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//! # Breadth First Search
//!
//! - Time Complexity: O(V + E)
//!
//! # Resources
//!
//! - [W. Fiset's video](https://www.youtube.com/watch?v=oDqjPvD54Ss&list=PLDV1Zeh2NRsDGO4--qE8yH72HFL1Km93P&index=5)
//! - [W. Fiset's video](https://www.youtube.com/watch?v=KiCBXu4P-2Y&list=PLDV1Zeh2NRsDGO4--qE8yH72HFL1Km93P&index=6)
use crate::algo::graph::UnweightedAdjacencyList;
use std::collections::VecDeque;
impl UnweightedAdjacencyList {
/// Perform a breadth first search on a graph a starting node `start`.
pub fn bfs(&self, start: usize) -> BfsResult {
// Each breadth first search layer gets separated by a DEPTH_TOKEN.
// DEPTH_TOKENs help count the distance from one node to another because
// we can increment the depth counter each time a DEPTH_TOKEN is encountered
const DEPTH_TOKEN: usize = usize::MAX;
// number of nodes
let n = self.node_count();
// tracks who the parent of `i` was
let mut prev = vec![None; n];
let mut visited = vec![false; n];
let mut queue = VecDeque::with_capacity(n);
// Start by visiting the `start` node and push it to the queue.
queue.push_back(start);
queue.push_back(DEPTH_TOKEN);
visited[start] = true;
let mut depth = 0;
// Continue until the BFS is done.
while let Some(node) = queue.pop_front() {
if queue.is_empty() {
break;
}
if node == DEPTH_TOKEN {
queue.push_back(DEPTH_TOKEN);
depth += 1;
continue;
}
let neighbours = &self[node];
// Loop through all edges attached to this node. Mark nodes as visited once they`re
// in the queue. This will prevent having duplicate nodes in the queue and speedup the BFS.
for &neighbour in neighbours {
if !visited[neighbour] {
visited[neighbour] = true;
prev[neighbour] = Some(node);
queue.push_back(neighbour);
}
}
}
BfsResult { prev, depth }
}
}
pub struct BfsResult {
prev: Vec<Option<usize>>,
pub depth: usize,
}
impl BfsResult {
pub fn path_to(&self, end: usize) -> Vec<usize> {
let mut path = Vec::new();
let mut at = end;
while let Some(prev_parent) = self.prev[at] {
at = prev_parent;
path.push(at);
}
path.reverse();
path
}
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_bfs_adjacency_list_iterative() {
let graph = UnweightedAdjacencyList::new_undirected(
13,
&[
[0, 7],
[0, 9],
[0, 11],
[7, 11],
[7, 6],
[7, 3],
[6, 5],
[3, 4],
[2, 3],
[2, 12],
[12, 8],
[8, 1],
[1, 10],
[10, 9],
[9, 8],
],
);
let (start, end) = (10, 5);
let bfs_result = graph.bfs(start);
let depth = bfs_result.depth;
assert_eq!(depth, 5);
let path = bfs_result.path_to(end);
let fmtpath = format_path(&path);
println!(
"The shortest path from {} to {} is: {}\n",
start, end, fmtpath
);
assert_eq!(&fmtpath, "10 -> 9 -> 0 -> 7 -> 6");
}
fn format_path(path: &Vec<usize>) -> String {
path.iter()
.map(|&x| x.to_string())
.collect::<Vec<_>>()
.join(" -> ")
}
}
pub mod fast_queue {
//! # Breadth First Search (Iterative Implementation)
//!
//! This implementation does not track the depth, and thus can make use of the faster fixed size queue.
use crate::algo::graph::UnweightedAdjacencyList;
use crate::data_structures::queue::Queue;
pub trait BfsReconstructPath {
fn bfs<T: Queue<usize>>(&self, start: usize) -> Vec<Option<usize>>;
fn reconstruct_path<T: Queue<usize>>(&self, start: usize, end: usize) -> Vec<usize> {
let prev = self.bfs::<T>(start);
let mut path = Vec::new();
let mut at = end;
while let Some(prev_parent) = prev[at] {
at = prev_parent;
path.push(at);
}
path.reverse();
path
}
}
impl BfsReconstructPath for UnweightedAdjacencyList {
/// Perform a breadth first search on a graph a starting node `start`.
fn bfs<T: Queue<usize>>(&self, start: usize) -> Vec<Option<usize>> {
// number of nodes
let n = self.node_count();
// tracks who the parent of `i` was
let mut prev = vec![None; n];
let mut visited = vec![false; n];
let mut queue = T::with_capacity(n);
// Start by visiting the `start` node and push it to the queue.
queue.push_back(start);
visited[start] = true;
// Continue until the BFS is donw.
while let Some(node) = queue.pop_front() {
let neighbours = &self[node];
// Loop through all edges attached to this node. Mark nodes as visited once they`re
// in the queue. This will prevent having duplicate nodes in the queue and speedup the BFS.
for &neighbour in neighbours {
if !visited[neighbour] {
visited[neighbour] = true;
prev[neighbour] = Some(node);
queue.push_back(neighbour);
}
}
}
prev
}
}
#[cfg(test)]
mod tests {
use super::*;
use crate::data_structures::queue::FixedCapacityQueue;
use std::collections::VecDeque;
#[test]
fn test_bfs_adjacency_list_iterative() {
let graph = UnweightedAdjacencyList::new_undirected(
13,
&[
[0, 7],
[0, 9],
[0, 11],
[7, 11],
[7, 6],
[7, 3],
[6, 5],
[3, 4],
[2, 3],
[2, 12],
[12, 8],
[8, 1],
[1, 10],
[10, 9],
[9, 8],
],
);
let (start, end) = (10, 5);
let path = graph.reconstruct_path::<VecDeque<usize>>(start, end);
let fmtpath = format_path(&path);
println!(
"The shortest path from {} to {} is: {}\n",
start, end, fmtpath
);
assert_eq!(&fmtpath, "10 -> 9 -> 0 -> 7 -> 6");
let path = graph.reconstruct_path::<FixedCapacityQueue<usize>>(start, end);
let fmtpath = format_path(&path);
println!(
"The shortest path from {} to {} is: {}\n",
start, end, fmtpath
);
assert_eq!(&fmtpath, "10 -> 9 -> 0 -> 7 -> 6");
}
fn format_path(path: &Vec<usize>) -> String {
path.iter()
.map(|&x| x.to_string())
.collect::<Vec<_>>()
.join(" -> ")
}
}
}