[C++] Graph Algorithms: Topological Sort (Kahn's Algorithm)

amanmehara · Mar 23, 2024 · d49dd9c · d49dd9c
1 parent 0dcb5f5
commit d49dd9c
Show file tree

Hide file tree

Showing 3 changed files with 42 additions and 3 deletions.
diff --git a/C++/README.md b/C++/README.md
@@ -7,6 +7,7 @@
 
 # Graph Algorithms
 * Topological Sort _(Depth-First Search)_
+* Topological Sort _(Kahn's Algorithm)_
 
 ## Mathematics
 ### Linear Algebra

diff --git a/C++/graph_algorithms/topological_sort.cpp b/C++/graph_algorithms/topological_sort.cpp
@@ -46,12 +46,47 @@ void dfs(int vertex, const vector<vector<int>>& adjacency_list,
 
 deque<int> dfs_topological_sort(const vector<vector<int>>& adjacency_list)
 {
-    vector<int> colors(adjacency_list.size());
+    int n = adjacency_list.size();
+    vector<int> colors(n);
     deque<int> order;
-    for (int i = 0; i < adjacency_list.size(); i++) {
+    for (int i = 0; i < n; i++) {
         dfs(i, adjacency_list, colors, order);
     }
     return order;
 }
 
+deque<int>
+kahns_algorithm_topological_sort(const vector<vector<int>>& adjacency_list)
+{
+    int n = adjacency_list.size();
+    deque<int> order;
+    vector<int> indegrees(n);
+    for (int i = 0; i < n; i++) {
+        for (const auto& neighbour : adjacency_list[i]) {
+            indegrees[neighbour]++;
+        }
+    }
+    deque<int> q;
+    for (int i = 0; i < n; i++) {
+        if (indegrees[i] == 0) {
+            q.push_back(i);
+        }
+    }
+    while (!q.empty()) {
+        int vertex = q.front();
+        q.pop_front();
+        order.push_back(vertex);
+        for (const auto& neighbour : adjacency_list[vertex]) {
+            indegrees[neighbour]--;
+            if (indegrees[neighbour] == 0) {
+                q.push_back(neighbour);
+            }
+        }
+    }
+    if (order.size() != n) {
+        throw logic_error("Graph has at least one cycle.");
+    }
+    return order;
+}
+
 } // namespace mehara::graph
diff --git a/C++/graph_algorithms/topological_sort.h b/C++/graph_algorithms/topological_sort.h
@@ -23,6 +23,9 @@ namespace mehara::graph {
 std::deque<int>
 dfs_topological_sort(const std::vector<std::vector<int>>& adjacency_list);
 
-}
+std::deque<int> kahns_algorithm_topological_sort(
+    const std::vector<std::vector<int>>& adjacency_list);
+
+} // namespace mehara::graph
 
 #endif // MEHARA_TOPOLOGICAL_SORT_H_