Merge pull request deutranium#249 from etzl/welshpowell

add c++ implementation of welsh powell algorithm

Author: codelixir

graphColoringAlgo/welshPowellAlgo/welshPowellAlgo.cpp

@@ -0,0 +1,108 @@
+#include <iostream>
+#include <vector>
+#include <algorithm>
+#include <list>
+#include <unordered_set>
+
+
+struct Vertex {
+    char id; // An upper-case character representing the node label
+    int degree;
+    std::vector<char> adj; // a list of all the adjacent nodes: with their letters
+    int label; // *color*
+
+    /** Add edge to undirected graph
+     * \param node Another node to connect to
+     * \return Void
+     */
+    void addEdge(Vertex& node)
+    {
+        adj.push_back(node.id);
+        degree++;
+
+        node.adj.push_back(id);
+        node.degree++;
+    }
+
+    /** Check whether current vertex is connected to the target vertex
+     * \param target Vertex to check against
+     * \return True if they're connected, false otherwise
+     */
+    bool isConnected(const Vertex& target)
+    {
+        return std::find(adj.begin(), adj.end(), target.id) != adj.end();
+    }
+};
+
+struct Graph {
+    // adding/deleting elements is more efficient
+    std::list<Vertex> vertices;
+
+    void addVertex(Vertex node)
+    {
+        vertices.push_back(node);
+    }
+    void addVertex(Vertex&& node)
+    {
+        vertices.push_back(node);
+    }
+};
+
+void welshPowell(Graph& graph)
+{
+    // sort vertices in descending order
+    graph.vertices.sort([](const Vertex& a, const Vertex& b) -> bool {
+        return a.degree > b.degree;
+    });
+
+    std::list<Vertex*> unlabeledVertices;
+    for (auto& vertex: graph.vertices) {
+        unlabeledVertices.push_back(&vertex);
+    }
+
+    int label = 1;
+    for (auto iter = unlabeledVertices.begin(); iter != unlabeledVertices.end(); ++label) {
+        (*iter)->label = label;
+
+        /** a set of all vertices with the same color, all operations has a
+         * constant time of O(1) on average
+         */
+        std::unordered_set<Vertex*> currentLabelVertices;
+        currentLabelVertices.insert(*iter);
+
+        // check if we can label any other vertex with the current color
+        auto nestedIter = iter; nestedIter++;
+        for (; nestedIter != unlabeledVertices.end(); ) {
+            // checking current vertex against any other colored vertex
+            if (std::none_of(currentLabelVertices.begin(), currentLabelVertices.end(),
+                [=](const Vertex* v){ return (*nestedIter)->isConnected(*v); })) {
+                (*nestedIter)->label = label;
+                currentLabelVertices.insert(*nestedIter);
+
+                nestedIter = unlabeledVertices.erase(nestedIter);
+            }
+            else {
+                nestedIter++;
+            }
+        }
+
+        iter = unlabeledVertices.erase(iter);
+    }
+}
+
+int main()
+{
+    Graph graph {{
+        {'A', 3, {'B', 'C', 'D'}},
+        {'B', 2, {'A', 'D'}},
+        {'C', 2, {'A', 'D'}},
+        {'D', 3, {'A', 'B', 'C'}}
+    }};
+
+    welshPowell(graph);
+
+    for (const auto& v: graph.vertices) {
+        std::cout << v.id << "-->" << v.label << '\n';
+    }
+    return 0;
+}