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// Copyright (c) 2016, 2017 Frank Fischer <frank-fischer@shadow-soft.de> // // This program is free software: you can redistribute it and/or // modify it under the terms of the GNU General Public License as // published by the Free Software Foundation, either version 3 of the // License, or (at your option) any later version. // // This program is distributed in the hope that it will be useful, but // WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU // General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see <http://www.gnu.org/licenses/> // //! General algorithms working on graphs. use graph::{Graph, Digraph, IndexGraph, IndexDigraph}; use vec::NodeVec; use builder::Builder; use std::collections::HashSet; use std::cmp::{min, max}; use std::usize; /// Returns the complement of `g`. /// /// # Example /// /// ``` /// use rs_graph::{LinkedListGraph, Graph, Builder}; /// use rs_graph::algorithms::complement; /// use rs_graph::classes::cycle; /// use std::cmp::{min, max}; /// /// let g: LinkedListGraph = cycle(5); /// let h: LinkedListGraph = complement(&g); /// /// assert_eq!(h.num_nodes(), 5); /// assert_eq!(h.num_edges(), 5); /// /// let mut edges: Vec<_> = h.edges().map(|e| { /// let (u, v) = h.enodes(e); /// let (u, v) = (h.node2id(u), h.node2id(v)); /// (min(u,v), max(u,v)) /// }).collect(); /// edges.sort(); /// assert_eq!(edges, vec![(0,2), (0,3), (1,3), (1,4), (2,4)]); /// ``` /// /// Note that this function assumes that `g` is a simple graph (no /// loops or double edges). It will work on multi-graphs, too, but /// only adjacencies are respected, no multiplicities. pub fn complement<'g, 'h, G, H>(g: &'g G) -> H where G: IndexGraph<'g>, H: Graph<'h>, { let mut edges = HashSet::new(); for e in g.edges() { let (u, v) = g.enodes(e); edges.insert((min(g.node_id(u), g.node_id(v)), max(g.node_id(u), g.node_id(v)))); } let n = g.num_nodes(); let mut h = H::Builder::with_capacities(n, n * (n-1) / 2 - g.num_edges()); let nodes = h.add_nodes(n); for i in 0..n { for j in i..n { if i < j && !edges.contains(&(i, j)) { h.add_edge(nodes[i], nodes[j]); } } } h.to_graph() } /// Returns the inverse directed graph of `g`. /// /// For $G=(V,A)$ the returned graph is $G=(V,A')$ with /// $A' := \{(v,u) \colon (u,v) \in A\}$. /// /// # Example /// /// ``` /// use rs_graph::{LinkedListGraph, IndexGraph, Graph, Digraph, Builder}; /// use rs_graph::algorithms::inverse; /// /// let mut g = LinkedListGraph::<usize>::new(); /// /// g.add_nodes(18); /// for u in g.nodes() { /// for v in g.nodes() { /// if g.node_id(v) > 0 && g.node_id(u) % g.node_id(v) == 0 { /// g.add_edge(u, v); /// } /// } /// } /// /// let h: LinkedListGraph = inverse(&g); /// assert_eq!(g.num_nodes(), h.num_nodes()); /// assert_eq!(g.num_edges(), h.num_edges()); /// for e in h.edges() { /// let (u,v) = (h.node_id(h.src(e)), h.node_id(h.snk(e))); /// assert!(u > 0 && v % u == 0); /// } /// ``` pub fn inverse<'g, 'h, G, H>(g: &'g G) -> H where G: IndexDigraph<'g>, H: Digraph<'h>, { let mut h = H::Builder::with_capacities(g.num_nodes(), g.num_edges()); let nodes = h.add_nodes(g.num_nodes()); for e in g.edges() { h.add_edge(nodes[g.node_id(g.snk(e))], nodes[g.node_id(g.src(e))]); } h.to_graph() } /// Determines if a graph is connected. /// /// The empty graph is connected. /// /// # Example /// /// ``` /// use rs_graph::{LinkedListGraph, Graph, Builder, classes, algorithms}; /// /// let mut g: LinkedListGraph = classes::cycle(5); /// assert!(algorithms::is_connected(&g)); /// /// g.add_node(); /// assert!(!algorithms::is_connected(&g)); /// /// ``` pub fn is_connected<'g, G>(g: &'g G) -> bool where G: IndexGraph<'g> { if g.num_nodes() == 0 { return true; } let mut seen = nodevec![g; false]; let mut q = vec![g.id2node(0)]; while let Some(u) = q.pop() { for (_, v) in g.neighs(u) { if !seen[v] { seen[v] = true; q.push(v); } } } seen.into_iter().all(|&u| u) } /// Determines all components of a graph. /// /// The function numbers all components and assigns each node the /// number its containing component. The number of components is /// returned. /// /// The empty graph has 0 components. /// /// # Example /// /// ``` /// use rs_graph::{LinkedListGraph, Graph, Builder, classes, algorithms}; /// /// let mut g: LinkedListGraph = classes::cycle(5); /// { /// let (ncomps, comps) = algorithms::components(&g); /// assert_eq!(ncomps, 1); /// for u in g.nodes() { assert_eq!(comps[u], 0); } /// } /// /// let v = g.add_node(); /// { /// let (ncomps, comps) = algorithms::components(&g); /// assert_eq!(ncomps, 2); /// for u in g.nodes() { assert_eq!(comps[u], if u == v { 1 } else { 0 }); } /// } /// ``` pub fn components<'g, G>(g: &'g G) -> (usize, NodeVec<'g, G, usize>) where G: IndexGraph<'g> { if g.num_nodes() == 0 { return (0, nodevec![g; 0]); } let mut components = nodevec![g; usize::MAX]; let mut q = vec![]; let mut nodes = g.nodes(); let mut ncomponents = 0; loop { // find next node that has not been seen, yet while let Some(u) = nodes.next() { if components[u] == usize::MAX { // found a node, start new component components[u] = ncomponents; q.push(u); ncomponents += 1; break; } } // no unseen node found -> stop if q.is_empty() { return (ncomponents, components); } // do dfs from this node while let Some(u) = q.pop() { for (_, v) in g.neighs(u) { if components[v] != components[u] { components[v] = components[u]; q.push(v); } } } } } #[cfg(test)] mod tests { use {Graph, IndexGraph, LinkedListGraph}; use linkedlistgraph::Edge; use classes::*; use algorithms::complement; use std::cmp::{min, max}; #[test] fn test_complement() { let g: LinkedListGraph = cycle(5); let h: LinkedListGraph = complement(&g); let l: LinkedListGraph = complement(&h); fn to_id(g: &LinkedListGraph, e: Edge) -> (usize, usize) { let (u, v) = g.enodes(e); let (u, v) = (g.node_id(u), g.node_id(v)); (min(u, v), max(u, v)) } let mut gedges: Vec<_> = g.edges().map(|e| to_id(&g, e)).collect(); gedges.sort(); let mut hedges: Vec<_> = h.edges().map(|e| to_id(&h, e)).collect(); hedges.sort(); let mut ledges: Vec<_> = g.edges().map(|e| to_id(&l, e)).collect(); ledges.sort(); assert_eq!(hedges, vec![(0, 2), (0, 3), (1, 3), (1, 4), (2, 4)]); assert_eq!(gedges, ledges); } }