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//! Apex forest predicate (ALGO-PR-120).
//!
//! A graph is an apex forest if there exists a vertex whose removal
//! makes the remaining graph a forest (acyclic). Equivalently, all
//! cycles in the graph pass through a common vertex.
//!
//! Every forest is trivially an apex forest (remove any vertex).
//! Every graph with a single cycle passing through one vertex is
//! an apex forest.
//!
//! Directed graphs are treated as undirected.
use crate::algorithms::paths::dijkstra::DijkstraMode;
use crate::algorithms::properties::is_forest::is_forest;
use crate::core::{Graph, IgraphResult};
/// Check whether a graph is an apex forest.
///
/// A graph is an apex forest if removing some single vertex yields a
/// forest. Tests each vertex as a candidate apex.
///
/// Directed graphs are treated as undirected.
///
/// # Examples
///
/// ```
/// use rust_igraph::{Graph, is_apex_forest};
///
/// // Triangle: remove any vertex → single edge (forest) ✓
/// let mut g = Graph::with_vertices(3);
/// g.add_edge(0, 1).unwrap();
/// g.add_edge(1, 2).unwrap();
/// g.add_edge(2, 0).unwrap();
/// assert!(is_apex_forest(&g).unwrap());
///
/// // Two disjoint triangles: no single vertex removal yields forest
/// let mut g = Graph::with_vertices(6);
/// g.add_edge(0, 1).unwrap();
/// g.add_edge(1, 2).unwrap();
/// g.add_edge(2, 0).unwrap();
/// g.add_edge(3, 4).unwrap();
/// g.add_edge(4, 5).unwrap();
/// g.add_edge(5, 3).unwrap();
/// assert!(!is_apex_forest(&g).unwrap());
/// ```
pub fn is_apex_forest(graph: &Graph) -> IgraphResult<bool> {
let n = graph.vcount();
if n == 0 {
return Ok(true);
}
if is_forest(graph, DijkstraMode::All)?.is_some() {
return Ok(true);
}
let n_usize = n as usize;
let mut adj = vec![vec![false; n_usize]; n_usize];
for v in 0..n {
let nbrs = graph.neighbors(v)?;
for &w in &nbrs {
adj[v as usize][w as usize] = true;
adj[w as usize][v as usize] = true;
}
}
for apex in 0..n_usize {
if is_forest_without(&adj, apex, n_usize) {
return Ok(true);
}
}
Ok(false)
}
/// Check if the graph minus vertex `removed` is a forest.
fn is_forest_without(adj: &[Vec<bool>], removed: usize, n: usize) -> bool {
let mut visited = vec![false; n];
visited[removed] = true;
let remaining = n - 1;
if remaining == 0 {
return true;
}
let mut edge_count = 0usize;
let mut component_count = 0usize;
let mut visited_count = 0usize;
for start in 0..n {
if visited[start] {
continue;
}
component_count += 1;
let mut stack = vec![start];
visited[start] = true;
while let Some(u) = stack.pop() {
visited_count += 1;
for (v, &is_adj) in adj[u].iter().enumerate() {
if v == removed || !is_adj {
continue;
}
edge_count += 1;
if !visited[v] {
visited[v] = true;
stack.push(v);
}
}
}
}
// Each edge counted twice (u→v and v→u)
edge_count /= 2;
// Forest iff edges == vertices - components
edge_count == visited_count - component_count
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn empty_graph() {
let g = Graph::with_vertices(0);
assert!(is_apex_forest(&g).unwrap());
}
#[test]
fn single_vertex() {
let g = Graph::with_vertices(1);
assert!(is_apex_forest(&g).unwrap());
}
#[test]
fn single_edge() {
let mut g = Graph::with_vertices(2);
g.add_edge(0, 1).unwrap();
assert!(is_apex_forest(&g).unwrap());
}
#[test]
fn triangle() {
let mut g = Graph::with_vertices(3);
g.add_edge(0, 1).unwrap();
g.add_edge(1, 2).unwrap();
g.add_edge(2, 0).unwrap();
assert!(is_apex_forest(&g).unwrap());
}
#[test]
fn tree() {
let mut g = Graph::with_vertices(5);
g.add_edge(0, 1).unwrap();
g.add_edge(1, 2).unwrap();
g.add_edge(1, 3).unwrap();
g.add_edge(3, 4).unwrap();
assert!(is_apex_forest(&g).unwrap());
}
#[test]
fn c4() {
// C_4: remove any vertex → P_3 (forest) ✓
let mut g = Graph::with_vertices(4);
g.add_edge(0, 1).unwrap();
g.add_edge(1, 2).unwrap();
g.add_edge(2, 3).unwrap();
g.add_edge(3, 0).unwrap();
assert!(is_apex_forest(&g).unwrap());
}
#[test]
fn k4() {
// K_4: remove any vertex → K_3 (triangle, NOT a forest).
// So K_4 is NOT an apex forest.
let mut g = Graph::with_vertices(4);
for i in 0..4u32 {
for j in (i + 1)..4 {
g.add_edge(i, j).unwrap();
}
}
assert!(!is_apex_forest(&g).unwrap());
}
#[test]
fn two_triangles_not_apex() {
let mut g = Graph::with_vertices(6);
g.add_edge(0, 1).unwrap();
g.add_edge(1, 2).unwrap();
g.add_edge(2, 0).unwrap();
g.add_edge(3, 4).unwrap();
g.add_edge(4, 5).unwrap();
g.add_edge(5, 3).unwrap();
assert!(!is_apex_forest(&g).unwrap());
}
#[test]
fn wheel_w4() {
// W_4: center 0, rim 1-2-3-4-1.
// Remove center → C_4 (has cycle) → not forest.
// Remove rim vertex 1 → 0 connected to 2,3,4; plus 2-3,3-4.
// Edges: 0-2,0-3,0-4,2-3,3-4. Has cycle 0-2-3-0 → not forest.
// K_4 subgraph minus one edge... still has cycle.
// Actually let's check: remove 1 from W_4.
// Remaining: 0,2,3,4 with edges 0-2,0-3,0-4,2-3,3-4.
// 4 vertices, 5 edges. Forest needs 3 edges. NOT forest.
// W_4 is NOT apex forest.
let mut g = Graph::with_vertices(5);
g.add_edge(0, 1).unwrap();
g.add_edge(0, 2).unwrap();
g.add_edge(0, 3).unwrap();
g.add_edge(0, 4).unwrap();
g.add_edge(1, 2).unwrap();
g.add_edge(2, 3).unwrap();
g.add_edge(3, 4).unwrap();
g.add_edge(4, 1).unwrap();
assert!(!is_apex_forest(&g).unwrap());
}
#[test]
fn diamond_apex() {
// Diamond: 0-1,0-2,0-3,1-2,1-3 (K_4 minus 2-3).
// Remove 0: remaining 1,2,3 with edges 1-2,1-3 → star → forest ✓.
let mut g = Graph::with_vertices(4);
g.add_edge(0, 1).unwrap();
g.add_edge(0, 2).unwrap();
g.add_edge(0, 3).unwrap();
g.add_edge(1, 2).unwrap();
g.add_edge(1, 3).unwrap();
assert!(is_apex_forest(&g).unwrap());
}
#[test]
fn theta_graph_apex() {
// Theta: two paths between 0 and 3: 0-1-3 and 0-2-3.
// Remove 0 → 1,2,3 with edges 1-3,2-3 → forest ✓.
let mut g = Graph::with_vertices(4);
g.add_edge(0, 1).unwrap();
g.add_edge(1, 3).unwrap();
g.add_edge(0, 2).unwrap();
g.add_edge(2, 3).unwrap();
assert!(is_apex_forest(&g).unwrap());
}
#[test]
fn edgeless() {
let g = Graph::with_vertices(4);
assert!(is_apex_forest(&g).unwrap());
}
#[test]
fn directed_treated_as_undirected() {
let mut g = Graph::new(3, true).unwrap();
g.add_edge(0, 1).unwrap();
g.add_edge(1, 2).unwrap();
g.add_edge(2, 0).unwrap();
assert!(is_apex_forest(&g).unwrap());
}
#[test]
fn two_triangles_shared_vertex() {
// 0-1-2-0 and 0-3-4-0. All cycles through 0.
// Remove 0 → 1-2, 3-4 (two edges, forest) ✓.
let mut g = Graph::with_vertices(5);
g.add_edge(0, 1).unwrap();
g.add_edge(1, 2).unwrap();
g.add_edge(2, 0).unwrap();
g.add_edge(0, 3).unwrap();
g.add_edge(3, 4).unwrap();
g.add_edge(4, 0).unwrap();
assert!(is_apex_forest(&g).unwrap());
}
}