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use std::collections::VecDeque;
use std::collections::HashSet;
/// A graph is represeted by as a weighted
/// [Adjenceny matrix](http://en.wikipedia.org/wiki/Adjacency_matrix)
pub struct Graph {
/// The underlaying graph represented here with weights as an i32 (should
/// probably be generic) the graph is represented as an
/// [Adjenceny matrix](http://en.wikipedia.org/wiki/Adjacency_matrix) of
/// Optionals, where None indicates that there doesn't exist a vertex and
/// Some<i32> indicates that There is a vertex of weight i32.
graph: Vec<Vec<Option<i32>>>
}
impl Graph {
/// `new` allows for initializing the graph struct with a given adjecency matrix
///
/// ## Arguments
/// * `input` - an adjecency matrix in made out of a two-dimensional `Vec` of
/// weights. Weights are represented as `i32`:s and can thus be positive or
/// negative numbers.
///
/// ## Example
/// ```ignore
/// let rawgraph = vec![vec![Some(0), Some(20), Some(80), Some(50), None, None],
/// vec![ None, Some(0), None, None, None, None],
/// vec![ None, None, Some(0), None, None, None],
/// vec![ None, None, None, Some(0), Some(50), None],
/// vec![ None, None, Some(20), None, Some(0), Some(50)],
/// vec![ None, None, None, None, None, Some(0)]];
/// let g = Graph::new(rawgraph);
/// ```
pub fn new(input: Vec<Vec<Option<i32>>>) -> Graph { Graph { graph: input } }
/*
1 procedure BFS(G,v) is
2 let Q be a queue
3 Q.push(v)
4 label v as discovered
5 while Q is not empty
6 v ← Q.pop()
7 for all edges from v to w in G.adjacentEdges(v) do
8 if w is not labeled as discovered
9 Q.push(w)
10 label w as discovered
*/
/// `breadth_first_search` implements breadth first search from `start` to the
/// `target` and returns the path found as a `VecDeque<usize>` of nodes. This
/// is an optional type as there might not be a path.
///
/// **NOTE** as this is breadth first search this search ignores any assigned
/// weight to nodes.
///
/// ## Arguments
/// * `start` - an `usize` designating the start node, or row in the adjecency matrix
/// * `target` - an `usize` designating the target node, or row in the adjecency matrix
///
/// ## Returns
/// Either the found path between start and target as a `VecDeque` of `usize`:s
/// or `None` if there is no path.
pub fn breadth_first_search(&self, start: usize, target: usize) -> Option<VecDeque<usize>> {
return self.inner_search(start, target, true)
}
/// `depth_first_search` implements depth first search from `start` to the
/// `target` and returns the path found as a `VecDeque<usize>` of nodes. This
/// is an optional type as there might not be a path.
///
/// **NOTE** as this is depth first search this search ignores any assigned
/// weight to nodes.
///
/// ## Arguments
/// * `start` - an `usize` designating the start node, or row in the adjecency matrix
/// * `target` - an `usize` designating the target node, or row in the adjecency matrix
///
/// ## Returns
/// Either the found path between start and target as a `VecDeque` of `usize`:s
/// or `None` if there is no path.
pub fn depth_first_search(&self, start: usize, target: usize) -> Option<VecDeque<usize>> {
return self.inner_search(start, target, false)
}
fn inner_search(&self, start: usize, target: usize, bfs: bool) -> Option<VecDeque<usize>> {
let mut q: VecDeque<usize> = VecDeque::new();
let mut discovered: HashSet<usize> = HashSet::new();
let mut prev: Vec<usize> = Vec::with_capacity(self.graph.len());
let mut pathfound = false;
for _ in (0..self.graph.len()) { prev.push(0); }
q.push_back(start);
discovered.insert(start);
while !q.is_empty() {
let mut v: Option<usize>;
if bfs {
v = q.pop_front()
} else {
v = q.pop_back();
}
match v {
None => {}, // q is empty
Some(v) => { // we are working on a new layer, branch the queue?
if !discovered.contains(&v) {
discovered.insert(v);
}
if v == target {
pathfound = true;
}
for i in (0..self.graph[v].len()) {
match self.graph[v][i] {
None => {}, // no vertex between v and i
Some(_) => {
if !discovered.contains(&i) {
q.push_back(i);
prev[i]=v; //track prev (v) on i
}
}
}
}
}
}
}
if pathfound {
let mut path: VecDeque<usize> = VecDeque::new();
let mut curr = target;
// backtrack over the prev array to construct the path
while curr != start {
path.push_front(curr);
curr = prev[curr];
}
path.push_front(start);
return Some(path)
}
return None
}
}
#[test]
fn breadth_first_search_test() {
let testgraph = vec![vec![Some(0), Some(20), Some(80), Some(50), None, None, None],
vec![ None, Some(0), None, None, None, None, None],
vec![ None, None, Some(0), None, None, None, Some(50)],
vec![ None, None, None, Some(0), Some(50), None, None],
vec![ None, None, Some(20), None, Some(0), Some(50), Some(40)],
vec![ None, None, None, None, None, Some(0), None],
vec![ None, None, None, None, None, None, Some(0)]];
let start: usize = 0;
let target: usize = 6;
let g = Graph::new(testgraph);
let res = g.breadth_first_search(start, target);
match res {
None => {
println!("Breadth first search returned None");
assert!(false);
}
Some(result) => {
println!("Breadth first search returned something: {:?}", result);
assert_eq!(result[result.len()-1], target);
assert_eq!(result[0], start);
}
}
}
#[test]
fn breadth_first_search_test_no_valid_path() {
let testgraph = vec![vec![Some(0), Some(20), Some(80), Some(50), None, None, None],
vec![ None, Some(0), None, None, None, None, None],
vec![ None, None, Some(0), None, None, None, Some(50)],
vec![ None, None, None, Some(0), Some(50), None, None],
vec![ None, None, Some(20), None, Some(0), None, Some(40)],
vec![ None, None, None, None, None, Some(0), None],
vec![ None, None, None, None, None, None, Some(0)]];
let start: usize = 0;
let target: usize = 5; // There is no valid path between 0 and 5
let g = Graph::new(testgraph);
let res = g.breadth_first_search(start, target);
// The expected return value is None
match res {
None => {
println!("Breadth first search returned None");
assert!(true);
}
Some(result) => {
println!("Breadth first search returned something: {:?}", result);
assert_eq!(result[result.len()-1], target);
assert_eq!(result[0], start);
assert!(false);
}
}
}
#[test]
fn depth_first_search_test() {
let testgraph = vec![vec![Some(0), Some(20), Some(80), Some(50), None, None, None],
vec![ None, Some(0), None, None, None, None, None],
vec![ None, None, Some(0), None, None, None, Some(50)],
vec![ None, None, None, Some(0), Some(50), None, None],
vec![ None, None, Some(20), None, Some(0), Some(50), Some(40)],
vec![ None, None, None, None, None, Some(0), None],
vec![ None, None, None, None, None, None, Some(0)]];
let start: usize = 0;
let target: usize = 6;
let g = Graph::new(testgraph);
let res = g.depth_first_search(start, target);
match res {
None => {
println!("Depth first search returned None");
assert!(false);
}
Some(result) => {
println!("Depth first search returned something: {:?}", result);
assert_eq!(result[result.len()-1], target);
assert_eq!(result[0], start);
}
}
}
#[test]
fn depth_first_search_test_no_valid_path() {
let testgraph = vec![vec![Some(0), Some(20), Some(80), Some(50), None, None, None],
vec![ None, Some(0), None, None, None, None, None],
vec![ None, None, Some(0), None, None, None, Some(50)],
vec![ None, None, None, Some(0), Some(50), None, None],
vec![ None, None, Some(20), None, Some(0), None, Some(40)],
vec![ None, None, None, None, None, Some(0), None],
vec![ None, None, None, None, None, None, Some(0)]];
let start: usize = 0;
let target: usize = 5; // There is no valid path between 0 and 5
let g = Graph::new(testgraph);
let res = g.depth_first_search(start, target);
// The expected return value is None
match res {
None => {
println!("Depth first search returned None");
assert!(true);
}
Some(result) => {
println!("Depth first search returned something: {:?}", result);
assert_eq!(result[result.len()-1], target);
assert_eq!(result[0], start);
assert!(false);
}
}
}