Perfect hashing (And Minimal perfect hashing)

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本文介绍了完美哈希的概念及其在哈希表查找中的应用。完美哈希是一种注入式的哈希函数，能确保每个有效输入映射到不同的哈希值，实现直接定位而无需额外搜索。此外还探讨了最小完美哈希，这是一种范围由连续整数组成的完美哈希函数，能够提供紧凑的哈希表结构，没有空闲槽位。

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Perfect Hashing:

A hash function that is injective—that is, maps each valid input to a different hash value—is said to be perfect.

With such a function one can directly locate the desired entry in a hash table, without any additional searching.

Minimal perfect Hashing:

A perfect hash function for n keys is said to be minimal if its range consists of n consecutive integers, usually from 0 to n−1. Besides providing single-step lookup, a minimal perfect hash function also yields a compact hash table, without any vacant slots. Minimal perfect hash functions are much harder to find than perfect ones with a wider range.