COMP90054 Chap.2 State-Space Search and Path Cost

State-Space Search and Path Cost

Define search node

The course material gives this chapter a concrete anchor: Week 2 materials cover search algorithms and practice questions on their guarantees. That search node anchor controls how frontier is explained and how path cost is tested in changed practice.

State-Space Search and Path Cost turns search node, frontier and path cost into executable reasoning.

The chapter's practical target is to compare breadth-first, depth-first and uniform-cost search by frontier rule and cost assumptions, so every explanation should connect syntax to program state, control flow and observable output.

Treat search node as a precise program object, not a loose label. Identify the value or responsibility of search node before execution, then trace what can read it, change it or depend on it.

This makes state changes visible before they become debugging guesses.

Trace frontier

Use frontier to explain the program's next move.

Work through one representative frontier input by hand and name the branch, iteration or call that follows. If the frontier trace cannot be stated, the code may run by accident rather than by understood design.

Bring in path cost as the test of structure.

Compare normal, boundary and invalid inputs for path cost; state the expected behaviour first; then use the mismatch between expectation and result to localise the defect.

For the application — compare breadth-first, depth-first and uniform-cost search by frontier rule and cost assumptions — write the smallest complete example that exposes the rule.

Explain why the path cost result works, what would break it and how the program should signal or recover from that failure.

Test with path cost

Before running an example involving search node, make a trace table with the important state before and after each operation. Include the value associated with search node, the control decision governed by frontier and the output or object affected by path cost.

The search node table turns an unexplained result into a sequence that can be tested one transition at a time.

Test three inputs: an ordinary case, a boundary case and an invalid case. State the expected path cost result for each before execution, then compare it with what the program actually does.

A useful test of frontier isolates one rule; changing several conditions at once cannot reveal which condition caused the failure.

Practise explaining the solution without reading the code.

For comp90054, name the data representation, the control flow, the responsibility of each function or class and the reason the chosen design supports compare breadth-first, depth-first and uniform-cost search by frontier rule and cost assumptions.

This path cost rehearsal matters when a written test or interview asks why the program works rather than whether it produces one correct output.

Transfer to State-Space Search and Path Cost

A complete response should make the task visible before the detail: identify what must be decided, define the relevant terms, connect the evidence to frontier, and use path cost to test the result.

The final sentence about path cost should answer the question actually asked rather than merely repeat the topic.

The controlling limit is specific: Completeness and optimality claims depend on branching, positive costs and duplicate handling.

Keep that path cost limit beside the worked example, because it separates a careful comp90054 answer from one that sounds confident but claims more than the task or evidence supports.

For revision, retrieve search node, frontier and path cost without notes, explain their relationship aloud, then complete a changed version of the application: compare breadth-first, depth-first and uniform-cost search by frontier rule and cost assumptions.

Record the first failed frontier reasoning move and repair it before attempting another case.

What this chapter covers

• 01

  search node

• 02

  frontier

• 03

  path cost

• 04

  Applying search node

• 05

  Limits of frontier and path cost

Choose a search algorithm

Key terms

search node

Record representing a state together with path, cost and frontier information used by a search algorithm. This chapter uses the concept when students compare breadth-first, depth-first and uniform-cost search by frontier rule and cost assumptions. Use this definition when the task is to compare breadth-first, depth-first and uniform-cost search by frontier rule and cost assumptions.

frontier

Set of generated nodes awaiting expansion. It helps explain the reasoning required to compare breadth-first, depth-first and uniform-cost search by frontier rule and cost assumptions. Use this definition when the task is to compare breadth-first, depth-first and uniform-cost search by frontier rule and cost assumptions.

path cost

Accumulated cost of actions from the initial state to a node. Its limit matters because completeness and optimality claims depend on branching, positive costs and duplicate handling. Use this definition when the task is to compare breadth-first, depth-first and uniform-cost search by frontier rule and cost assumptions.

State-Space Search and Path Cost FAQ

Exam move

Reconstruct the relationship among search node, frontier and path cost; complete the chapter application without notes; then test the result against this limit: Completeness and optimality claims depend on branching, positive costs and duplicate handling.

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