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Mediumhashingprobing

~75s

Where linear probing lands

Keys are inserted into a hash table of size 10 with h(k) = k mod 10 and linear probing. The keys 12, 22 and 32 are inserted in that order into an empty table. At which index does 32 end up?

Show the answer and the worked solution

Correct answer: C.

4

Worked solution

  1. 12 mod 10 = 2, so 12 takes index 2.
  2. 22 mod 10 = 2 as well; index 2 is occupied, so probing puts 22 at index 3.
  3. 32 mod 10 = 2; indices 2 and 3 are both taken, so probing continues to index 4, which is free.

Answer: 4.

The idea

Open addressing keeps every key inside the table, so collisions displace keys into neighbouring slots. Deletions then need tombstones, or the probe sequence for later keys breaks.

Shortcut. All three keys hash to 2, so they fill consecutive slots from 2 in insertion order, and the third lands at 2 + 2 = 4.

Common trap. 3 probes only one step past the home slot, forgetting that 22 already took index 3.

Data Structures & Algorithms

31 of 40

Level

Medium

Target time

~75s

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Where linear probing lands — Aptitude Question

Where linear probing lands: Keys are inserted into a hash table of size 10 with h(k) = k mod 10 and linear probing. Answer and worked solution on CodeKairo.

Question

Keys are inserted into a hash table of size 10 with h(k) = k mod 10 and linear probing. The keys 12, 22 and 32 are inserted in that order into an empty table. At which index does 32 end up?

Options

  1. 2
  2. 3
  3. 4
  4. 5
Show the answer and the worked solution

Correct answer: C. 4

Worked solution

  1. 12 mod 10 = 2, so 12 takes index 2.
  2. 22 mod 10 = 2 as well; index 2 is occupied, so probing puts 22 at index 3.
  3. 32 mod 10 = 2; indices 2 and 3 are both taken, so probing continues to index 4, which is free.

Answer: 4.

The idea

Open addressing keeps every key inside the table, so collisions displace keys into neighbouring slots. Deletions then need tombstones, or the probe sequence for later keys breaks.

Shortcut. All three keys hash to 2, so they fill consecutive slots from 2 in insertion order, and the third lands at 2 + 2 = 4.

Common trap. 3 probes only one step past the home slot, forgetting that 22 already took index 3.

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