Shortest Path (Unweighted, via BFS)

BFS explores a graph layer by layer, so the first time it reaches a vertex is along a shortest path. Track dist[v] and parent[v] while exploring, then walk parents back from the target to reconstruct the route.

Algorithm

On the canonical graph from graph-adjacency-list, the shortest path from 1 to 6 is [1, 2, 4, 5, 6] with distance 4. The path is rebuilt from parent: 6 -> 5 -> 4 -> 2 -> 1, reversed.

Basic Implementation

basic.rs

use std::collections::HashMap;
use std::collections::VecDeque;
fn main() {
	let mut adj: HashMap<i32, Vec<i32>> = HashMap::new();
	adj.insert(1, vec![2, 3]);
	adj.insert(2, vec![1, 4]);
	adj.insert(3, vec![1, 4]);
	adj.insert(4, vec![2, 3, 5]);
	adj.insert(5, vec![4, 6]);
	adj.insert(6, vec![5]);
	let src = 1;
	let dst = 6;
	let mut dist: HashMap<i32, i32> = HashMap::new();
	let mut parent: HashMap<i32, i32> = HashMap::new();
	dist.insert(src, 0);
	parent.insert(src, 0);
	let mut queue: VecDeque<i32> = VecDeque::new();
	queue.push_back(src);
	while let Some(v) = queue.pop_front() {
		for &nb in &adj[&v] {
			if !dist.contains_key(&nb) {
				let d = dist[&v] + 1;
				dist.insert(nb, d);
				parent.insert(nb, v);
				queue.push_back(nb);
			}
		}
	}
	let mut path: Vec<i32> = Vec::new();
	let mut node = dst;
	while node != 0 {
		path.push(node);
		node = parent[&node];
	}
	path.reverse();
	println!("{:?}", path);
	println!("{}", dist[&dst]);
}

Complexity

Time: O(V + E)
Space: O(V)

Implementation notes

Rust: a dist HashMap doubles as the visited check, parent records predecessors (0 marks the source), and a VecDeque gives FIFO order.
The replay shows dist, parent, and the queue filling in, then the reconstructed path, matching the lesson spec.

layers equal distance BFS order equals distance in an unweighted graph.