use std::cmp::Reverse;
use std::collections::BinaryHeap;

/// Computes shortest distances from `start` in a directed, non-negative graph.
///
/// Each adjacency-list entry contains `(neighbor, edge_weight)`.
fn dijkstra(graph: &[Vec<(usize, u64)>], start: usize) -> Vec<Option<u64>> {
    assert!(start < graph.len(), "start vertex is out of bounds");

    let mut distances = vec![None; graph.len()];
    let mut queue = BinaryHeap::new();

    distances[start] = Some(0);
    queue.push(Reverse((0_u64, start)));

    while let Some(Reverse((distance, vertex))) = queue.pop() {
        // Ignore stale queue entries.
        if distances[vertex] != Some(distance) {
            continue;
        }

        for &(neighbor, weight) in &graph[vertex] {
            assert!(neighbor < graph.len(), "neighbor is out of bounds");

            // An overflowing path cannot be represented by u64.
            let Some(candidate) = distance.checked_add(weight) else {
                continue;
            };

            if distances[neighbor].is_none_or(|current| candidate < current) {
                distances[neighbor] = Some(candidate);
                queue.push(Reverse((candidate, neighbor)));
            }
        }
    }

    distances
}

fn main() {
    let graph = vec![
        vec![(1, 4), (2, 1)],
        vec![(3, 1)],
        vec![(1, 2), (3, 5)],
        vec![],
    ];

    println!("{:?}", dijkstra(&graph, 0));
}

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

    #[test]
    fn finds_shortest_paths() {
        let graph = vec![
            vec![(1, 4), (2, 1)],
            vec![(3, 1)],
            vec![(1, 2), (3, 5)],
            vec![],
        ];

        assert_eq!(
            dijkstra(&graph, 0),
            vec![Some(0), Some(3), Some(1), Some(4)]
        );
    }

    #[test]
    fn leaves_unreachable_vertices_unset() {
        let graph = vec![vec![(1, 7)], vec![], vec![]];

        assert_eq!(dijkstra(&graph, 0), vec![Some(0), Some(7), None]);
    }
}