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Programming › Algorithm Cookbook › Chapter 5. Hashing and Maps ›

5.8 Counting Maps

5.8 Counting Maps Problem You need to count how many times each key appears in a dataset. A standard map stores one value per key. In counting problems, the value is a frequency. The task is to update counts efficiently while scanning input once. Solution Use a map from key to integer count. freq: Map<Key, Int> For each key, read the current count, then increment. count(items): freq = empty map...

Programming › Algorithm Cookbook › Chapter 5. Hashing and Maps ›

5.7 Maps

5.7 Maps Problem You need to associate each key with a value and retrieve the value quickly by key. A set answers membership questions. A map answers lookup questions. It stores pairs of the form (key, value) and maintains the rule that each key appears at most once. Solution Implement the map as a hash table whose entries store both keys and values. Entry: key value HashMap: buckets: array of...

Programming › Algorithm Cookbook › Chapter 5. Hashing and Maps ›

5.9 Grouping Keys

5.9 Grouping Keys Problem You need to partition items into groups according to a derived key. A counting map records how many times each key appears. A grouping map records the actual items associated with each key. This is useful when the later algorithm needs to process each group separately. Solution Use a map from group key to list of items. groups: Map<Key, List<Item>> For each item, compute its group...

Programming › Algorithm Cookbook ›

Chapter 5. Hashing and Maps

Chapter 5. Hashing and Maps This chapter studies hashing as a practical mechanism for constant time access under realistic constraints. The focus is not on idealized O(1) claims, but on how hash tables behave under load, how collisions are handled, and how design choices affect predictability, memory locality, and adversarial robustness. A hash table implements a partial function from keys to values by mapping keys into a finite index space....

Maths › 00. General Mathematics ›

04.2 Morphisms and Mappings

4.2 Morphisms and Mappings A morphism is a map that preserves structure. It is the correct notion of transformation for a given mathematical setting. A plain function sends elements of one set to elements of another set. $$ f : X \to Y $$ A morphism does more. It respects the operations, relations, or laws that define the structures on $X$ and $Y$. For groups, the morphisms are group homomorphisms....

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5.8 Counting Maps

5.7 Maps

5.9 Grouping Keys

Chapter 5. Hashing and Maps

04.2 Morphisms and Mappings