petgraph/algo/
k_shortest_path.rs

1use std::collections::{BinaryHeap, HashMap};
2
3use std::hash::Hash;
4
5use crate::algo::Measure;
6use crate::scored::MinScored;
7use crate::visit::{EdgeRef, IntoEdges, NodeCount, NodeIndexable, Visitable};
8
9/// \[Generic\] k'th shortest path algorithm.
10///
11/// Compute the length of the k'th shortest path from `start` to every reachable
12/// node.
13///
14/// The graph should be `Visitable` and implement `IntoEdges`. The function
15/// `edge_cost` should return the cost for a particular edge, which is used
16/// to compute path costs. Edge costs must be non-negative.
17///
18/// If `goal` is not `None`, then the algorithm terminates once the `goal` node's
19/// cost is calculated.
20///
21/// Computes in **O(k * (|E| + |V|*log(|V|)))** time (average).
22///
23/// Returns a `HashMap` that maps `NodeId` to path cost.
24/// # Example
25/// ```rust
26/// use petgraph::Graph;
27/// use petgraph::algo::k_shortest_path;
28/// use petgraph::prelude::*;
29/// use std::collections::HashMap;
30///
31/// let mut graph : Graph<(),(),Directed>= Graph::new();
32/// let a = graph.add_node(()); // node with no weight
33/// let b = graph.add_node(());
34/// let c = graph.add_node(());
35/// let d = graph.add_node(());
36/// let e = graph.add_node(());
37/// let f = graph.add_node(());
38/// let g = graph.add_node(());
39/// let h = graph.add_node(());
40/// // z will be in another connected component
41/// let z = graph.add_node(());
42///
43/// graph.extend_with_edges(&[
44///     (a, b),
45///     (b, c),
46///     (c, d),
47///     (d, a),
48///     (e, f),
49///     (b, e),
50///     (f, g),
51///     (g, h),
52///     (h, e)
53/// ]);
54/// // a ----> b ----> e ----> f
55/// // ^       |       ^       |
56/// // |       v       |       v
57/// // d <---- c       h <---- g
58///
59/// let expected_res: HashMap<NodeIndex, usize> = [
60///      (a, 7),
61///      (b, 4),
62///      (c, 5),
63///      (d, 6),
64///      (e, 5),
65///      (f, 6),
66///      (g, 7),
67///      (h, 8)
68///     ].iter().cloned().collect();
69/// let res = k_shortest_path(&graph,b,None,2, |_| 1);
70/// assert_eq!(res, expected_res);
71/// // z is not inside res because there is not path from b to z.
72/// ```
73pub fn k_shortest_path<G, F, K>(
74    graph: G,
75    start: G::NodeId,
76    goal: Option<G::NodeId>,
77    k: usize,
78    mut edge_cost: F,
79) -> HashMap<G::NodeId, K>
80where
81    G: IntoEdges + Visitable + NodeCount + NodeIndexable,
82    G::NodeId: Eq + Hash,
83    F: FnMut(G::EdgeRef) -> K,
84    K: Measure + Copy,
85{
86    let mut counter: Vec<usize> = vec![0; graph.node_count()];
87    let mut scores = HashMap::new();
88    let mut visit_next = BinaryHeap::new();
89    let zero_score = K::default();
90
91    visit_next.push(MinScored(zero_score, start));
92
93    while let Some(MinScored(node_score, node)) = visit_next.pop() {
94        counter[graph.to_index(node)] += 1;
95        let current_counter = counter[graph.to_index(node)];
96
97        if current_counter > k {
98            continue;
99        }
100
101        if current_counter == k {
102            scores.insert(node, node_score);
103        }
104
105        //Already reached goal k times
106        if goal.as_ref() == Some(&node) && current_counter == k {
107            break;
108        }
109
110        for edge in graph.edges(node) {
111            visit_next.push(MinScored(node_score + edge_cost(edge), edge.target()));
112        }
113    }
114    scores
115}
petgraph/algo/k_shortest_path.rs

petgraph/algo/
k_shortest_path.rs
