hash table

[TOC]

direct address

适用于数量小且没有重复的key的情况
都是O(1)时间

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hash table

with direct address, key k store in slot k; while with hashing, we have a hash function h(k)

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collision

collision: two keys hash to the same slot.
solution: chaining; open addressing

chaining

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load factor = n/m, n is total elements, m is the number of slots.

Search element
worst-case: all elements in the same slots
average case: O(1)
choose a simple uniform hashing (各个元素均匀地分布在各个slots)

Open addressing

每个slot只有一个element，但我们在search的时候，可能要search多个slots

hash function h 不仅需要input k, 还需要input一个i

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当删除一个key的时候，不能找到这个key之后直接标记为null，而应当标记为deleted，不然会影响后面的search

Double hashing效果不错：h(i, k) = (h1(k) + i * h2(k)) mod m

linear probing

如果slot已经被占据了，就看下一个slot

会使得average search time 增加

quadratic probing

类似linear probing，但不是看下一个slot，而是通过加上一个次方的数再mode，寻找下一个探测是否能够插入的slot

double hashing

计算h的时候使用另外两个hash function

hash functions

a good hash function should be simple uniform hashing.

division method

h(k) = k mod m

get the remainder as h(k) ---- 取一个质数，并且这个质数和keys的分布没有关联

a prime not too close to an exact power of 2 is often a good choice of m

The multiplication method

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