Chapter 12 · Simulation

Open Addressing Simulator

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Formula

h(k, i) = (h(k) + i) mod 13
occupied✗ DEFUNCT (deleted)probed (number = probe order)home slot h(k)

Probe sequence

  1. No operations yet.

History

  1. No operations yet.

Choose an operation.

Keys n0
Load factor λ0.00
✗ markers0
Last probes–

Open Addressing Simulator

With open addressing, every key lives directly in the table array. If the home slot h(k) = k mod N is taken, the key follows the probe sequence j = (h(k) + f(i)) mod N for i = 0, 1, 2, … until it finds a usable slot.

Controls

  • Type an integer key and choose Insert, Search or Delete. Probed slots are numbered in probe order, and the home slot is outlined.
  • Pick the probing method and the table size N. Changing either one rebuilds the table and reloads the sample keys (18, 41, 22, 44, 59, 32, 31, 73).
  • The probe sequence panel lists every probe of the last operation; the counters show the number of keys n, the load factor λ = n / N, the number of ✗ markers and the probes used.

Probing methods

Methodf(i)Note
LineariSimple, but builds long runs (primary clustering).
Quadratici²Breaks up runs but may miss some slots; with a prime N, λ ≤ 0.5 guarantees an empty slot is found.
Double hashingi · h₂(k)h₂(k) = R − (k mod R), R = 7 (R = 5 when N = 7); the step is never 0.

Deleting with DEFUNCT markers

Emptying a slot would cut every probe sequence that passes through it, so a deletion leaves a ✗ DEFUNCT marker behind. Search skips markers and stops only at a truly empty slot; insertion, once it knows the key is not in the table, may reuse the first marker it met.

Load factor

The expected number of probes climbs steeply as λ approaches 1. Open-addressing tables are usually kept at λ ≤ 0.5 and rehashed into a larger table once they pass it; the λ box is highlighted above 0.5.