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Results tagged with combinatorics
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user 2205
Questions related to combinatorics and discrete mathematical structures
2
votes
Number of possible min heaps
The second level can contain other numbers than 2 and 3. See for example
1
/ \
2 5
/ \
3 7
/ \
4 6
It is also unclear if you count isomorphic trees. See this …
- 12.3k
27
votes
Accepted
How many different max-heaps exist for a list of n integers?
I did not find a closed form, but according to this entry in the Online Encyclopedia of Integer Sequences the sequence starts with
1, 1, 1, 2, 3, 8, 20, 80, 210, 896, 3360, 19200, 79200, 506880, 274 …
- 22.8k
37
votes
How can one byte hold 256 possibilities?
I just did a quick animation to convince you. Yellow is one, blue is zero.
- 12.3k
7
votes
Accepted
Simplify complexity of n multichoose k
Edit: This answer is for $k<n$. Without bounding $k$ in terms of $n$ the expression is unbounded.
If $k=n-1$ then your expression becomes
$O\left ({{2(n-1)}\choose{n-1}}\right)$. Notice that by Stir …
- 12.3k
3
votes
What is the probability of friendship conditioned on the number of mutual friends
Okay, this is my approach to this problem. I think the key concept here is the clustering coefficient $c$. The value of $c$ is denotes how likely it is that two nodes are connected by an edge, if the …
- 12.3k