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use petgraph::graph::{EdgeReference, NodeIndex};
use petgraph::prelude::*;
use petgraph::visit::EdgeRef;
use petgraph::visit::IntoNodeIdentifiers;
// use petgraph::visit::IntoNeighborsDirected;
/// The `NegCycleFinder` struct is used to find negative cycles in a directed graph.
///
/// Properties:
///
/// * `digraph`: The `digraph` property is a reference to a directed graph (`DiGraph`) that the
/// `NegCycleFinder` is operating on. It is annotated with a lifetime `'a`, indicating that the
/// reference is valid for a certain scope.
/// * `pred`: The `pred` property is a `HashMap` that maps a `NodeIndex` to a tuple containing the
/// previous node index and an `EdgeReference`. This is used to keep track of the predecessor node and
/// the edge that leads to that node during the process of finding negative cycles in a directed graph
#[derive(Debug, Clone)]
pub struct NegCycleFinder<'a, V, D> {
pub digraph: &'a DiGraph<V, D>,
pub pred: std::collections::HashMap<NodeIndex, (NodeIndex, EdgeReference<'a, D>)>,
}
impl<'a, V, D> NegCycleFinder<'a, V, D>
where
D: std::ops::Add<Output = D> + std::cmp::PartialOrd + Copy,
{
/// The `new` function creates a new `NegCycleFinder` object with an empty predecessor map.
///
/// Arguments:
///
/// * `digraph`: A reference to a directed graph (`DiGraph`) that the `NegCycleFinder` will operate on.
///
/// Returns:
///
/// The `new` function is returning an instance of the `NegCycleFinder<V, D>` struct.
/// Creates a new [`NegCycleFinder<V, D>`].
pub fn new(digraph: &'a DiGraph<V, D>) -> Self {
Self {
digraph,
pred: std::collections::HashMap::new(),
}
}
/// The `find_cycle` function in Rust returns the first node in a cycle found in a directed graph.
///
/// Returns:
///
/// The function `find_cycle` returns an `Option<NodeIndex>`.
pub fn find_cycle(&self) -> Option<NodeIndex> {
let mut visited = std::collections::HashMap::new();
for vtx in self.digraph.node_identifiers() {
if visited.contains_key(&vtx) {
continue;
}
let mut utx = vtx;
while !visited.contains_key(&utx) {
visited.insert(utx, vtx);
if !self.pred.contains_key(&utx) {
break;
}
let result = *self.pred.get(&utx).unwrap();
utx = result.0;
if visited.contains_key(&utx) {
if visited[&utx] == vtx {
return Some(utx);
}
break;
}
}
}
None
}
/// The `relax` function updates the distances between nodes in a graph based on the weights of the
/// edges, and returns a boolean indicating whether any distances were changed.
///
/// Arguments:
///
/// * `dist`: `dist` is a mutable reference to a slice of type `D`. It represents the distances from
/// a source node to each node in a graph.
/// * `get_weight`: The `get_weight` parameter is a closure that takes an `EdgeReference<D>` as
/// input and returns a value of type `D`. This closure is used to calculate the weight of each edge
/// in the graph. The `EdgeReference<D>` represents a reference to an edge in the graph, and
///
/// Returns:
///
/// a boolean value.
pub fn relax<F>(&mut self, dist: &mut [D], get_weight: F) -> bool
where
F: Fn(EdgeReference<D>) -> D,
{
let mut changed = false;
for utx in self.digraph.node_identifiers() {
for edge in self.digraph.edges(utx) {
let vtx = edge.target();
let weight = get_weight(edge);
// for utx in self.digraph.node_indices() {
// for vtx in self
// .digraph
// .neighbors_directed(utx, petgraph::Direction::Outgoing)
// {
// let weight = get_weight((utx, vtx));
let distance = dist[utx.index()] + weight;
if dist[vtx.index()] > distance {
dist[vtx.index()] = distance;
self.pred.insert(vtx, (utx, edge));
changed = true;
}
}
}
changed
}
/// The `howard` function implements Howard's algorithm for finding negative cycles in a directed
/// graph.
///
/// Arguments:
///
/// * `dist`: `dist` is a mutable reference to an array of type `D`. This array is used to store the
/// distances from the source vertex to each vertex in the graph. The algorithm will update the
/// distances during the execution.
/// * `get_weight`: `get_weight` is a closure that takes an `EdgeReference<D>` and returns the
/// weight of that edge. The `howard` function uses this closure to get the weight of each edge in
/// the graph.
///
/// Returns:
///
/// The `howard` function returns an `Option<Vec<EdgeReference<'a, D>>>`.
/// Howard's algorithm for finding negative cycles
///
/// # Examples
///
/// ```
/// use petgraph::prelude::*;
/// use netoptim_rs::neg_cycle::NegCycleFinder;
/// let digraph = DiGraph::<(), i32>::from_edges([
/// (0, 1, 1),
/// (0, 2, 1),
/// (0, 3, 1),
/// (1, 3, 1),
/// (2, 1, 1),
/// (3, 2, -3),
/// ]);
/// let mut ncf = NegCycleFinder::new(&digraph);
/// let mut dist = [0, 0, 0, 0];
/// let result = ncf.howard(&mut dist, |e| { *e.weight()});
/// assert!(result.is_some());
/// ```
/// # Example: Graph with no negative cycle
/// ```rust
/// use petgraph::prelude::*;
/// use netoptim_rs::neg_cycle::NegCycleFinder;
/// use num::rational::Ratio;
/// let digraph = DiGraph::<(), Ratio<i32>>::from_edges([
/// (0, 1, Ratio::new(1, 1)),
/// (1, 2, Ratio::new(1, 1)),
/// (2, 3, Ratio::new(1, 1)),
/// ]);
/// let mut ncf = NegCycleFinder::new(&digraph);
/// let mut dist = [
/// Ratio::new(0, 1),
/// Ratio::new(0, 1),
/// Ratio::new(0, 1),
/// Ratio::new(0, 1),
/// ];
/// let result = ncf.howard(&mut dist, |e| { *e.weight()});
/// assert!(result.is_none());
/// ```
pub fn howard<F>(&mut self, dist: &mut [D], get_weight: F) -> Option<Vec<EdgeReference<'a, D>>>
where
F: Fn(EdgeReference<D>) -> D,
{
self.pred.clear();
while self.relax(dist, &get_weight) {
let v_opt = self.find_cycle();
if let Some(vtx) = v_opt {
return Some(self.cycle_list(vtx));
}
}
None
}
/// The function `cycle_list` takes a node index as input and returns a vector of edge references
/// that form a cycle in a graph.
///
/// Arguments:
///
/// * `handle`: The `handle` parameter is of type `NodeIndex`. It represents the starting node index
/// from which the cycle traversal will begin.
///
/// Returns:
///
/// The function `cycle_list` returns a vector of `EdgeReference` objects.
fn cycle_list(&self, handle: NodeIndex) -> Vec<EdgeReference<'a, D>> {
let mut vtx = handle;
let mut cycle = Vec::new();
loop {
let (utx, edge) = self.pred[&vtx];
cycle.push(edge);
vtx = utx;
if vtx == handle {
break;
}
}
cycle
}
}
#[cfg(test)]
mod tests {
use super::*;
use num::rational::Ratio;
#[test]
fn it_works() {
let result = 2 + 2;
assert_eq!(result, 4);
}
#[test]
fn test_neg_cycle1() {
let digraph = DiGraph::<(), Ratio<i32>>::from_edges([
(0, 1, Ratio::new(1, 1)),
(0, 2, Ratio::new(1, 1)),
(0, 3, Ratio::new(1, 1)),
(1, 3, Ratio::new(1, 1)),
(2, 1, Ratio::new(1, 1)),
(3, 2, Ratio::new(-3, 1)),
]);
let mut ncf = NegCycleFinder::new(&digraph);
let mut dist = [
Ratio::new(0, 1),
Ratio::new(0, 1),
Ratio::new(0, 1),
Ratio::new(0, 1),
];
let result = ncf.howard(&mut dist, |e| *e.weight());
assert!(result.is_some());
}
#[test]
fn test_neg_cycle2() {
let mut graph = DiGraph::new();
let a = graph.add_node("a");
let b = graph.add_node("b");
let c = graph.add_node("c");
let d = graph.add_node("d");
let e = graph.add_node("e");
let f = graph.add_node("f");
let g = graph.add_node("g");
let h = graph.add_node("h");
let i = graph.add_node("i");
graph.add_edge(a, b, Ratio::new(1, 1));
graph.add_edge(a, c, Ratio::new(1, 1));
graph.add_edge(b, d, Ratio::new(1, 1));
graph.add_edge(c, d, Ratio::new(1, 1));
graph.add_edge(d, e, Ratio::new(-3, 1));
graph.add_edge(d, f, Ratio::new(1, 1));
graph.add_edge(e, g, Ratio::new(1, 1));
graph.add_edge(f, g, Ratio::new(1, 1));
graph.add_edge(g, h, Ratio::new(1, 1));
graph.add_edge(h, i, Ratio::new(1, 1));
graph.add_edge(i, f, Ratio::new(1, 1));
let mut ncf = NegCycleFinder::new(&graph);
let mut dist = [
Ratio::new(0, 1),
Ratio::new(0, 1),
Ratio::new(0, 1),
Ratio::new(0, 1),
Ratio::new(0, 1),
Ratio::new(0, 1),
Ratio::new(0, 1),
Ratio::new(0, 1),
Ratio::new(0, 1),
];
let result = ncf.howard(&mut dist, |e| *e.weight());
assert!(result.is_none());
}
#[test]
fn test_neg_cycle_no_edges() {
let digraph = DiGraph::<(), Ratio<i32>>::new();
let mut ncf = NegCycleFinder::new(&digraph);
let mut dist = [];
let result = ncf.howard(&mut dist, |e| *e.weight());
assert!(result.is_none());
}
#[test]
fn test_neg_cycle_self_loop() {
let mut digraph = DiGraph::<(), Ratio<i32>>::new();
let n0 = digraph.add_node(());
digraph.add_edge(n0, n0, Ratio::new(-1, 1));
let mut ncf = NegCycleFinder::new(&digraph);
let mut dist = [Ratio::new(0, 1)];
let result = ncf.howard(&mut dist, |e| *e.weight());
assert!(result.is_some());
let cycle = result.unwrap();
assert_eq!(cycle.len(), 1);
assert_eq!(cycle[0].source(), n0);
assert_eq!(cycle[0].target(), n0);
}
#[test]
fn test_neg_cycle_multiple_cycles() {
let digraph = DiGraph::<(), Ratio<i32>>::from_edges([
(0, 1, Ratio::new(1, 1)),
(1, 0, Ratio::new(-2, 1)), // Cycle 1: 0 -> 1 -> 0 (weight -1)
(2, 3, Ratio::new(1, 1)),
(3, 2, Ratio::new(-2, 1)), // Cycle 2: 2 -> 3 -> 2 (weight -1)
(0, 2, Ratio::new(1, 1)),
]);
let mut ncf = NegCycleFinder::new(&digraph);
let mut dist = [
Ratio::new(0, 1),
Ratio::new(0, 1),
Ratio::new(0, 1),
Ratio::new(0, 1),
];
let result = ncf.howard(&mut dist, |e| *e.weight());
assert!(result.is_some());
// The algorithm finds one of the negative cycles.
// We can't assert which one, but we can assert it's a negative cycle.
let cycle = result.unwrap();
let cycle_weight: Ratio<i32> = cycle.iter().map(|e| *e.weight()).sum();
assert!(cycle_weight < Ratio::new(0, 1));
}
#[test]
fn test_neg_cycle_unreachable_cycle() {
let digraph = DiGraph::<(), Ratio<i32>>::from_edges([
(0, 1, Ratio::new(1, 1)),
(1, 2, Ratio::new(1, 1)),
(2, 0, Ratio::new(-3, 1)), // Cycle 1: 0 -> 1 -> 2 -> 0 (weight -1)
(3, 4, Ratio::new(1, 1)),
(4, 3, Ratio::new(-2, 1)), // Cycle 2: 3 -> 4 -> 3 (weight -1) - unreachable from 0
]);
let mut ncf = NegCycleFinder::new(&digraph);
let mut dist = [
Ratio::new(0, 1),
Ratio::new(0, 1),
Ratio::new(0, 1),
Ratio::new(0, 1),
Ratio::new(0, 1),
];
let result = ncf.howard(&mut dist, |e| *e.weight());
assert!(result.is_some());
let cycle = result.unwrap();
let cycle_weight: Ratio<i32> = cycle.iter().map(|e| *e.weight()).sum();
assert!(cycle_weight < Ratio::new(0, 1));
// The found cycle should be the one reachable from the initial dist (all zeros, effectively reachable from all nodes)
// In this case, it should find the 0->1->2->0 cycle.
let expected_cycle_nodes: Vec<NodeIndex> = cycle.iter().map(|e| e.source()).collect();
assert!(expected_cycle_nodes.contains(&NodeIndex::new(0)));
assert!(expected_cycle_nodes.contains(&NodeIndex::new(1)));
assert!(expected_cycle_nodes.contains(&NodeIndex::new(2)));
assert!(!expected_cycle_nodes.contains(&NodeIndex::new(3)));
assert!(!expected_cycle_nodes.contains(&NodeIndex::new(4)));
}
}