From 944013f0dcb168f046772d58a12e96be25f475ac Mon Sep 17 00:00:00 2001
From: Aman Mehara <amanmehara@hotmail.com>
Date: Sat, 23 Mar 2024 21:43:18 +0530
Subject: [PATCH] [C++] Graph Algorithms: Topological Sort (Depth-First Search)

---
 C++/CMakeLists.txt                        |  1 +
 C++/README.md                             |  3 ++
 C++/graph_algorithms/topological_sort.cpp | 57 +++++++++++++++++++++++
 C++/graph_algorithms/topological_sort.h   | 28 +++++++++++
 4 files changed, 89 insertions(+)
 create mode 100644 C++/graph_algorithms/topological_sort.cpp
 create mode 100644 C++/graph_algorithms/topological_sort.h

diff --git a/C++/CMakeLists.txt b/C++/CMakeLists.txt
index 36c4c21..e859a9e 100644
--- a/C++/CMakeLists.txt
+++ b/C++/CMakeLists.txt
@@ -18,6 +18,7 @@ set_target_properties(programming PROPERTIES LINKER_LANGUAGE CXX)
 
 enable_testing()
 add_subdirectory(data_structures)
+add_subdirectory(graph_algorithms)
 add_subdirectory(mathematics)
 add_subdirectory(randomized_algorithms)
 add_subdirectory(search)
diff --git a/C++/README.md b/C++/README.md
index a52eb0a..53d3d45 100644
--- a/C++/README.md
+++ b/C++/README.md
@@ -5,6 +5,9 @@
 * Queue
 * Segment Tree
 
+# Graph Algorithms
+* Topological Sort _(Depth-First Search)_
+
 ## Mathematics
 ### Linear Algebra
 * Compute Determinant _(Gaussian Elimination)_
diff --git a/C++/graph_algorithms/topological_sort.cpp b/C++/graph_algorithms/topological_sort.cpp
new file mode 100644
index 0000000..acd0d3c
--- /dev/null
+++ b/C++/graph_algorithms/topological_sort.cpp
@@ -0,0 +1,57 @@
+// 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 "topological_sort.h"
+
+#include <algorithm>
+#include <deque>
+#include <stdexcept>
+#include <vector>
+
+namespace mehara::graph {
+
+using namespace std;
+
+namespace {
+
+void dfs(int vertex, const vector<vector<int>>& adjacency_list,
+         vector<int>& colors, deque<int>& order)
+{
+    if (colors[vertex] == 2) {
+        return;
+    }
+    if (colors[vertex] == 1) {
+        throw logic_error("Graph has at least one cycle.");
+    }
+    colors[vertex] = 1;
+    for (const auto& neighbour : adjacency_list[vertex]) {
+        dfs(neighbour, adjacency_list, colors, order);
+    }
+    colors[vertex] = 2;
+    order.push_front(vertex);
+}
+
+} // namespace
+
+deque<int> dfs_topological_sort(const vector<vector<int>>& adjacency_list)
+{
+    vector<int> colors(adjacency_list.size());
+    deque<int> order;
+    for (int i = 0; i < adjacency_list.size(); i++) {
+        dfs(i, adjacency_list, colors, order);
+    }
+    return order;
+}
+
+} // namespace mehara::graph
diff --git a/C++/graph_algorithms/topological_sort.h b/C++/graph_algorithms/topological_sort.h
new file mode 100644
index 0000000..b9998d8
--- /dev/null
+++ b/C++/graph_algorithms/topological_sort.h
@@ -0,0 +1,28 @@
+// 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_TOPOLOGICAL_SORT_H_
+#define MEHARA_TOPOLOGICAL_SORT_H_
+
+#include <deque>
+#include <vector>
+
+namespace mehara::graph {
+
+std::deque<int>
+dfs_topological_sort(const std::vector<std::vector<int>>& adjacency_list);
+
+}
+
+#endif // MEHARA_TOPOLOGICAL_SORT_H_