use crate::algo::graph::UnweightedAdjacencyList;
#[derive(Debug)]
pub enum EulerianPathError {
DisconnectedGraph,
InvalidDegrees,
}
impl UnweightedAdjacencyList {
fn count_in_out_degrees(&self) -> [Vec<usize>; 2] {
let mut in_degrees = vec![0; self.node_count()];
let mut out_degrees = vec![0; self.node_count()];
for [from, to] in self.edges() {
out_degrees[from] += 1;
in_degrees[to] += 1;
}
[in_degrees, out_degrees]
}
pub fn eulerian_path(&self) -> Result<Vec<usize>, EulerianPathError> {
let n = self.node_count();
let has_eulerian_path = |[in_degrees, out_degrees]: [&[usize]; 2]| {
let mut start = None;
let mut has_end = false;
let mut start_default = None;
for (node, (&i, &o)) in in_degrees.iter().zip(out_degrees.iter()).enumerate() {
if (i as isize - o as isize).abs() > 1 {
return None;
}
if i.wrapping_sub(o) == 1 {
if has_end {
return None;
} else {
has_end = true;
}
}
if o.wrapping_sub(i) == 1 {
if start.is_some() {
return None;
} else {
start = Some(node)
}
}
if start_default.is_none() && o > 0 {
start_default = Some(node);
}
}
if start.is_some() ^ has_end {
None
} else {
Some(start.unwrap_or_else(|| start_default.unwrap()))
}
};
let [i, mut o] = self.count_in_out_degrees();
fn _dfs(
g: &UnweightedAdjacencyList,
out: &mut Vec<usize>,
path: &mut Vec<usize>,
at: usize,
) {
while out[at] > 0 {
out[at] -= 1;
let next = g[at][out[at]];
_dfs(g, out, path, next);
}
path.push(at);
};
has_eulerian_path([&i, &o]).map_or(Err(EulerianPathError::InvalidDegrees), |start| {
let mut path = Vec::with_capacity(n);
_dfs(self, &mut o, &mut path, start);
path.reverse();
if path.len() == self.edge_count() + 1 {
Ok(path)
} else {
Err(EulerianPathError::DisconnectedGraph)
}
})
}
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_eulerian_path() {
let g = UnweightedAdjacencyList::new_directed(
7,
&[
[1, 2],
[1, 3],
[2, 2],
[2, 4],
[2, 4],
[3, 1],
[3, 2],
[3, 5],
[4, 3],
[4, 6],
[5, 6],
[6, 3],
],
);
let path = g.eulerian_path().unwrap();
assert_eq!(&path, &[1, 3, 5, 6, 3, 2, 4, 3, 1, 2, 2, 4, 6]);
let g = UnweightedAdjacencyList::new_directed(
5,
&[[0, 1], [1, 2], [1, 4], [1, 3], [2, 1], [4, 1]],
);
let path = g.eulerian_path().unwrap();
assert_eq!(&path, &[0, 1, 4, 1, 2, 1, 3]);
}
#[test]
fn test_eulerian_path_invalid1() {
let g = UnweightedAdjacencyList::new_directed(2, &[[0, 1], [0, 1]]);
assert!(matches!(
g.eulerian_path(),
Err(EulerianPathError::InvalidDegrees)
));
}
#[test]
fn test_eulerian_path_invalid2() {
let g = UnweightedAdjacencyList::new_directed(3, &[[0, 1], [1, 0], [1, 2], [2, 0], [2, 0]]);
assert!(matches!(
g.eulerian_path(),
Err(EulerianPathError::InvalidDegrees)
));
}
#[test]
fn test_eulerian_path_invalid3() {
let g = UnweightedAdjacencyList::new_directed(
4,
&[
[0, 2],
[2, 1],
[2, 3],
[3, 0],
[3, 1],
[1, 3],
[1, 0],
[1, 2],
[0, 3],
[2, 0],
],
);
assert!(matches!(
g.eulerian_path(),
Err(EulerianPathError::InvalidDegrees)
));
}
#[test]
fn test_eulerian_path_invalid4() {
let g = UnweightedAdjacencyList::new_directed(
8,
&[
[0, 1],
[1, 2],
[2, 3],
[3, 1],
[4, 5],
[5, 6],
[6, 7],
[7, 4],
],
);
assert!(matches!(
g.eulerian_path(),
Err(EulerianPathError::DisconnectedGraph)
));
}
}