feat(graph): add Tarjan SCC

README.md

@@ -66,7 +66,7 @@ Minimum supported Rust version: 1.74 (edition 2021).
 
 ### Graph
 - Breadth-first, Depth-first, Dijkstra, Bellman–Ford, Kruskal, Prim,
-  Topological sort, Floyd–Warshall, A* search
+  Topological sort, Floyd–Warshall, A* search, Tarjan SCC
 
 ### Dynamic Programming
 - Fibonacci (memoised), 0/1 Knapsack, Longest Common Subsequence,

src/graph/mod.rs

@@ -17,3 +17,5 @@ pub mod topological_sort;
 pub mod floyd_warshall;
 
 pub mod a_star;
+
+pub mod tarjan_scc;

src/graph/tarjan_scc.rs

@@ -0,0 +1,125 @@
+//! Tarjan's strongly-connected components algorithm. Single-pass DFS with
+//! discovery / low-link bookkeeping. O(V + E).
+
+/// Returns the strongly-connected components of a directed graph as a list
+/// of node lists. Each component is sorted ascending; the components are
+/// returned in reverse-topological order (sinks of the condensation first).
+pub fn tarjan_scc(graph: &[Vec<usize>]) -> Vec<Vec<usize>> {
+    let n = graph.len();
+    let mut state = TarjanState {
+        disc: vec![usize::MAX; n],
+        low: vec![0; n],
+        on_stack: vec![false; n],
+        stack: Vec::new(),
+        components: Vec::new(),
+        index: 0,
+    };
+    for u in 0..n {
+        if state.disc[u] == usize::MAX {
+            strongconnect(graph, u, &mut state);
+        }
+    }
+    state.components
+}
+
+struct TarjanState {
+    disc: Vec<usize>,
+    low: Vec<usize>,
+    on_stack: Vec<bool>,
+    stack: Vec<usize>,
+    components: Vec<Vec<usize>>,
+    index: usize,
+}
+
+fn strongconnect(graph: &[Vec<usize>], u: usize, st: &mut TarjanState) {
+    st.disc[u] = st.index;
+    st.low[u] = st.index;
+    st.index += 1;
+    st.stack.push(u);
+    st.on_stack[u] = true;
+
+    for &v in &graph[u] {
+        if st.disc[v] == usize::MAX {
+            strongconnect(graph, v, st);
+            st.low[u] = st.low[u].min(st.low[v]);
+        } else if st.on_stack[v] {
+            st.low[u] = st.low[u].min(st.disc[v]);
+        }
+    }
+
+    if st.low[u] == st.disc[u] {
+        let mut component = Vec::new();
+        loop {
+            let v = st.stack.pop().unwrap();
+            st.on_stack[v] = false;
+            component.push(v);
+            if v == u {
+                break;
+            }
+        }
+        component.sort_unstable();
+        st.components.push(component);
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::tarjan_scc;
+
+    fn sort_components(mut comps: Vec<Vec<usize>>) -> Vec<Vec<usize>> {
+        comps.iter_mut().for_each(|c| c.sort_unstable());
+        comps.sort_by_key(|c| c[0]);
+        comps
+    }
+
+    #[test]
+    fn empty() {
+        let g: Vec<Vec<usize>> = vec![];
+        assert!(tarjan_scc(&g).is_empty());
+    }
+
+    #[test]
+    fn single_node() {
+        let g = vec![vec![]];
+        assert_eq!(tarjan_scc(&g), vec![vec![0]]);
+    }
+
+    #[test]
+    fn two_disconnected() {
+        let g = vec![vec![], vec![]];
+        let c = sort_components(tarjan_scc(&g));
+        assert_eq!(c, vec![vec![0], vec![1]]);
+    }
+
+    #[test]
+    fn classic_clrs_example() {
+        // Edges: a->b, b->c, b->e, b->f, c->d, c->g, d->c, d->h,
+        // e->a, e->f, f->g, g->f, g->h, h->h
+        // Vertices a..h = 0..7
+        let g = vec![
+            vec![1],       // a
+            vec![2, 4, 5], // b
+            vec![3, 6],    // c
+            vec![2, 7],    // d
+            vec![0, 5],    // e
+            vec![6],       // f
+            vec![5, 7],    // g
+            vec![7],       // h
+        ];
+        let c = sort_components(tarjan_scc(&g));
+        assert_eq!(c, vec![vec![0, 1, 4], vec![2, 3], vec![5, 6], vec![7]]);
+    }
+
+    #[test]
+    fn self_loop() {
+        let g = vec![vec![0]];
+        assert_eq!(tarjan_scc(&g), vec![vec![0]]);
+    }
+
+    #[test]
+    fn one_big_cycle() {
+        let g = vec![vec![1], vec![2], vec![3], vec![0]];
+        let c = sort_components(tarjan_scc(&g));
+        assert_eq!(c, vec![vec![0, 1, 2, 3]]);
+    }
+}