Dijkstra's Algorithm Implementation in Rust programming | the shortest path between nodes in a graph
What Dijkstra’s Algorithm Does
Finds the shortest path between nodes in a graph.
Common use case: routing (e.g., road networks).
Weights (or costs) represent distances or times between nodes.
⚙️ Rust Implementation Setup
Dependencies and Traits
Brought into scope:
std:cmp:Ordering
std::collections::BinaryHeap
Derived traits for the custom State struct: Copy, Clone, PartialEq, etc.
Struct Definitions
State: represents a current node with a cost and position.
Edge: represents a connection from one node to another with a cost.
Custom Ordering
Implemented Ord and PartialOrd so BinaryHeap acts like a min-heap using the cost.
🛠️ Main Function: shortest path
Inputs:
graph: reference to a vector of vectors of Edge structs.
start, goal: indices of start and end nodes.
Returns:
Option usize: either shortest cost as Some(cost) or None if path doesn't exist.
Key Steps in Logic:
Initialize all distances to usize::MAX (infinity).
Use a binary heap (BinaryHeap) to manage nodes to explore.
Push starting node with cost 0.
Use a loop to pop the lowest-cost path and explore connected edges.
If a shorter path is found, update distance and push it to the heap.
✅ Test Case Setup
The graph is recreated in code using the adjacency list style.
Nodes are 0-indexed (Rust-style).
Undirected edges are manually added in both directions.
// Sample graph structure
// Node 0: (1,6), (2,4), (3,1)
// Node 1: (0,6), (2,3)
// Node 2: (0,4), (1,3), (3,1)
// Node 3: (0,1), (2,1)
Called shortest_path(&graph, 0, 1) and asserted result is Some(5).
✅ Result
Successfully passed the test: Shortest path from Node 0 to Node 1 is 5.
Path: 0 → 3 → 2 → 1 with weights 1 + 1 + 3 = 5.
📌 Takeaway
This is a clean and idiomatic Rust implementation of Dijkstra's algorithm using:
Custom structs and trait implementations
Binary heap for performance
Clear handling of unreachable paths
Would you like me to summarize this with comments in the actual Rust code or help visualize the graph?
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