Indexing and B+ Trees Short Notes for GATE DA: Concepts, Formulas, Worked Examples & Practice

Indexing and B+ Trees short notes for GATE DA: 2 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

B+ Tree Quick Reference

Core Formulas

Non-Leaf Max Pointers ( $p$ ): $p = ⌊ \frac{B + V}{P _{t r} + V} ⌋$
Leaf Max Entries ( $p_{l e a f}$ ): $p_{l e a f} = ⌊ \frac{B - P _{n e x t}}{V + P _{d}} ⌋$

Structural Constraints

Root: Min 2 pointers (if internal).
Internal Node: Min $⌈ p /2 ⌉$ pointers.
Leaf Node: Min $⌈ p_{l e a f} /2 ⌉$ entries.

Insertion Golden Rules

Leaf overflow $\to$ Split $\to$ Copy middle key up.
Internal overflow $\to$ Split $\to$ Push middle key up.
Tree height increases if and only if the root splits.

Index Selection Exam Checklist

Exam Checklist

Identify Equality First: Prioritize = conditions for the leftmost position.

Range Conditions Second: Place >, <, BETWEEN after equality columns.

Check SARGability: No functions, math, or implicit casts on the indexed column.

Estimate Selectivity: If matching

&gt; 15\text{--}20\%

, expect a Full Table Scan.

Avoid Bookmark Lookups: Use composite indexes covering all selected columns.

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Indexing and B+ Trees Short Notes for GATE DA: Concepts, Formulas, Worked Examples & Practice

Indexing and B+ Trees short notes for GATE DA: 2 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

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