[C++] Graph Algorithms: Transitive Closure

C++/README.md

@@ -8,6 +8,7 @@
 # Graph Algorithms
 * Topological Sort _(Depth-First Search)_
 * Topological Sort _(Kahn's Algorithm)_
+* Transitive Closure
 
 ## Mathematics
 ### Linear Algebra

C++/graph_algorithms/CMakeLists.txt

@@ -1,4 +1,6 @@
 target_sources(programming
     PRIVATE
     topological_sort.h
-    topological_sort.cpp)
+    topological_sort.cpp
+    transitive_closure.h
+    transitive_closure.cpp)

C++/graph_algorithms/transitive_closure.cpp

@@ -0,0 +1,46 @@
+// Copyright 2024 Aman Mehara
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include "transitive_closure.h"
+
+#include <vector>
+
+namespace mehara::graph {
+
+using namespace std;
+
+vector<vector<bool>>
+transitive_closure(const vector<vector<int>>& adjacency_list)
+{
+    int n = adjacency_list.size();
+    vector<vector<bool>> tc(n, vector<bool>(n, false));
+    for (int i = 0; i < n; i++) {
+        for (const auto& neighbour : adjacency_list[i]) {
+            tc[i][neighbour] = true;
+        }
+    }
+    for (int i = 0; i < n; i++) {
+        tc[i][i] = true;
+    }
+    for (int k = 0; k < n; k++) {
+        for (int i = 0; i < n; i++) {
+            for (int j = 0; j < n; j++) {
+                tc[i][j] = tc[i][j] || (tc[i][k] && tc[k][j]);
+            }
+        }
+    }
+    return tc;
+}
+
+} // namespace mehara::graph

C++/graph_algorithms/transitive_closure.h

@@ -0,0 +1,27 @@
+// Copyright 2024 Aman Mehara
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#ifndef MEHARA_TRANSITIVE_CLOSURE_H_
+#define MEHARA_TRANSITIVE_CLOSURE_H_
+
+#include <vector>
+
+namespace mehara::graph {
+
+std::vector<std::vector<bool>>
+transitive_closure(const std::vector<std::vector<int>>& adjacency_list);
+
+} // namespace mehara::graph
+
+#endif // MEHARA_TRANSITIVE_CLOSURE_H_