Dijkstra’s Algorithm - Part 1 (theory)
In this article, we'll talk about the theory of Dijkstra’s Algorithm in the easiest, funnest way possible!
Hello again, amazing coders 👨💻. In today’s article, we’ll be diving into a very important topic in the software engineering world! As we always do, let’s make the topic fun using story telling 📖.
Imagine you're playing your favorite video game. You're the hero 🦸♂️, and you need to get from point A to point B, but there are multiple paths, obstacles, and enemies along the way. You want to choose the shortest path (because, who doesn't love finishing levels faster, right?).
But how do you decide which path is the fastest?
This is exactly where Dijkstra’s Algorithm comes in! It's like your trusty map 🗺 that tells you the best way to get from one place to another, based on a Graph Data Structure. In this article, we'll talk about the theory of Dijkstra’s Algorithm in the easiest, funniest way possible. Ready? Let’s go Ala barakati Lah!
What is Dijkstra’s Algorithm?
Dijkstra’s Algorithm is like a super-smart, efficient way to find the shortest path from a starting point (node) to a destination in a network of roads (edges).
How Does It Work?
Okay, let’s break this down into a few simple steps. Imagine your map has nodes (locations) and edges (the roads between them). Your job is to find the shortest road to travel between two nodes.
Here’s what Dijkstra does:
Start at the beginning (the starting node).
Look at all the roads (edges) connected to your current location.
Pick the shortest one and go there.
Once you arrive, repeat the process until you reach the destination.
Along the way, you keep track of the shortest distance from the starting point to each node.
Pretty cool, right? Okay, let’s start the real fun now!
The Dijkstra Algorithm Adventure
Let’s walk through a fun little story to explain how this works. Imagine you’re a brave knight 🤺, and you need to deliver a royal scroll 📜 from your castle 🏰 (point A) to the princess in a faraway tower 😉😅 (point B). The kingdom is a maze of roads, and each road takes a certain amount of time to travel.
Here's how you can use Dijkstra’s algorithm to plan the quickest route:
Step 1: Start at Your Castle 🏰
You’re standing at your castle (node A), ready to start your journey. You don’t know how to get to the princess yet, so you look at all the roads that lead from the castle. Some roads are shorter (they take less time), and some are longer.
Step 2: Measure the Distances 📏
You know you’ll need a map that tells you the distance (or time) to each destination. So, you measure how far each road takes from your starting point. You write these down:
Road 1 (A to C) takes 2 hours
Road 2 (A to D) takes 5 hours
Road 3 (A to E) takes 4 hours
Right now, you just know the direct distances from your castle, but we’ll figure out the best route soon.
Step 3: Choose the Shortest Path First
Next, you’re going to choose the shortest road. Since road 1 (A to C) takes only 2 hours, you pick that one. Now you're at node C!
Step 4: Look at New Paths from C
Now that you’re at C, you look at all the new roads you can take from here:
C to B: 3 hours
C to D: 1 hour
You’ll choose the road that takes the least time, so you go from C to D (because it’s only 1 hour).
Step 5: Repeat Until You Reach the Princess
Now you're at D. You check your map and see:
D to B: 2 hours
D to E: 4 hours
You pick D to B (2 hours) because it's shorter.
Congrats, you've reached the princess! 🏰👸 (Give her the scroll and go back! No flirting haha)
Key Principles of Dijkstra’s Algorithm
Let’s review the key principles of Dijkstra’s Algorithm that make it so special:
Start from the Beginning: You start at your starting point (node A), and you figure out the shortest possible distance to each connected node.
Pick the Shortest Path: At every step, you pick the shortest road (edge) to the next node.
Avoid Repeating: You don’t go back and forth or revisit nodes that you’ve already visited with a shorter path. You’ll only move forward, and always take the shortest available road.
Keep Track of the Shortest Distance: Every time you pick a road, you update your map to reflect the shortest distance to each node. This means you’re always optimizing as you go!
Example: A Visual Map
Here’s a simple map to show what we mean:
(4)
A -------- C
| |
(2)| |(1)
| |
D -------- E
(5)
A to C: 2 hours
A to D: 5 hours
A to E: 4 hours
C to B: 3 hours
C to D: 1 hour
D to B: 2 hours
Step-by-step Walkthrough:
Start at A: Distance to A = 0, Distance to C = 2, Distance to D = 5, Distance to E = 4.
Move to C (shortest path from A): Distance to C = 2.
From C, move to D (since 1 hour is less than 5 hours from A to D): Distance to D = 3 (2 from A to C + 1 from C to D).
From D, move to B (shortest from D to B): Distance to B = 5 (3 from A to C to D + 2 from D to B).
And boom, you’re done! You've found the shortest path from A to B, with a total time of 5 hours.
Conclusion: You’re Ready for the Next Level (Part 2)!
Now you know the theory behind Dijkstra’s Algorithm. It’s like a magical map that always knows the best way to get you where you need to go in a network of roads or connections.
In the next article, we’ll move beyond the theory and show you how to implement Dijkstra’s Algorithm in code 👨💻. But for now, feel free to enjoy your new magical algorithm!
Stay tuned for the next one!
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