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Add example of finding MST using Kruskal's algorithm

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+ Using example graph and pseudocode from MIT Algorithms
This commit is contained in:
Shaun Reed
2021-07-16 18:16:04 -04:00
parent 835dbc7f7d
commit 23c4f0e491
4 changed files with 176 additions and 58 deletions
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42
cpp/algorithms/graphs/weighted/lib-graph.cpp
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@@ -33,18 +33,18 @@ InfoBFS Graph::BFS(const Node& startNode) const
// Check if we have already discovered all the adjacentNodes to thisNode
for (const auto &adjacent : thisNode->adjacent) {
if (searchInfo[adjacent.GetNumber()].discovered == White) {
std::cout << "Found undiscovered adjacentNode: " << adjacent.GetNumber()
if (searchInfo[adjacent.first].discovered == White) {
std::cout << "Found undiscovered adjacentNode: " << adjacent.first
<< "\n";
// Mark the adjacent node as in progress
searchInfo[adjacent.GetNumber()].discovered = Gray;
searchInfo[adjacent.GetNumber()].distance =
searchInfo[adjacent.first].discovered = Gray;
searchInfo[adjacent.first].distance =
searchInfo[thisNode->number].distance + 1;
searchInfo[adjacent.GetNumber()].predecessor =
searchInfo[adjacent.first].predecessor =
&GetNode(thisNode->number);
// Add the discovered node the the visitQueue
visitQueue.push(&GetNode(adjacent.GetNumber()));
visitQueue.push(&GetNode(adjacent.first));
}
}
// We are finished with this node and the adjacent nodes; Mark it discovered
@@ -154,12 +154,12 @@ void Graph::DFSVisit(int &time, const Node& startNode, InfoDFS &searchInfo) cons
// Check the adjacent nodes of the startNode
for (const auto &adjacent : startNode.adjacent) {
auto iter = std::find(nodes_.begin(), nodes_.end(),
Node(adjacent.GetNumber(), {}));
Node(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.GetNumber()).number << std::endl;
<< GetNode(adjacent.first).number << std::endl;
// Visiting the undiscovered node will check it's adjacent nodes
DFSVisit(time, *iter, searchInfo);
}
@@ -187,3 +187,29 @@ std::vector<Node> Graph::TopologicalSort(const Node &startNode) const
return order;
}
InfoMST Graph::KruskalMST() const
{
InfoMST searchInfo(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) {
// 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 they are not, add the edge to our MST
searchInfo.edgesMST.emplace(edge);
searchInfo.weightMST += edge.first;
// Update the forest to reflect this change
searchInfo.Union(u, v);
}
}
return searchInfo;
}