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pub mod kosaraju {
//Importng necessary libraries
use std::{
collections::VecDeque,
io::{stdin, stdout, Write},
};
/// The Kosaraju's algorithm is used to find strongly connected components.
/// Given a directed graph represented as an adjacency list (Vec[Vec[]]), returns a vector of strongly connected components.
///
/// # Arguments
///
/// * `adj_list` - A directed graph represented as an adjacency list. Each vector in the adjacency list represents the vertices that the corresponding vertex has an outgoing edge to.
///
/// # Returns
///
/// * `list_of_scc` - A list of strongly connected components which are internally in sorted order represented as Vec[Vec[]].
///
/// # Example
/// ```
/// use kosaraju::kosaraju_algorithm;
///
/// let adj_list = vec![
/// vec![1], // Node 0 has edge to node 1
/// vec![2], // Node 1 has edge to node 2
/// vec![0, 3], // Node 2 has edges to nodes 0 and 3
/// vec![4], // Node 3 has edge to node 4
/// vec![5], // Node 4 has edge to node 5
/// vec![3], // Node 5 has edge to node 3
/// ];
///
/// kosaraju_algorithm(&adj_list);
///
pub fn kosaraju_algorithm(adj_list: &Vec<Vec<usize>>) -> Vec<Vec<usize>> {
// Creating a reversed graph
let mut adj_list_reversed = vec![Vec::new(); adj_list.len()]; //Creating empty adjacency list for the reversed graph
for (u, e) in adj_list.iter().enumerate() {
//Iterating through each vertex
for &v in e {
//Iterating through each neighbor adjacent to u
adj_list_reversed[v].push(u); //Adding each vertex to the neighboring list in reversed graph
}
}
let mut visited = vec![false; adj_list.len()]; //Creating a vector to keep track of visited vertices and initializing it with false
let mut order = VecDeque::new(); //Creating an empty deque to store the vertices order
for u in 0..adj_list.len() {
if !visited[u] {
dfs_reversed(u, &adj_list_reversed, &mut visited, &mut order); //Calling dfs_reversed function for unvisited vertices
}
}
fn dfs_reversed(
u: usize,
adj_list: &Vec<Vec<usize>>,
visited: &mut Vec<bool>,
order: &mut VecDeque<usize>,
) {
// DFS function for the reversed graph
visited[u] = true; //Marking the vertex as visited
for &v in &adj_list[u] {
//Iterating through adjacent vertices of u
if !visited[v] {
dfs_reversed(v, adj_list, visited, order); //Recursively calling the DFS function for unvisited
}
}
order.push_front(u); //Adding vertex u to the front of the order deque
}
//perform DFS on the graph obtained above
let mut visited = vec![false; adj_list.len()]; //Resetting the visited vector
let mut list_of_scc = Vec::new(); //To store strongly connected components in a new vector
while let Some(u) = order.pop_front() {
// Iterating through vertices in the order obtained from previous DFS
if !visited[u] {
//If the vertex is unvisited, it belongs to a new SCC
let mut scc = Vec::new(); //To store nodes in the current SCC
dfs(u, adj_list, &mut visited, &mut scc); //Call dfs function for unvisited vertices
scc.sort(); // Sort the SCC
list_of_scc.push(scc); //Adding nodes in the current SCC
}
}
list_of_scc.sort(); //Sorting the SCC
fn dfs(
u: usize,
adj_list: &Vec<Vec<usize>>,
visited: &mut Vec<bool>,
scc: &mut Vec<usize>,
) {
//DFS function for the original graph
visited[u] = true; //Marking the vertex as visited
scc.push(u); //Adding the vertex to the SCC
for &v in &adj_list[u] {
//Iterating through neighbors of u
if !visited[v] {
dfs(v, adj_list, visited, scc); //Recursively calling the DFS function for unvisited neighbor
}
}
}
list_of_scc //Returning the list of SCCs
}
/// Performs Kosaraju's algorithm on a given directed graph represented as an adjacency list.
/// Prints a vector of vectors, where each inner vector contains the nodes of a strongly connected component in sorted order.
///
/// # Input
///
/// * `Number of vertices` - Number of vertices in the graph. When this is 0, the output will be an empty vector.
/// * `Number of neighbors for each vertex`
/// * `Next neighbor for each vertex`
///
/// # Output
///
/// Prints Strongly connected components(SCC) of the graph
///
/// # Sample input
/// ```
/// Please Enter Number of Vertices : 6
/// Please enter the number of neighbors for vertex 0 : 1
/// Please enter the next neighbor for vertex 0 : 1
/// Please enter the number of neighbors for vertex 1 : 1
/// Please enter the next neighbor for vertex 1 : 2
/// Please enter the number of neighbors for vertex 2 : 2
/// Please enter the next neighbor for vertex 2 : 0
/// Please enter the next neighbor for vertex 2 : 3
/// Please enter the number of neighbors for vertex 3 : 1
/// Please enter the next neighbor for vertex 3 : 4
/// Please enter the number of neighbors for vertex 4 : 1
/// Please enter the next neighbor for vertex 4 : 5
/// Please enter the number of neighbors for vertex 5 : 1
/// Please enter the next neighbor for vertex 5 : 3
///
/// ```
/// # Sample output
/// ```
/// The strongly connected components are:
/// [[0, 1, 2], [3, 4, 5]]
pub fn kosaraju() {
println!("******Kosaraju Algorithm*******");
println!("******************");
let mut buffer = String::new(); // Create a variable named buffer to read user input
// Read the number of vertices from the user
print!("Please Enter Number of Vertices : ");
let _ = stdout().flush(); // Flushing stdout inorder to ensure that prompt is displayed
stdin()
.read_line(&mut buffer)
.expect("Please Enter Valid number for vertices.");
let vertices: usize = buffer
.trim()
.parse()
.expect("Invalid input for number of vertices");
buffer.clear();
// Read the adjacency list for each vertex
let mut adj_list: Vec<Vec<usize>> = vec![Vec::new(); vertices]; // Creating an empty adjacency list
for i in 0..vertices {
print!("Please enter the number of neighbors for vertex {} : ", i);
let _ = stdout().flush();
stdin()
.read_line(&mut buffer)
.expect("Please Enter Valid number for neighbors.");
let num_neighbors: usize = buffer
.trim()
.parse()
.expect("Invalid input for number of neighbors");
buffer.clear();
//neighbors input for each vertex
let mut neighbors: Vec<usize> = Vec::new(); // Creating an empty list of neighbors
for _j in 0..num_neighbors {
print!("Please enter the next neighbor for vertex {} : ", i);
let _ = stdout().flush();
stdin()
.read_line(&mut buffer)
.expect("Please Enter Valid number for next neighbor.");
let neighbor: usize = buffer.trim().parse().expect("Invalid input for neighbor");
buffer.clear(); // Clearing the buffer for next input
neighbors.push(neighbor); // Adding neighbor to list of neighbors
}
adj_list[i] = neighbors;
}
// Call the kosaraju function with the adjacency list
let res = kosaraju_algorithm(&adj_list);
println!("******************");
println!("The strongly connected components are:");
println!("{:?}", res); // Printing the result of kosaraju algorithm
}
}
#[cfg(test)]
mod tests {
use super::kosaraju::kosaraju_algorithm;
#[test]
fn test_kosaraju_algorithm1() {
let adj_list = vec![
vec![1],
vec![2],
vec![3, 4],
vec![0],
vec![5],
vec![6],
vec![4, 7],
vec![],
];
let expected_result = vec![vec![0, 1, 2, 3], vec![4, 5, 6], vec![7]];
let result = kosaraju_algorithm(&adj_list);
assert_eq!(result, expected_result);
}
#[test]
fn test_kosaraju_algorithm2() {
let adj_list = vec![vec![2, 3], vec![0], vec![1], vec![4], vec![]];
let expected_result = vec![vec![0, 1, 2], vec![3], vec![4]];
let result = kosaraju_algorithm(&adj_list);
assert_eq!(result, expected_result);
}
#[test]
fn test_kosaraju_algorithm3() {
//test for disconnected graph
let adj_list = vec![
vec![1],
vec![2],
vec![0, 3],
vec![4],
vec![3],
vec![],
vec![7],
vec![5, 6],
];
let expected_result = vec![vec![0, 1, 2], vec![3, 4], vec![5], vec![6, 7]];
let result = kosaraju_algorithm(&adj_list);
assert_eq!(result, expected_result);
}
}