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use petgraph::algo::dinics;
use petgraph::prelude::Graph;
#[test]
fn test_dinics_a() {
// Example from https://downey.io/blog/max-flow-ford-fulkerson-algorithm-explanation/
// Graph Image: https://images.downey.io/max-flow/max-flow-3.png
let mut graph = Graph::<usize, u16>::new();
let source = graph.add_node(0);
let _ = graph.add_node(1);
let _ = graph.add_node(2);
let sink = graph.add_node(3);
graph.extend_with_edges([(0, 1, 3), (0, 2, 2), (1, 2, 5), (1, 3, 2), (2, 3, 3)]);
let (max_flow, _) = dinics(&graph, source, sink);
assert_eq!(5, max_flow);
}
#[test]
fn test_dinics_b() {
// Example from https://brilliant.org/wiki/ford-fulkerson-algorithm/
let mut graph = Graph::<usize, f32>::new();
let source = graph.add_node(0);
let _ = graph.add_node(1);
let _ = graph.add_node(2);
let _ = graph.add_node(3);
let _ = graph.add_node(4);
let sink = graph.add_node(5);
graph.extend_with_edges([
(0, 1, 4.),
(0, 2, 3.),
(1, 3, 4.),
(2, 4, 6.),
(3, 2, 3.),
(3, 5, 2.),
(4, 5, 6.),
]);
let (max_flow, _) = dinics(&graph, source, sink);
assert_eq!(7.0, max_flow);
}
#[test]
fn test_dinics_c() {
// Example from https://cp-algorithms.com/graph/edmonds_karp.html
let mut graph = Graph::<usize, f32>::new();
let source = graph.add_node(0);
let _ = graph.add_node(1);
let _ = graph.add_node(2);
let _ = graph.add_node(3);
let _ = graph.add_node(4);
let sink = graph.add_node(5);
graph.extend_with_edges([
(0, 1, 7.),
(0, 2, 4.),
(1, 3, 5.),
(1, 4, 3.),
(2, 1, 3.),
(2, 4, 2.),
(3, 5, 8.),
(4, 3, 3.),
(4, 5, 5.),
]);
let (max_flow, _) = dinics(&graph, source, sink);
assert_eq!(10.0, max_flow);
}
#[test]
fn test_dinics_d() {
// Example from https://www.programiz.com/dsa/ford-fulkerson-algorithm (corrected: result not 6 but 5)
let mut graph = Graph::<u8, f32>::new();
let source = graph.add_node(0);
let _ = graph.add_node(1);
let _ = graph.add_node(2);
let _ = graph.add_node(3);
let _ = graph.add_node(4);
let sink = graph.add_node(5);
graph.extend_with_edges([
(0, 1, 8.),
(0, 2, 3.),
(1, 3, 9.),
(2, 3, 7.),
(2, 4, 4.),
(3, 5, 2.),
(4, 5, 5.),
]);
let (max_flow, _) = dinics(&graph, source, sink);
assert_eq!(5.0, max_flow);
}
#[test]
fn test_dinics_e() {
let mut graph = Graph::<u8, u8>::new();
let source = graph.add_node(0);
let _ = graph.add_node(1);
let _ = graph.add_node(2);
let _ = graph.add_node(3);
let _ = graph.add_node(4);
let sink = graph.add_node(5);
graph.extend_with_edges([
(0, 1, 16),
(0, 2, 13),
(1, 2, 10),
(1, 3, 12),
(2, 1, 4),
(2, 4, 14),
(3, 2, 9),
(3, 5, 20),
(4, 3, 7),
(4, 5, 4),
]);
let (max_flow, _) = dinics(&graph, source, sink);
assert_eq!(23, max_flow);
}
#[test]
fn test_dinics_f() {
// Example taken from https://medium.com/@jithmisha/solving-the-maximum-flow-problem-with-ford-fulkerson-method-3fccc2883dc7
let mut graph = Graph::<u8, u8>::new();
let source = graph.add_node(0);
let _ = graph.add_node(1);
let _ = graph.add_node(2);
let _ = graph.add_node(3);
let _ = graph.add_node(4);
let sink = graph.add_node(5);
graph.extend_with_edges([
(0, 1, 10),
(0, 2, 10),
(1, 2, 2),
(1, 3, 4),
(1, 4, 8),
(2, 4, 9),
(3, 5, 10),
(4, 3, 6),
(4, 5, 10),
]);
let (max_flow, _) = dinics(&graph, source, sink);
assert_eq!(19, max_flow);
}
#[test]
fn test_dinics_g() {
// Example that can lead to invalid answers if backward edges
// in residual network are not considered, resulting in a flow of 3
// instead of the maximum 4
let mut g = Graph::<(), u32>::new();
let s = g.add_node(());
let a = g.add_node(());
let b = g.add_node(());
let c = g.add_node(());
let d = g.add_node(());
let t = g.add_node(());
g.add_edge(s, a, 2);
g.add_edge(s, b, 2);
g.add_edge(a, c, 1); // misleading edge
g.add_edge(a, d, 2);
g.add_edge(b, c, 2);
g.add_edge(c, t, 2);
g.add_edge(d, t, 2);
let (flow, _) = dinics(&g, s, t);
assert_eq!(flow, 4);
}
#[cfg(feature = "stable_graph")]
#[test]
fn test_dinics_stable_graph() {
use petgraph::prelude::StableGraph;
// Example from https://downey.io/blog/max-flow-ford-fulkerson-algorithm-explanation/
// Graph Image: https://images.downey.io/max-flow/max-flow-3.png
let mut graph = StableGraph::<usize, u16>::new();
let source = graph.add_node(0);
let _ = graph.add_node(1);
let _ = graph.add_node(2);
let node_to_remove = graph.add_node(3);
let sink = graph.add_node(4);
graph.extend_with_edges([
(0, 1, 3),
(0, 2, 2),
(1, 2, 5),
(1, 4, 2),
(2, 4, 3),
(0, 3, 1),
(3, 4, 3),
(1, 3, 3),
]);
graph.remove_node(node_to_remove);
let (max_flow, _) = dinics(&graph, source, sink);
assert_eq!(5, max_flow);
}
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