Linked Questions

0
votes
1answer
2k views

Hashing and number of comparisons [duplicate]

Say, I want to put N objects into a hash table. How do I figure out how big the size of the table needs to be to have K comparisons on average when the table is: half full? three quarters full? all ...
26
votes
10answers
7k views

“For small values of n, O(n) can be treated as if it's O(1)”

I've heard several times that for sufficiently small values of n, O(n) can be thought about/treated as if it's O(1). Example: The motivation for doing so is based on the incorrect idea that O(1) ...
7
votes
3answers
16k views

How are hash table's values stored physically in memory?

Question: How are hash table's values stored in memory such that space if efficiently used and values don't have to be relocated often? My current understanding (could be wrong): Let's say I have 3 ...
18
votes
5answers
2k views

For what kind of data are hash table operations O(1)?

From the answers to (When) is hash table lookup O(1)?, I gather that hash tables have $O(1)$ worst-case behavior, at least amortized, when the data satisfies certain statistical conditions, and there ...
6
votes
5answers
2k views

Hash table collisions: why use a linked list if we can use a hash set?

One way to deal with the problem of collisions for a hash table is to have a linked list for each bucket. But then the lookup time is no longer constant. Why not use a hash set instead of a linked ...
8
votes
2answers
2k views

How are hash tables O(1) taking into account hashing speed?

Hash tables are said to be amortized $\Theta(1)$ using say simple chaining and doubling at a certain capacity. However, this assumes the lengths of the elements are constant. Computing the hash of an ...
6
votes
2answers
2k views

More efficient algorithm for determining if one list is a sublist of another list

I'm trying to build an algorithm which takes two lists of natural numbers and finds if every element of the first list is displayed at least once in the second list. What if the list is sorted? An ...
9
votes
4answers
2k views

Can element uniqueness be solved in deterministic linear time?

Consider the following problem: Input: lists $X,Y$ of integers Goal: determine whether there exists an integer $x$ that is in both lists. Suppose both lists $X,Y$ are of size $n$. Is there a ...
0
votes
1answer
578 views

Sorting when there are only O(log n) many different numbers

We have $n$ integers with lot's of repeated numbers. In this list, the number of distinct elements is $O(\log n)$. What's the best asymptotic number of comparisons for sorting this list? Any idea or ...
3
votes
1answer
2k views

Are dictionaries and associative arrays the same thing?

With respect to abstract datatypes (ADTs), are the terms "dictionary" and "associative array" perfect synonyms or are there slight differences between them?
0
votes
3answers
890 views

What is the average search complexity of perfect hashing?

The lookup time in perfect hash-tables is $O(1)$ in the worst case. Does that simply mean that the average should be $\leq O(1)$?
6
votes
1answer
392 views

Best data structure for a queue with random reads?

Well, it's not exactly a queue if it allows for random reads. This question is about a data structure which behaves like a queue for insertions and a sorted dictionary for reads. Imagine an algorithm ...
1
vote
1answer
1k views

Average number of collisions before successful insertion into hash table

I want to compute the average number of collisions before sucessfully adding an item into a hash table. Let $m$ be the size of a hash table $H$. I was thinking that since it is a linear probing and ...
10
votes
2answers
232 views

Determining the particular number in $O(n)$ time and space (worst case)

$\newcommand\ldotd{\mathinner{..}}$Given that $A[1\ldotd n]$ are integers such that $0\le A[k]\le m$ for all $1\le k\le n$, and the occurrence of each number except a particular number in $A[1\ldotd n]...
2
votes
1answer
243 views

Does my simple, static hash table have O(1) worst case lookup?

Will the following simple hash table construction algorithm be able to construct a static hash table in $O(n)$ expected time, and will the worst case access time be $O(1)$? If not, what are the ...

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