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

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This commit is contained in:
Aditya Borate
2024-10-15 20:30:54 +05:30
parent 7aa59ac1a9
commit 13fff24f42
1 changed files with 61 additions and 16 deletions
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77
graph/number_of_paths.cpp
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@@ -21,6 +21,33 @@
*/
namespace graph {
/**
* @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_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 && !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)
@@ -31,20 +58,9 @@ namespace graph {
* @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<int>> &A, int u, int v, int n) {
if (u == v) {
return 1; // Base case: Reached the destination node
}
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`
}
}
return path_count;
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