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Interactive Python Lab

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Interactive Python Lab

AI Wisdom

Interactive Python Lab

Dijkstra's Shortest Path

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Replay·Step by step

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Data Flow Pipeline

mastery Track

Dijkstra's Shortest Path

0/1 Knapsack DP

Longest Common Subsequence

Coin Change DP

Topological Sort (Kahn's)

Kruskal's MST

Trie (Prefix Tree)

Floyd-Warshall All-Pairs Shortest Path

Segment Tree for Range Queries

Bit Manipulation Tricks

Explain

Line 3

dijkstra(graph, start=0) called. Initialize distance table.

Why this approach?

We call dijkstra with start=0. The function will compute shortest distances from node 0 to all other nodes using a greedy approach with a min-heap.

Structured Explanation

Overview

Dijkstra finds shortest paths from a source to all nodes with non-negative edge weights.

Analogy

Expanding a bubble of finalized shortest distances outward from the start city.

Step-by-step

Set dist[source]=0, others=∞; push source into min-heap.
While heap not empty:
Pop node u with smallest dist.
Relax each edge (u,v,w): if dist[u]+w < dist[v], update and push v.
Extracted nodes have final distances.

Visual

Visited set grows; frontier edges relax distances into a shortest-path tree.

Common mistakes

Using Dijkstra when edges can be negative (incorrect).
Not skipping stale heap entries after better distances are found.
Using an array priority queue leading to O(V²) on large graphs.

Practice questions

Run on a 5-node weighted graph and tabulate dist each step.
Reconstruct paths with parent pointers.
Compare binary heap vs Fibonacci heap complexity.

Time

O((V+E) log V) with a binary heap

Space

O(V) for dist/parent/visited

Complexity

Time

O((V + E) log V)

Space

O(V)

Complexity Overview

O(1)

O(log n)

O(n)

O(n log n)

O(n²)

n = 8range 1-20

AT N = 8

Complexity	Operations
O(1)	1
O(log n)	3
O(n)	8
O(n log n)	24
O(n²)	64

Challenge

Add a new node 4 connected from node 3 with weight 2. What is the shortest path from 0 to 4?

Hint

Prioritize exploring the cheapest known path aggressively before touching heavier routes.

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