
bool isValid = false;
do {
// If we have reached the start node, we have found a valid path
@ -74,7 +74,7 @@ std::deque<Node> Graph::PathBFS(const Node &start, const Node &finish) const
path.emplace_front(*next);
// Move to the next node
next = searchInfo[next->number].predecessor;
next = bfs.nodeInfo[next->number].predecessor;
} while (next != nullptr);
// Use emplace_back to call Node copy constructor
path.emplace_back(finish);
@ -89,85 +89,83 @@ std::deque<Node> Graph::PathBFS(const Node &start, const Node &finish) const
InfoDFS Graph::DFS() const
{
// Track the nodes we have discovered
InfoDFS searchInfo;
InfoDFS dfs;
int time = 0;
// Visit each node in the graph
for (const auto& node : nodes_) {
for (const auto & node : nodes_) {
std::cout << "Visiting node " << node.number << std::endl;
// If the node is undiscovered, visit it
if (searchInfo[node.number].discovered == White) {
if (dfs.nodeInfo[node.number].discovered == White) {
std::cout << "Found undiscovered node: " << node.number << std::endl;
// Visiting the undiscovered node will check it's adjacent nodes
DFSVisit(time, node, searchInfo);
DFSVisit(time, node, dfs);
}
}
return searchInfo;
return dfs;
}
InfoDFS Graph::DFS(const Node &startNode) const
{
// Track the nodes we have discovered
InfoDFS searchInfo;
InfoDFS dfs;
int time = 0;
auto startIter = std::find(nodes_.begin(), nodes_.end(),
Node(startNode.number, {})
);
auto startIter =
std::find(nodes_.begin(), nodes_.end(), Node(startNode.number, { }));
// beginning at startNode, visit each node in the graph until we reach the end
while (startIter != nodes_.end()) {
std::cout << "Visiting node " << startIter->number << std::endl;
// If the startIter is undiscovered, visit it
if (searchInfo[startIter->number].discovered == White) {
std::cout << "Found undiscovered node: " << startIter->number << std::endl;
if (dfs.nodeInfo[startIter->number].discovered == White) {
std::cout << "Found undiscovered node: " << startIter->number
<< std::endl;
// Visiting the undiscovered node will check it's adjacent nodes
DFSVisit(time, *startIter, searchInfo);
DFSVisit(time, *startIter, dfs);
}
startIter++;
}
// Once we reach the last node, check the beginning for unchecked nodes
startIter = nodes_.begin();
// Once we reach the initial startNode, we have checked all nodes
while (*startIter != startNode) {
std::cout << "Visiting node " << startIter->number << std::endl;
// If the startIter is undiscovered, visit it
if (searchInfo[startIter->number].discovered == White) {
if (dfs.nodeInfo[startIter->number].discovered == White) {
std::cout << "Found undiscovered node: " << startIter->number << std::endl;
// Visiting the undiscovered node will check it's adjacent nodes
DFSVisit(time, *startIter, searchInfo);
DFSVisit(time, *startIter, dfs);
}
startIter++;
}
return searchInfo;
return dfs;
}
void Graph::DFSVisit(int &time, const Node& startNode, InfoDFS &searchInfo) const
void Graph::DFSVisit(int &time, const Node& startNode, InfoDFS &dfs) const
{
searchInfo[startNode.number].discovered = Gray;
dfs.nodeInfo[startNode.number].discovered = Gray;
time++;
searchInfo[startNode.number].discoveryFinish.first = time;
dfs.nodeInfo[startNode.number].discoveryFinish.first = time;
// Check the adjacent nodes of the startNode
for (const auto &adjacent : startNode.adjacent) {
auto iter = std::find(nodes_.begin(), nodes_.end(),
Node(adjacent.first, {}));
for (const auto & adjacent : startNode.adjacent) {
const auto node = GetNode(adjacent.first);
// If the adjacentNode is undiscovered, visit it
// + Offset by 1 to account for 0 index of discovered vector
if (searchInfo[iter->number].discovered == White) {
std::cout << "Found undiscovered adjacentNode: "
<< GetNode(adjacent.first).number << std::endl;
if (dfs.nodeInfo[node.number].discovered == White) {
std::cout << "Found undiscovered adjacentNode: " << adjacent.first
<< " with weight of " << adjacent.second << std::endl;
// Visiting the undiscovered node will check it's adjacent nodes
DFSVisit(time, *iter, searchInfo);
dfs.totalWeight += adjacent.second;
DFSVisit(time, node, dfs);
}
}
searchInfo[startNode.number].discovered = Black;
dfs.nodeInfo[startNode.number].discovered = Black;
time++;
searchInfo[startNode.number].discoveryFinish.second = time;
dfs.nodeInfo[startNode.number].discoveryFinish.second = time;
}
std::vector<Node> Graph::TopologicalSort(const Node &startNode) const
@ -177,8 +175,8 @@ std::vector<Node> Graph::TopologicalSort(const Node &startNode) const
std::vector<Node> order(nodes_);
auto comp = [&topological](const Node &a, const Node &b) {
return (topological[a.number].discoveryFinish.second <
topological[b.number].discoveryFinish.second);
return (topological.nodeInfo[a.number].discoveryFinish.second <
topological.nodeInfo[b.number].discoveryFinish.second);
};
std::sort(order.begin(), order.end(), comp);
@ -190,26 +188,26 @@ std::vector<Node> Graph::TopologicalSort(const Node &startNode) const
InfoMST Graph::KruskalMST() const
{
InfoMST searchInfo(nodes_);
InfoMST mst(nodes_);
// The ctor for InfoMST initializes all edges within the graph into a multimap
// + Key for multimap is edge weight, so they're already sorted in ascending
// For each edge in the graph, check if they are part of the same tree
// + Since we do not want to create a cycle in the MST forest -
// + we don't connect nodes that are part of the same tree
for (const auto &edge : searchInfo.edges) {
for (const auto &edge : mst.edges) {
// Two integers representing the node.number for the connected nodes
const int u = edge.second.first;
const int v = edge.second.second;
// Check if the nodes are of the same tree
if (searchInfo.FindSet(u) != searchInfo.FindSet(v)) {
if (mst.FindSet(u) != mst.FindSet(v)) {
// If they are not, add the edge to our MST
searchInfo.edgesMST.emplace(edge);
searchInfo.weightMST += edge.first;
mst.edgesMST.emplace(edge);
mst.totalWeight += edge.first;
// Update the forest to reflect this change
searchInfo.Union(u, v);
mst.Union(u, v);
}
}
return searchInfo;
return mst;
}

57
cpp/algorithms/graphs/weighted/lib-graph.hpp
View File

@ -69,18 +69,29 @@ enum Color {
Black
};
// Information used in all searches
struct SearchInfo {
// Information used in all searches tracked for each node
struct NodeInfo {
// Coloring of the nodes is used in both DFS and BFS
Color discovered = White;
};
// Template for tracking graph information gathered during traversals
// + Used for DFS, BFS, and MST
template <typename T>
struct GraphInfo {
// Store search information in unordered_maps so we can pass it around easily
// + Allows each node to store relative information on the traversal
std::unordered_map<int, T> nodeInfo;
// Track total weight for all traversals
int totalWeight = 0;
};
/******************************************************************************/
// BFS search information struct
// Information that is only used in BFS
struct BFS : SearchInfo {
// Node search information that is only used in BFS
struct BFS : NodeInfo {
// Used to represent distance from start node
int distance = 0;
// Used to represent the parent node that discovered this node
@ -88,16 +99,14 @@ struct BFS : SearchInfo {
const Node *predecessor = nullptr;
};
// Store search information in unordered_maps so we can pass it around easily
// + Allows each node to store relative information on the traversal
using InfoBFS = std::unordered_map<int, struct BFS>;
struct InfoBFS : GraphInfo<BFS> {/* Members inherited from GraphInfo */};
/******************************************************************************/
// DFS search information struct
// Information that is only used in DFS
struct DFS : SearchInfo {
struct DFS : NodeInfo {
// Create a pair to track discovery / finish time
// + Discovery time is the iteration the node is first discovered
// + Finish time is the iteration the node has been checked completely
@ -105,18 +114,19 @@ struct DFS : SearchInfo {
std::pair<int, int> discoveryFinish;
};
struct InfoDFS : GraphInfo<DFS> {/* Members inherited from GraphInfo */};
/******************************************************************************/
// MST search information struct
struct MST : SearchInfo {
struct MST : NodeInfo {
int32_t parent = INT32_MIN;
int rank = 0;
};
using InfoDFS = std::unordered_map<int, struct DFS>;
using Edges = std::multimap<int, std::pair<int, int>>;
struct InfoMST {
struct InfoMST : GraphInfo<MST>{
explicit InfoMST(const std::vector<Node> &nodes)
{
for (const auto &node : nodes) {
@ -134,20 +144,17 @@ struct InfoMST {
}
}
std::unordered_map<int, struct MST> searchInfo;
// All of the edges within our graph
// + Since each node stores its own edges, this is initialized in InfoMST ctor
Edges edges;
// A multimap of the edges found for our MST
Edges edgesMST;
// The total weight of our resulting MST
int weightMST = 0;
void MakeSet(int x)
{
searchInfo[x].parent = x;
searchInfo[x].rank = 0;
nodeInfo[x].parent = x;
nodeInfo[x].rank = 0;
}
void Union(int x, int y)
@ -157,23 +164,23 @@ struct InfoMST {
void Link(int x, int y)
{
if (searchInfo[x].rank > searchInfo[y].rank) {
searchInfo[y].parent = x;
if (nodeInfo[x].rank > nodeInfo[y].rank) {
nodeInfo[y].parent = x;
}
else {
searchInfo[x].parent = y;
if (searchInfo[x].rank == searchInfo[y].rank) {
searchInfo[y].rank += 1;
nodeInfo[x].parent = y;
if (nodeInfo[x].rank == nodeInfo[y].rank) {
nodeInfo[y].rank += 1;
}
}
}
int FindSet(int x)
{
if (x != searchInfo[x].parent) {
searchInfo[x].parent = FindSet(searchInfo[x].parent);
if (x != nodeInfo[x].parent) {
nodeInfo[x].parent = FindSet(nodeInfo[x].parent);
}
return searchInfo[x].parent;
return nodeInfo[x].parent;
}
};
@ -195,7 +202,7 @@ public:
// An alternate DFS that checks each node of the graph beginning at startNode
InfoDFS DFS(const Node &startNode) const;
// Visit function is used in both versions of DFS
void DFSVisit(int &time, const Node& startNode, InfoDFS &searchInfo) const;
void DFSVisit(int &time, const Node& startNode, InfoDFS &dfs) const;
// Topological sort, using DFS
std::vector<Node> TopologicalSort(const Node &startNode) const;
// Kruskal's MST