Elementary Sorting Algorithms Short Notes for GATE DA: Concepts, Formulas, Worked Examples & Practice

    Elementary Sorting Algorithms short notes for GATE DA: 2 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

    Summary: Quick Reference for Pass Analysis

    Summary: Quick Reference

    Pass Invariants (After passes)

    • Bubble: largest elements locked at the right end.
    • Selection: smallest elements locked at the left end.
    • Insertion: First elements are sorted (left prefix).

    Comparison Counts (Total for full sort)

    • Bubble (Standard): (Fixed)
    • Selection: (Fixed, invariant to data)
    • Insertion: Depends on data (Min: , Max: )

    Critical Exam Traps

    1. Optimized Bubble: Stops early if no swaps. Best case comparisons = .
    2. Insertion Shifts vs Swaps: Standard uses shifts, not adjacent swaps. Total shifts = total inversions.
    3. Selection Sort Data: Comparisons are never reduced by partially sorted data.

    Summary: Insertion Sort Metrics

    Summary: Insertion Sort Metrics

    Core Metrics

    • Total Shifts/Swaps: Exactly (Total Inversions).
    • Total Comparisons: (where = elements hitting the left boundary).
    • Best Case (Sorted): shifts, comparisons, time.
    • Worst Case (Reverse): shifts, comparisons, time.

    Exam Weapons

    1. Unknown Pattern: Split array into Left, , Right. Sum inversions in all 4 regions (Left, Right, Left-vs-, -vs-Right).
    2. -Sorted Arrays: Max inversions . Time complexity .
    3. Terminology: "Swaps" in Insertion Sort = Shifts = Inversions. Never answer 0.

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    Elementary Sorting Algorithms Short Notes for GATE DA: Concepts, Formulas, Worked Examples & Practice

    Elementary Sorting Algorithms short notes for GATE DA: 2 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

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