Dependency Graphs Math Example 1

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Example 1

easy
Three tasks have the following dependencies: Task B depends on Task A, and Task C depends on Task B. Draw the dependency graph and determine a valid execution order.

Solution

  1. 1
    Identify the dependencies: A→BA \to B (B depends on A) and B→CB \to C (C depends on B).
  2. 2
    Draw the directed graph: A→B→CA \to B \to C. An arrow from XX to YY means XX must be completed before YY.
  3. 3
    Perform a topological sort: start with the node that has no incoming edges (A), then B, then C.
  4. 4
    The valid execution order is A,B,CA, B, C.

Answer

A→B→CA \to B \to C
A dependency graph is a directed acyclic graph (DAG) where edges represent prerequisite relationships. A topological sort gives a valid ordering that respects all dependencies, ensuring no task is started before its prerequisites are complete.

About Dependency Graphs

A dependency graph is a directed graph where nodes are variables and arrows show which variables directly influence which others.

Learn more about Dependency Graphs →

More Dependency Graphs Examples

Example 2 medium

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Example 3 medium

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Example 4 medium

A project has tasks with dependencies: [formula] depends on [formula]; [formula] depends on [formula

Example 5 hard

Given the dependency graph with edges [formula], [formula], [formula], [formula], [formula], [formul

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