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

/// Computes shortest-path distances from `source` in a graph with non-negative weights.
///
/// The graph is an adjacency list where `graph[u]` contains `(v, weight)` edges.
/// Unreachable vertices are returned as `None`.
pub fn dijkstra(graph: &[Vec<(usize, u64)>], source: usize) -> Vec<Option<u64>> {
    let mut dist = vec![u64::MAX; graph.len()];

    if source >= graph.len() {
        return vec![None; graph.len()];
    }

    let mut heap = BinaryHeap::new();
    dist[source] = 0;
    heap.push(Reverse((0_u64, source)));

    while let Some(Reverse((cost, u))) = heap.pop() {
        // Ignore stale heap entries produced before a shorter path was found.
        if cost != dist[u] {
            continue;
        }

        for &(v, weight) in &graph[u] {
            if v >= graph.len() {
                continue;
            }

            if let Some(next_cost) = cost.checked_add(weight) {
                if next_cost < dist[v] {
                    dist[v] = next_cost;
                    heap.push(Reverse((next_cost, v)));
                }
            }
        }
    }

    dist.into_iter()
        .map(|d| if d == u64::MAX { None } else { Some(d) })
        .collect()
}

#[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 marks_unreachable_vertices() {
        let graph = vec![
            vec![(1, 7)],
            vec![],
            vec![(0, 3)],
        ];

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