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Lec09 Hashing

笔记很迷惑 不推荐看

一、General Idea

哈希表（Hash Table）：也叫做散列表。是根据关键码值（Key Value）直接进行访问的数据结构。

哈希表通过「键 key 」和「映射函数 Hash(key) 」计算出对应的「值 value」，把关键码值映射到表中一个位置来访问记录，以加快查找的速度。这个映射函数叫做「哈希函数（散列函数）」，存放记录的数组叫做「哈希表（散列表）」。

二、Hash Function

  1. 简单，且能最小化冲突数
  2. 均匀的， That is, for any x and any i, we have that \(Probability(f(x)=i)=1/b\)

三、Separate Chaining

四、Open Addressing

1. Linear Probing

2. Quadratic Probing

【Theorem】

  • If quadratic probing is used, and the table size is prime, then a new element can always be inserted if the table is at least half empty.

3.Double Hashing

五、Rehashing

Build another table that is about twice as big; Scan down the entire original hash table for non-deleted elements; Use a new function to hash those elements into the new table.

六、题目

The average search time of searching a hash table with N elements is:

  • A.O(1)
  • B.O(logN)
  • C.O(N)
  • D.cannot be determined
  • D:

What is a collision in hashing?

  • A.Everything else are the same for the two elements except their keys
  • B.Two elements have different data but share the same key
  • C.Two elements with different keys share the same hash value
  • D.Two elements with different hash values share the same key
  • C