Adds deterministic version for boruvka and dijkstra algorithm. (#398)

* Adds deterministic version for boruvka and dijkstra algorithm.

* Add unit tests for deterministic boruvka and dijkstra.

---------

Co-authored-by: FSB <f.brezna@era.aero>

Author: fajlip

include/CXXGraph/Graph/Algorithm/Boruvka_impl.hpp

@@ -123,5 +123,104 @@ const MstResult Graph<T>::boruvka() const {
   return result;
 }
 
+template <typename T>
+const MstResult Graph<T>::boruvka_deterministic() const {
+  MstResult result;
+  result.success = false;
+  result.errorMessage = "";
+  result.mstCost = INF_DOUBLE;
+  if (!isUndirectedGraph()) {
+    result.errorMessage = ERR_DIR_GRAPH;
+    return result;
+  }
+  const auto nodeSet = Graph<T>::getNodeSet();
+  const auto n = nodeSet.size();
+
+  // Use std map for storing n subsets.
+  auto subsets = make_shared<std::unordered_map<CXXGraph::id_t, Subset>>();
+
+  // Initially there are n different trees.
+  // Finally there will be one tree that will be MST
+  auto numTrees = n;
+
+  // check if all edges are weighted and store the weights
+  // in a map whose keys are the edge ids and values are the edge weights
+  const auto edgeSet = Graph<T>::getEdgeSet();
+  std::unordered_map<CXXGraph::id_t, double> edgeWeight;
+  for (const auto &edge : edgeSet) {
+    if (edge->isWeighted().has_value() && edge->isWeighted().value())
+      edgeWeight[edge->getId()] =
+          (std::dynamic_pointer_cast<const Weighted>(edge))->getWeight();
+    else {
+      // No Weighted Edge
+      result.errorMessage = ERR_NO_WEIGHTED_EDGE;
+      return result;
+    }
+  }
+
+  for (const auto &node : nodeSet) {
+    Subset set{node->getId(), 0};
+    (*subsets)[node->getId()] = set;
+  }
+
+  result.mstCost = 0;  // we will store the cost here
+  // exit when only 1 tree i.e. mst
+  while (numTrees > 1) {
+    // Everytime initialize cheapest map
+    // It stores index of the cheapest edge of subset.
+    std::unordered_map<CXXGraph::id_t, CXXGraph::id_t> cheapest;
+    for (const auto &node : nodeSet) cheapest[node->getId()] = INT_MAX;
+
+    // Traverse through all edges and update
+    // cheapest of every component
+    for (const auto &edge : edgeSet) {
+      auto elem = edge->getNodePair();
+      auto edgeId = edge->getId();
+      // Find sets of two corners of current edge
+      auto set1 = Graph<T>::setFind(subsets, elem.first->getId());
+      auto set2 = Graph<T>::setFind(subsets, elem.second->getId());
+
+      // If two corners of current edge belong to
+      // same set, ignore current edge
+      if (set1 == set2) continue;
+
+      // Else check if current edge is closer to previous
+      // cheapest edges of set1 and set2
+      if (cheapest[set1] == INT_MAX ||
+                (edgeWeight[cheapest[set1]] > edgeWeight[edgeId]) ||
+                (edgeWeight[cheapest[set1]] == edgeWeight[edgeId] && cheapest[set1] > edgeId)
+          )
+          cheapest[set1] = edgeId;
+
+      if (cheapest[set2] == INT_MAX ||
+                (edgeWeight[cheapest[set2]] > edgeWeight[edgeId]) ||
+                (edgeWeight[cheapest[set2]] == edgeWeight[edgeId] && cheapest[set2] > edgeId)
+          )
+          cheapest[set2] = edgeId;
+    }
+
+    // iterate over all the vertices and add picked
+    // cheapest edges to MST
+    for (const auto &[nodeId, edgeId] : cheapest) {
+      // Check if cheapest for current set exists
+      if (edgeId != INT_MAX) {
+        auto cheapestNode = Graph<T>::getEdge(edgeId).value()->getNodePair();
+        auto set1 = Graph<T>::setFind(subsets, cheapestNode.first->getId());
+        auto set2 = Graph<T>::setFind(subsets, cheapestNode.second->getId());
+        if (set1 == set2) continue;
+        result.mstCost += edgeWeight[edgeId];
+        auto newEdgeMST = std::make_pair(cheapestNode.first->getUserId(),
+                                         cheapestNode.second->getUserId());
+        result.mst.push_back(newEdgeMST);
+        // take union of set1 and set2 and decrease number of trees
+        Graph<T>::setUnion(subsets, set1, set2);
+        numTrees--;
+      }
+    }
+  }
+  result.success = true;
+  return result;
+}
+
 }  // namespace CXXGraph
 #endif  // __CXXGRAPH_BORUVKA_IMPL_H__