CodeBlanks Logo Icon CodeBlanks
Login Register

Dependency order

Find a dependency order in a DAG.

Dependency order

Topological sorting orders nodes in a directed acyclic graph (DAG) by their dependencies. Each node comes after all nodes it depends on.

It is used wherever dependencies exist, like build tasks or course prerequisites. If a cycle exists, no order is possible.

Adjacency list

The graph is represented as an adjacency list of each node's successors. For example graph[0] = [1, 2] shows edges from 0 to 1 and 2.

This representation clearly expresses dependencies. Each node lists only the nodes that depend on it.

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, 2], [3], [3], []]
print(init_graph())

Expected output

[[1, 2], [3], [3], []]

Questions and answers

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

1 In which graph is topological sort possible?

  • Directed acyclic (DAG) Correct answer
  • Undirected
  • Directed cyclic
  • Fully connected

Explanation: Topological sort is possible in a DAG.

2 Edge definition

Question 
graph[0] = [____, 2]
Answer 
graph[0] = [1, 2]

Explanation: 1 is right.

3 Dependency order: match the terms

Term Meaning
graph[0] 0 to 1,2
graph[1] 1 to 3
graph[2] 2 to 3
graph[3] no exit

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