CodeBlanks Logo Icon CodeBlanks
Login Register

Single source

Shortest path from one source to all vertices.

Single source

Dijkstra's algorithm finds shortest paths from a single source node to all other nodes in a graph. It requires non-negative weights.

The output is a distance array: dist[i] is the shortest distance from the source to i. The algorithm fails if there are negative edges.

Adjacency list

The graph is represented as a list of neighbors for each node. Each element is a (neighbor, weight) pair; for example graph[0] = [(1, 4), (2, 1)].

This representation saves space in sparse graphs and lets Dijkstra run efficiently.

Practice init_graph function

Write init_graph(). Return the adjacency list. Print it with print(init_graph()).

Starter code

solution.py
def init_graph():
    # Return adjacency list

Sample solution

solution.py
def init_graph():
    # Return adjacency list
    return [[(1, 4), (2, 1)], [(3, 1)], [(1, 2), (3, 5)], []]
print(init_graph())

Expected output

[[(1, 4), (2, 1)], [(3, 1)], [(1, 2), (3, 5)], []]

Questions and answers

Review the lesson questions together with their answers. To test yourself, solve the lesson interactively.

1 Which case does Dijkstra not support?

  • Negative weights Correct answer
  • Non-negative weights
  • Zero weights
  • Integer weights

Explanation: Dijkstra does not support negative weights.

2 Edge weight

Question 
graph[0] = [(1, ____)]
Answer 
graph[0] = [(1, 4)]

Explanation: 4 is right.

3 Single source: match the terms

Term Meaning
graph[0] [(1,4),(2,1)]
graph[1] [(3,1)]
graph[2] [(1,2),(3,5)]
graph[3] []

All lessons in Advanced

1 DP - Memoization

  1. What is memoization?
  2. Fibonacci memoization
  3. Dict-based cache
  4. Summary - Memoization

2 DP - Tabulation

  1. What is tabulation?
  2. Building the table
  3. Fibonacci tabulation
  4. Summary - Tabulation

3 LCS

  1. LCS definition
  2. DP table
  3. Backtracking the table
  4. Summary - LCS

4 Knapsack

  1. Knapsack problem
  2. 0/1 knapsack DP
  3. Decision table
  4. Summary - Knapsack

5 DP project

  1. Project: Overview
  2. Cost table
  3. DP solution
  4. Print the result

6 Matrix chain

  1. Multiplication order
  2. DP table
  3. Split point
  4. Summary - Matrix chain

7 Floyd-Warshall

  1. All pairs
  2. Triple loop
  3. Table update
  4. Summary - Floyd-Warshall

8 Dijkstra

  1. Single source
  2. Priority queue
  3. Relaxation
  4. Summary - Dijkstra

9 Bellman-Ford

  1. Negative weights
  2. Edge relaxation loop
  3. Negative cycle
  4. Summary - Bellman-Ford

10 Kruskal

  1. Minimum spanning tree
  2. Edge sorting
  3. Cycle check
  4. Summary - Kruskal

11 Prim

  1. Prim idea
  2. Priority queue
  3. Visited set
  4. Summary - Prim

12 Topological sort

  1. Dependency order
  2. DFS-based sort
  3. Kahn algorithm
  4. Summary - Topological sort

13 Union-find, trie, segment tree

  1. Union-find
  2. Trie
  3. Segment tree
  4. Summary - Advanced structures

14 Advanced final

  1. Challenge 1
  2. Challenge 2
  3. Challenge 3
  4. Challenge 4