📚 Hash Functions: Principles and Applications | 哈希函数原理及其应用
A hash function is a mathematical algorithm that takes an input (or 'key') of arbitrary length and produces a fixed-size output, typically called a hash value, digest, or hash code. In computer science, hash functions underpin many essential data structures and security protocols.
哈希函数是一种数学算法，它将任意长度的输入（或称“键”）转换为固定长度的输出，通常称为哈希值、摘要或哈希码。在计算机科学中，哈希函数是许多重要数据结构与安全协议的基础。
1. What Is a Hash Function? | 什么是哈希函数
Formally, a hash function h maps a domain D of potentially unbounded size to a finite, fixed range of size m. For a given key K, the function returns h(K), which can be used as an index into an array of size m.
从形式上讲，哈希函数 h 将可能无限大的定义域 D 映射到大小为 m 的有限固定值域。对于给定的键 K，函数返回 h(K)，该值可以作为大小为 m 的数组的下标。
h(K) → index in [0, m - 1]
Consider a simple hash function for integer keys: h(K) = K mod m. If m = 10 and K = 47, then h(47) = 7, so the key 47 would be stored at array position 7. The same calculation is repeated every time the key is searched for.
考虑一个简单的整数键哈希函数：h(K) = K mod m。若 m = 10，K = 47，则 h(47) = 7，因此键 47 将被存储在数组的位置 7。每次查找该键时都重复同样的计算。
2. Key Properties of Hash Functions | 哈希函数的核心性质
A good hash function must satisfy several important properties. First, it must be deterministic: the same input always produces the same output. Second, it should be efficient to compute, ideally in O(1) time or O(L) time where L is the length of the input.
良好的哈希函数必须满足若干重要性质。首先，它必须是确定性的：相同的输入总是产生相同的输出。其次，它应当计算高效，理想情况下为 O(1) 时间，或 O(L) 时间，其中 L 是输入长度。
Third, the output must have a fixed length regardless of the input size. Fourth, the outputs should be uniformly distributed across the range, meaning that each index is roughly equally likely to be produced
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