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    Hashing and Collision Resolution Short Notes for GATE CS

    Hashing and Collision Resolution short notes for GATE CS: 16 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions

    hashing and collision resolution short notes

    Formula Matrix

    h_i = (h + i) mod m
    Linear: step=1, i≥0
    h_i = (h + i²) mod m
    Quadratic: m prime, α<0.5
    h_i = (h₁ + i·h₂) mod m
    Double: gcd(h₂,m)=1, h₂>0
    Full coverage
    Step and m are coprime
    Prime shortcut
    Any 1≤s<m is coprime
    Secondary cluster
    Same initial hash, same path

    If You See This, Do This

    "linear probing" + "empty slots"
    Trace insertions; update state after every collision.
    "quadratic probing" + "sequence"
    Use i² offsets. Verify m prime, α<0.5.
    "double hashing" + "final slot"
    Compute h₂ once. Add i·h₂ for each probe.
    "guarantee full coverage"
    Check gcd(h₂, m)=1. If m not prime, restrict h₂.
    "h₂ evaluates to 0"
    Infinite loop. Check h₂(k) > 0 for all k.
    "same slot, same path"
    Secondary clustering. Eliminated by double hashing.
    "contiguous block"
    Primary clustering. Present in linear probing.

    Traps and Invariants

    Probe index starts at 1 instead of 0.
    Check: substitute i=0; result must equal h(k).
    h₂(k) evaluates to 0 or shares factor with m.
    Check: verify h₂(k) > 0 and gcd(h₂(k), m) = 1.
    Assume quadratic probing always finds empty slot if table not full.
    Check: verify m is prime and α < 0.5.

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    Hashing and Collision Resolution Short Notes for GATE CS

    Hashing and Collision Resolution short notes for GATE CS: 16 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

    Formula Matrix

    h_i = (h + i) mod m
    Linear: step=1, i≥0
    h_i = (h + i²) mod m
    Quadratic: m prime, α<0.5
    h_i = (h₁ + i·h₂) mod m
    Double: gcd(h₂,m)=1, h₂>0
    Full coverage
    Step and m are coprime
    Prime shortcut
    Any 1≤s<m is coprime
    Secondary cluster
    Same initial hash, same path

    If You See This, Do This

    "linear probing" + "empty slots"
    Trace insertions; update state after every collision.
    "quadratic probing" + "sequence"
    Use i² offsets. Verify m prime, α<0.5.
    "double hashing" + "final slot"
    Compute h₂ once. Add i·h₂ for each probe.
    "guarantee full coverage"
    Check gcd(h₂, m)=1. If m not prime, restrict h₂.
    "h₂ evaluates to 0"
    Infinite loop. Check h₂(k) > 0 for all k.
    "same slot, same path"
    Secondary clustering. Eliminated by double hashing.
    "contiguous block"
    Primary clustering. Present in linear probing.

    Traps and Invariants

    Probe index starts at 1 instead of 0.
    Check: substitute i=0; result must equal h(k).
    h₂(k) evaluates to 0 or shares factor with m.
    Check: verify h₂(k) > 0 and gcd(h₂(k), m) = 1.
    Assume quadratic probing always finds empty slot if table not full.
    Check: verify m is prime and α < 0.5.

    Recall Check

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