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What does the modulo (%) operation do in hashing? How is it related to indices?

Data StructuresJunior~1 min read
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The modulo (%) operation in hashing is used to turn a large hash value into a valid array index where the hash table's data is stored.

How it works

  1. The hash function returns an integer, sometimes a very large one.
  2. The table has a limited size N (for example, 100 slots).
  3. To "fit" the hash into the index range [0 ... N-1], we compute:
javascript
index = hash(key) % N
  1. The result is an index, the position in the array where the element will be placed.

Example

javascript
hash("dog") = 123456 N = 10 index = 123456 % 10 = 6

So the element with key "dog" lands in slot #6.

Why the modulo specifically

  • % gives an even distribution across the index range;
  • it guarantees that the index never goes out of the array's bounds.

Summary

The modulo operation ties the "abstract" hash to a specific storage location in the table: it turns the hash into a real array index where the data lives.

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