algorithms_edu/algo/graph/network_flow/
dinic.rs

1//! Implementation of Dinic's network flow algorithm. The algorithm works by first constructing a
2//! level graph using a BFS and then finding augmenting paths on the level graph using multiple DFSs.
3//!
4//! - Time Complexity: O(EV²)
5//!
6//! # Resources
7//!
8//! - [W. Fiset's video 1](https://www.youtube.com/watch?v=M6cm8UeeziI&list=PLDV1Zeh2NRsDGO4--qE8yH72HFL1Km93P&index=42)
9//! - [W. Fiset's video 2](https://www.youtube.com/watch?v=_SdF4KK_dyM&list=PLDV1Zeh2NRsDGO4--qE8yH72HFL1Km93P&index=43)
10//! - [Wikipedia](https://www.wikiwand.com/en/Dinic%27s_algorithm)
11
12use super::{Edge, MaxFlowSolver, NetworkFlowAdjacencyList};
13use std::{cell::RefCell, collections::VecDeque, rc::Rc};
14pub struct DinicSolver<'a> {
15    g: &'a mut NetworkFlowAdjacencyList,
16    n: usize,
17    levels: Vec<isize>,
18}
19
20const INF: i32 = i32::MAX / 2;
21
22impl<'a> DinicSolver<'a> {
23    fn init(g: &'a mut NetworkFlowAdjacencyList) -> Self {
24        let n = g.node_count();
25        Self {
26            g,
27            n,
28            levels: vec![0; n],
29        }
30    }
31    fn solve(&mut self) -> i32 {
32        let mut max_flow = 0;
33
34        while self.bfs() {
35            // `next[i]` indicates the next unused edge index in the adjacency list for node `i`. This is part
36            // of the Shimon Even and Alon Itai optimization of pruning deads ends as part of the DFS phase.
37            let mut next = vec![0usize; self.n];
38            // Find max flow by adding all augmenting path flows.
39            let mut f = -1;
40            while f != 0 {
41                f = self.dfs(self.g.source, &mut next, INF);
42                max_flow += f;
43            }
44        }
45        max_flow
46    }
47
48    // for i in 0..self.n if (self.levels[i] != -1) minCut[i] = true;
49    // }
50
51    // Do a BFS from source to sink and compute the depth/level of each node
52    // which is the minimum number of edges from that node to the source.
53    fn bfs(&mut self) -> bool {
54        self.levels = vec![-1; self.n];
55        self.levels[self.g.source] = 0;
56        let mut q = VecDeque::with_capacity(self.n);
57        q.push_back(self.g.source);
58        while let Some(node) = q.pop_front() {
59            for edge in &self.g[node] {
60                let edge = edge.borrow();
61                let rcap = edge.reamaining_capacity();
62                if rcap > 0 && self.levels[edge.to] == -1 {
63                    self.levels[edge.to] = self.levels[node] + 1;
64                    q.push_back(edge.to)
65                }
66            }
67        }
68        self.levels[self.g.sink] != -1
69    }
70
71    fn dfs(&mut self, at: usize, next: &mut [usize], flow: i32) -> i32 {
72        if at == self.g.sink {
73            return flow;
74        }
75        let num_edges = self.g[at].len();
76        while next[at] < num_edges {
77            let edge = unsafe { &*(&self.g[at][next[at]] as *const Rc<RefCell<Edge>>) };
78            let mut _edge = edge.borrow_mut();
79            let rcap = _edge.reamaining_capacity();
80            if rcap > 0 && self.levels[_edge.to] == self.levels[at] + 1 {
81                let bottleneck = self.dfs(_edge.to, next, std::cmp::min(flow, rcap));
82                if bottleneck > 0 {
83                    _edge.augment(bottleneck);
84                    return bottleneck;
85                }
86            }
87            next[at] += 1;
88        }
89
90        0
91    }
92}
93
94impl<'a> MaxFlowSolver for DinicSolver<'a> {
95    fn max_flow(graph: &mut NetworkFlowAdjacencyList) -> i32 {
96        let mut s = DinicSolver::init(graph);
97        s.solve()
98    }
99}
100
101#[cfg(test)]
102mod tests {
103    use super::*;
104
105    fn test_max_flow(n: usize, edges: &[(usize, usize, i32)], expected_max_flow: i32) {
106        let mut graph = NetworkFlowAdjacencyList::from_edges(n, edges);
107        let max_flow = DinicSolver::max_flow(&mut graph);
108        assert_eq!(max_flow, expected_max_flow);
109    }
110
111    #[test]
112    fn test_small_graph() {
113        test_max_flow(
114            6,
115            &[
116                // Source edges
117                (5, 0, 10),
118                (5, 1, 10),
119                // Sink edges
120                (2, 4, 10),
121                (3, 4, 10),
122                // Middle edges
123                (0, 1, 2),
124                (0, 2, 4),
125                (0, 3, 8),
126                (1, 3, 9),
127                (3, 2, 6),
128            ],
129            19,
130        );
131    }
132
133    #[test]
134    fn test_disconnected() {
135        test_max_flow(4, &[(3, 0, 9), (1, 2, 9)], 0);
136    }
137
138    #[test]
139    fn test_medium_graph() {
140        test_max_flow(
141            12,
142            &[
143                // from source
144                (11, 0, 5),
145                (11, 1, 20),
146                (11, 2, 10),
147                // to sink
148                (7, 10, 7),
149                (8, 10, 15),
150                (9, 10, 60),
151                // middle
152                (0, 1, 3),
153                (0, 5, 4),
154                (1, 4, 14),
155                (1, 5, 14),
156                (2, 1, 5),
157                (2, 3, 4),
158                (3, 4, 3),
159                (3, 9, 11),
160                (4, 6, 4),
161                (4, 8, 22),
162                (5, 6, 8),
163                (5, 7, 3),
164                (6, 7, 12),
165                (7, 8, 9),
166                (8, 9, 11),
167            ],
168            29,
169        );
170    }
171}
algorithms_edu/algo/graph/network_flow/dinic.rs

algorithms_edu/algo/graph/network_flow/
dinic.rs
