Added dikjstra algorithm

exercises/Algorithms/Dijkstra Algorithm/.gitignore

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+/target

exercises/Algorithms/Dijkstra Algorithm/Cargo.lock

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+# This file is automatically @generated by Cargo.
+# It is not intended for manual editing.
+version = 3
+
+[[package]]
+name = "graph-in-rust"
+version = "0.1.0"

exercises/Algorithms/Dijkstra Algorithm/Cargo.toml

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+[package]
+name = "graph-in-rust"
+version = "0.1.0"
+edition = "2021"
+
+# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
+
+[dependencies]

exercises/Algorithms/Dijkstra Algorithm/readme.md

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+## Dijsktra Algorithm in Rust 
+
+The `src` directory consist of 2 files: `main.rs` and `graph.in`. The `graph.in` file consist of a `vec![]` which is a `vector` of data as: `(source, destination, cost)`. This graph is comprised of `6` nodes and their `cost`. 
+
+The algorithm returns the shortest path between 2 nodes. The function `shortest_path(g: &Graph, start: Node, goal: Node)` takes start and end nodes and returns the total cost to reach the goal. 

exercises/Algorithms/Dijkstra Algorithm/src/graph.in

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+vec![
+    (0, 1, 5), 
+    (0, 2, 10), 
+    (1, 2, 7), 
+    (1, 4, 3), 
+    (2, 4, 5), 
+    (4, 5, 10), 
+    (5, 6, 7)
+]

exercises/Algorithms/Dijkstra Algorithm/src/main.rs

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+use std::cmp::Ordering;
+use std::collections::{BinaryHeap, HashMap, HashSet};
+type Node = usize;
+type Cost = usize;
+
+struct Graph {
+    edges: HashMap<Node, Vec<(Node, Cost)>>,
+    nodes: HashSet<Node>,
+}
+#[warn(clippy::redundant_closure)]
+impl Graph {
+    fn from_edge_list(edge_list: &[(Node, Node, Cost)]) -> Self {
+        let mut adjacency_list: HashMap<Node, Vec<(Node, Cost)>> = HashMap::new();
+        let mut nodes = HashSet::new();
+
+        for &(source, destination, cost) in edge_list.iter() {
+            let destinations = adjacency_list.entry(source).or_insert_with(|| Vec::new());
+
+            destinations.push((destination, cost));
+            nodes.insert(source);
+            nodes.insert(destination);
+        }
+
+        Graph {
+            edges: adjacency_list,
+            nodes,
+        }
+    }
+}
+
+// #[derive(Clone, PartialEq, Eq)]
+#[derive(Eq, PartialEq)]
+struct Curr {
+    cost: Cost,
+    position: Node,
+    path: Vec<Node>,
+}
+impl Curr {
+    fn new(position: Node, cost: Cost, path: Vec<Node>) -> Self {
+        Curr {
+            cost,
+            position,
+            path,
+        }
+    }
+    fn new_start(start: Node) -> Self {
+        Curr {
+            cost: 0,
+            position: start,
+            path: vec![],
+        }
+    }
+}
+
+
+impl Ord for Curr {
+    fn cmp(&self, other: &Self) -> Ordering {
+        other
+            .cost
+            .cmp(&self.cost)
+            .then_with(|| self.position.cmp(&other.position))
+    }
+}
+
+impl PartialOrd for Curr {
+    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
+        Some(self.cmp(other))
+    }
+}
+
+fn shortest_path(g: &Graph, start: Node, goal: Node) -> Option<(Vec<Node>, Cost)> {
+    let mut priority_queue = BinaryHeap::new();
+    priority_queue.push(Curr::new_start(start));
+
+    let mut dist: HashMap<Node, Cost> = g
+        .nodes
+        .iter()
+        .map(|&x| if x == start { (x, 0) } else { (x, usize::MAX) })
+        .collect();
+
+    while let Some(Curr {
+        cost,
+        position,
+        mut path,
+    }) = priority_queue.pop()
+    {
+        if position == goal {
+            path.push(position);
+            return Some((path, cost));
+        }
+
+        // pq. push (cost+ currcost, start->next, path.add(start) )
+        // So iterate, through all the nodes of start node which are in g
+        // g[start]= Vec[node, cost]
+
+        if let Some(connected_nodes) = &g.edges.get(&position) {
+            for &(next_node, next_cost) in connected_nodes.iter() {
+                if next_cost < dist[&next_node] {
+                    let mut next = Curr::new(next_node, cost + next_cost, path.clone());
+                    next.path.push(position);
+                    priority_queue.push(next);
+
+                    if let Some(past_cost) = dist.get_mut(&next_node) {
+                        *past_cost = next_cost;
+                    }
+                }
+            }
+        }
+    }
+
+    None
+}
+
+fn main() {
+    let edge_list = include!("graph.in");
+    let g = Graph::from_edge_list(&edge_list);
+
+    if let Some((path, cost)) = shortest_path(&g, 1, 6) {
+        println!("Shortest distance from 1 to 6 is: , {path:?} {cost}");
+    };
+}
+
+#[test]
+fn large_graph() {
+    let edge_list = include!("graph.in");
+    let g = Graph::from_edge_list(&edge_list);
+
+    let path = shortest_path(&g, 1, 6);
+    assert!(path.is_some());
+    assert_eq!(path.unwrap().1, 20);
+}