What is Dijkstra’s Algorithm and When Should You Use It?
💡 Concept Name
Dijkstra’s Algorithm – A step-by-step process for quickly finding the shortest path between two points in a weighted graph, as long as the weights are non-negative.
📘 Quick Intro
Created by computer scientist Edsger Dijkstra, this algorithm is the heart of modern GPS apps, internet routing, and more. It calculates the fastest way to get from one spot to another, taking road lengths (weights) into account.
🧠 Analogy / Short Story
Imagine you’re lost in a new city. You ask locals about every route from your hotel to your favorite restaurant, always choosing the one with the shortest remaining distance. By following the quickest known paths step by step, you always reach your destination by the fastest route. That’s exactly what Dijkstra’s algorithm does in a graph!
🔧 Technical Explanation
- Start by marking the source node’s distance as 0 and every other node as infinity (unknown).
- Place all nodes in a min-priority queue, sorted by current shortest distance.
- Each step, pick the node with the smallest distance, update its neighbors’ distances if a quicker path is found through it, then mark it as done (visited).
- Repeat until all nodes are processed or the destination is reached.
- Works perfectly when all edge weights are zero or positive. Time complexity: O((V + E) log V) using a heap or priority queue.
🌍 Purpose & Use Case
- ✅ Used in mapping and navigation apps (like Google Maps or Uber)
- ✅ Network routers to find the quickest path for internet traffic
- ✅ AI in video games to move characters efficiently
- ✅ Scheduling or project planning for finding optimal paths in workflows
💻 Real Code Example
// C# example: Dijkstra’s algorithm (using .NET 6+ PriorityQueue)
public static Dictionary<int, int> Dijkstra(
Dictionary<int, List<(int neighbor, int weight)>> graph, int source)
{
var distances = graph.ToDictionary(kvp => kvp.Key, kvp => int.MaxValue);
distances[source] = 0;
var pq = new PriorityQueue<int, int>();
pq.Enqueue(source, 0);
while (pq.Count > 0)
{
int current = pq.Dequeue();
foreach (var (neighbor, weight) in graph[current])
{
int alt = distances[current] + weight;
if (alt < distances[neighbor])
{
distances[neighbor] = alt;
pq.Enqueue(neighbor, alt);
}
}
}
return distances;
}
❓ Interview Q&A
Q1: What does Dijkstra’s algorithm calculate?
A: The shortest (minimum weight) path from a source node to all others in a graph.
Q2: Why doesn’t Dijkstra work with negative weights?
A: It may miss shorter paths that appear later if negative edges “undo” earlier costs.
Q3: What is the key data structure for efficiency?
A: A min-priority queue or min-heap, so you always expand the node with the smallest current distance.
Q4: Can it handle disconnected graphs?
A: Yes—nodes that can’t be reached will keep their distance as infinity.
Q5: Is Dijkstra’s algorithm greedy or dynamic programming?
A: It’s a classic greedy algorithm—always picks the locally best choice at each step.
Q6: Where is Dijkstra’s used in tech products?
A: In navigation (GPS), network routing, video game AI, and even robotics pathfinding.
Q7: What’s the difference between Dijkstra and Bellman-Ford?
A: Bellman-Ford handles negative weights but is slower. Dijkstra is faster but can’t use negative edges.
Q8: What is the initialization step for Dijkstra’s algorithm?
A: Set all distances to infinity except the starting node, which is zero.
Q9: What’s a common pitfall in implementation?
A: Not updating the priority queue correctly after relaxing edges.
Q10: Is Dijkstra’s algorithm guaranteed to find the single shortest path?
A: Yes, if all edge weights are non-negative.
📝 MCQs
Q1. What does Dijkstra's algorithm find?
- Shortest path
- Longest path
- Cycle
- Minimum spanning tree
Q2. What must edge weights be for Dijkstra’s algorithm to work?
- Non-negative
- Negative
- Zero
- Any
Q3. Which data structure is crucial in Dijkstra’s algorithm?
- Stack
- HashSet
- Min-priority queue
- Binary tree
Q4. Who invented Dijkstra’s algorithm?
- Alan Turing
- Edsger Dijkstra
- Grace Hopper
- John von Neumann
Q5. What is the initial distance to all nodes except the source?
- Zero
- One
- Infinity
- Negative one
Q6. Is Dijkstra’s algorithm greedy?
- Yes
- No
- Sometimes
- Only with cycles
Q7. What’s a famous real-world use of Dijkstra’s algorithm?
- Web servers
- Image processing
- GPS navigation
- File compression
Q8. How does Dijkstra pick the next node to process?
- Random
- Any neighbor
- Node with minimum known distance
- Alphabetically
Q9. Which algorithm handles negative weights safely?
- Dijkstra
- Bellman-Ford
- A*
- Prim
Q10. What’s the time complexity using a min-heap?
- O(V^2)
- O(V+E)
- O((V + E) log V)
- O(log V)
💡 Bonus Insight
Dijkstra’s algorithm is the backbone for even more advanced pathfinding, like the A* algorithm, which uses a heuristic to get to the goal even faster. Learning Dijkstra makes understanding other graph algorithms much easier!
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