fix: updated number_of_paths algorithm, added more test cases, and set unsigned int as parameter

Author: adi776borate

graph/number_of_paths.cpp

@@ -22,31 +22,47 @@
 namespace graph {
 
     /**
-     * @brief Counts the number of paths from node `u` to node `v` in a directed graph
-     * using Depth First Search (DFS)
-     * 
+     * @brief Helper function to perform DFS and count the number of paths from node `u` to node `v`
      * @param A adjacency matrix representing the graph (1: edge exists, 0: no edge)
      * @param u the starting node
      * @param v the destination node
      * @param n the number of nodes in the graph
+     * @param visited a vector to keep track of visited nodes in the current DFS path
      * @returns the number of paths from node `u` to node `v`
      */
-    int count_paths(const std::vector<std::vector<int>> &A, int u, int v, int n) {
+    int count_paths_dfs(const std::vector<std::vector<unsigned int>>& A, int u, int v, int n, std::vector<bool>& visited) {
         if (u == v) {
             return 1; // Base case: Reached the destination node
         }
 
+        visited[u] = true; // Mark the current node as visited
         int path_count = 0; // Count of all paths from `u` to `v`
 
         for (int i = 0; i < n; i++) {
-            if (A[u][i] == 1) { // Check if there is an edge from `u` to `i`
-                path_count += count_paths(A, i, v, n); // Recursively explore paths from `i` to `v`
+            if (A[u][i] == 1 && !visited[i]) { // Check if there is an edge and the node is not visited
+                path_count += count_paths_dfs(A, i, v, n, visited); // Recursively explore paths from `i` to `v`
             }
         }
 
+        visited[u] = false; // Unmark the current node as visited (backtracking)
         return path_count;
     }
 
+    /**
+     * @brief Counts the number of paths from node `u` to node `v` in a directed graph
+     * using Depth First Search (DFS)
+     * 
+     * @param A adjacency matrix representing the graph (1: edge exists, 0: no edge)
+     * @param u the starting node
+     * @param v the destination node
+     * @param n the number of nodes in the graph
+     * @returns the number of paths from node `u` to node `v`
+     */
+    int count_paths(const std::vector<std::vector<unsigned int>>& A, int u, int v, int n) {
+        std::vector<bool> visited(n, false); // Initialize a visited vector for tracking nodes
+        return count_paths_dfs(A, u, v, n, visited);
+    }
+
 } // namespace graph
 
 /**
@@ -55,7 +71,7 @@ namespace graph {
  */
 static void test() {
     // Test case 1: Simple directed graph with multiple paths
-    std::vector<std::vector<int>> graph1 = {
+    std::vector<std::vector<unsigned int>> graph1 = {
         {0, 1, 0, 1, 0}, 
         {0, 0, 1, 0, 1}, 
         {0, 0, 0, 0, 1}, 
@@ -64,10 +80,39 @@ static void test() {
     };
     int n1 = 5, u1 = 0, v1 = 4;
     assert(graph::count_paths(graph1, u1, v1, n1) == 3);  // There are 3 paths from node 0 to 4
+
+    // Test case 2: No possible path (disconnected graph)
+    std::vector<std::vector<unsigned int>> graph2 = {
+        {0, 1, 0, 0, 0}, 
+        {0, 0, 0, 0, 0}, 
+        {0, 0, 0, 0, 1}, 
+        {0, 0, 1, 0, 0}, 
+        {0, 0, 0, 0, 0}  
+    };
+    int n2 = 5, u2 = 0, v2 = 4;
+    assert(graph::count_paths(graph2, u2, v2, n2) == 0);  // No path from node 0 to 4
+
+    // Test case 3: Cyclic graph with multiple paths
+    std::vector<std::vector<unsigned int>> graph3 = {
+        {0, 1, 0, 0, 0}, 
+        {0, 0, 1, 1, 0}, 
+        {1, 0, 0, 0, 1}, 
+        {0, 0, 1, 0, 1}, 
+        {0, 0, 0, 0, 0}  
+    };
+    int n3 = 5, u3 = 0, v3 = 4;
+    assert(graph::count_paths(graph3, u3, v3, n3) == 3);  // There are 3 paths from node 0 to 4
+
+    // Test case 4: Single node graph (self-loop)
+    std::vector<std::vector<unsigned int>> graph4 = {
+        {0}
+    };
+    int n4 = 1, u4 = 0, v4 = 0;
+    assert(graph::count_paths(graph4, u4, v4, n4) == 1);  // There is self-loop, so 1 path from node 0 to 0
+
     std::cout << "All tests have successfully passed!\n";
 }
 
-
 /**
  * @brief Main function
  * @returns 0 on exit