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Results tagged with algorithms
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user 13249
An algorithm is a sequence of well-defined steps that defines an abstract solution to a problem. Use this tag when your issue is related to design and analysis of algorithms.
4
votes
Accepted
Designing a prefix code for integers?
The following code is often used as a standard prefix-code for natural numbers, which bounds the length of each codeword by $\log n+O(\log\log n)$:
At first, we identify the natural numbers by binary …
- 994
3
votes
Accepted
Which algorithms have runtime recurrences like $T(n) = \sqrt{n}\,T(\sqrt{n}) + O(n)$?
Think of an algorithm, which do something linear with an integer list of length $n$, for example computes the maximum. Afterwards, the algorithm divides the list of length $n$ into $\sqrt{n}$ lists of …
- 994
2
votes
Storing the stream in less space
Unfortunately you will always need space $\Omega(nk)$ to support your operations.
Consider all possible contents of your stream, i.e. all subsets of $[n]\times [k]$. There are $2^{nk}$ such subsets. …
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1
vote
Algorithm for random generation of two connected partitions of a finite set
There do not exist such partitions $D_1$ and $D_2$. Recall your assumptions: $$\bigcup\limits_{i=1}^{p} A_i=X,\;\bigcup\limits_{i=1}^{q} B_i=X$$
It follows, that for each $x\in X$ there exists a set $ …
- 994
1
vote
Which is the proper algorithm to figure repeated substrings of longest total length?
You describe the first step of the "greedy off-line textual substitution" described in
Alberto Apostolico, Stefano Lonardi: Off-Line Compression by Greedy Textual Substitution. Proc. IEEE, vol. 88 n …
- 994
1
vote
Accepted
Cost of find operation on a tree data-structure
Since my two comments already form the solution, I can also write the answer in total.
If you have a datastructure consisting of a bunch of trees, then the worst-case cost of a Find-Operation is the …
- 994
1
vote
Accepted
Understanding a proof in the sweep line algorithm when finding all line segment intersections
The proof is absolutely correct. Of course, the algorithm only computes something when the sweep line comes to an eventpoint. Nevertheless you can think of the sweep line as a continiously moving line …
- 994