algorithms-edu 0.2.7

//! Implementation of Dinic's network flow algorithm. The algorithm works by first constructing a
//! level graph using a BFS and then finding augmenting paths on the level graph using multiple DFSs.
//!
//! - Time Complexity: O(EV²)
//!
//! # Resources
//!
//! - [W. Fiset's video 1](https://www.youtube.com/watch?v=M6cm8UeeziI&list=PLDV1Zeh2NRsDGO4--qE8yH72HFL1Km93P&index=42)
//! - [W. Fiset's video 2](https://www.youtube.com/watch?v=_SdF4KK_dyM&list=PLDV1Zeh2NRsDGO4--qE8yH72HFL1Km93P&index=43)
//! - [Wikipedia](https://www.wikiwand.com/en/Dinic%27s_algorithm)

use super::{Edge, MaxFlowSolver, NetworkFlowAdjacencyList};
use std::{cell::RefCell, collections::VecDeque, rc::Rc};
pub struct DinicSolver<'a> {
    g: &'a mut NetworkFlowAdjacencyList,
    n: usize,
    levels: Vec<isize>,
}

const INF: i32 = i32::MAX / 2;

impl<'a> DinicSolver<'a> {
    fn init(g: &'a mut NetworkFlowAdjacencyList) -> Self {
        let n = g.node_count();
        Self {
            g,
            n,
            levels: vec![0; n],
        }
    }
    fn solve(&mut self) -> i32 {
        let mut max_flow = 0;

        while self.bfs() {
            // `next[i]` indicates the next unused edge index in the adjacency list for node `i`. This is part
            // of the Shimon Even and Alon Itai optimization of pruning deads ends as part of the DFS phase.
            let mut next = vec![0usize; self.n];
            // Find max flow by adding all augmenting path flows.
            let mut f = -1;
            while f != 0 {
                f = self.dfs(self.g.source, &mut next, INF);
                max_flow += f;
            }
        }
        max_flow
    }

    // for i in 0..self.n if (self.levels[i] != -1) minCut[i] = true;
    // }

    // Do a BFS from source to sink and compute the depth/level of each node
    // which is the minimum number of edges from that node to the source.
    fn bfs(&mut self) -> bool {
        self.levels = vec![-1; self.n];
        self.levels[self.g.source] = 0;
        let mut q = VecDeque::with_capacity(self.n);
        q.push_back(self.g.source);
        while let Some(node) = q.pop_front() {
            for edge in &self.g[node] {
                let edge = edge.borrow();
                let rcap = edge.reamaining_capacity();
                if rcap > 0 && self.levels[edge.to] == -1 {
                    self.levels[edge.to] = self.levels[node] + 1;
                    q.push_back(edge.to)
                }
            }
        }
        self.levels[self.g.sink] != -1
    }

    fn dfs(&mut self, at: usize, next: &mut [usize], flow: i32) -> i32 {
        if at == self.g.sink {
            return flow;
        }
        let num_edges = self.g[at].len();
        while next[at] < num_edges {
            let edge = unsafe { &*(&self.g[at][next[at]] as *const Rc<RefCell<Edge>>) };
            let mut _edge = edge.borrow_mut();
            let rcap = _edge.reamaining_capacity();
            if rcap > 0 && self.levels[_edge.to] == self.levels[at] + 1 {
                let bottleneck = self.dfs(_edge.to, next, std::cmp::min(flow, rcap));
                if bottleneck > 0 {
                    _edge.augment(bottleneck);
                    return bottleneck;
                }
            }
            next[at] += 1;
        }

        0
    }
}

impl<'a> MaxFlowSolver for DinicSolver<'a> {
    fn max_flow(graph: &mut NetworkFlowAdjacencyList) -> i32 {
        let mut s = DinicSolver::init(graph);
        s.solve()
    }
}

#[cfg(test)]
mod tests {
    use super::*;

    fn test_max_flow(n: usize, edges: &[(usize, usize, i32)], expected_max_flow: i32) {
        let mut graph = NetworkFlowAdjacencyList::from_edges(n, edges);
        let max_flow = DinicSolver::max_flow(&mut graph);
        assert_eq!(max_flow, expected_max_flow);
    }

    #[test]
    fn test_small_graph() {
        test_max_flow(
            6,
            &[
                // Source edges
                (5, 0, 10),
                (5, 1, 10),
                // Sink edges
                (2, 4, 10),
                (3, 4, 10),
                // Middle edges
                (0, 1, 2),
                (0, 2, 4),
                (0, 3, 8),
                (1, 3, 9),
                (3, 2, 6),
            ],
            19,
        );
    }

    #[test]
    fn test_disconnected() {
        test_max_flow(4, &[(3, 0, 9), (1, 2, 9)], 0);
    }

    #[test]
    fn test_medium_graph() {
        test_max_flow(
            12,
            &[
                // from source
                (11, 0, 5),
                (11, 1, 20),
                (11, 2, 10),
                // to sink
                (7, 10, 7),
                (8, 10, 15),
                (9, 10, 60),
                // middle
                (0, 1, 3),
                (0, 5, 4),
                (1, 4, 14),
                (1, 5, 14),
                (2, 1, 5),
                (2, 3, 4),
                (3, 4, 3),
                (3, 9, 11),
                (4, 6, 4),
                (4, 8, 22),
                (5, 6, 8),
                (5, 7, 3),
                (6, 7, 12),
                (7, 8, 9),
                (8, 9, 11),
            ],
            29,
        );
    }
}