Uninformed Search and Heuristic Search Short Notes for GATE DA: Concepts, Formulas, Worked Examples & Practice

Uninformed Search and Heuristic Search short notes for GATE DA: 2 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

Topic Summary: Uninformed Search Essentials

Key Takeaways

1. BFS

Structure: FIFO Queue.
Pros: Complete, Optimal (unit cost).
Cons: High Memory $O (b^{d})$ .
Best for: Shallow solutions.

2. DFS

Structure: LIFO Stack.
Pros: Low Memory $O (b \cdot m)$ .
Cons: Not Complete (infinite spaces), Not Optimal.
Best for: Deep solutions, memory constraints.

3. Strategy Selection

No heuristic? → Uninformed.
Have heuristic? → Informed (A*).
Cycles present? → Use Graph Search (Explored Set).

4. Complexity

Time is generally exponential for both.
Space is the differentiator: BFS is exponential, DFS is linear.

Topic Summary: A* Exam Readiness

A* Search: Final Revision Checklist

1. The Formula

$f (n) = g (n) + h (n)$ . Always expand the lowest $f (n)$ . Tie-break with lowest $h (n)$ , then alphabetical.

2. Admissibility

Rule: $0 \leq h (n) \leq h^{*} (n)$ . Meaning: Never overestimates. Guarantees optimality in Tree Search.

3. Consistency (Monotonicity)

Rule: $h (n) \leq c (n, n^{'}) + h (n^{'})$ . Meaning: Satisfies triangle inequality. Guarantees optimality and no re-expansion in Graph Search. Fact: Consistent $⟹$ Admissible. (The reverse is false).

4. Combining Heuristics

If $h_{1}$ and $h_{2}$ are admissible, $max (h_{1}, h_{2})$ is always admissible and dominates (better). $min (h_{1}, h_{2})$ is admissible but weaker.

5. Tracing Protocol

Maintain a strict table of $g$ , $h$ , and $f$ . Update a node's parent only if the new $g$ value is strictly lower than the existing one.

More short notes in this unit

Adversarial Search, Minimax and Alpha-Beta Pruning Short Notes

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Uninformed Search and Heuristic Search Short Notes for GATE DA: Concepts, Formulas, Worked Examples & Practice

Uninformed Search and Heuristic Search short notes for GATE DA: 2 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice ques

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