Problem Detail: This is the recursive formula for which I’m trying to find an asymptotic closed form by the master theorem: $$T(n)=9T(n/27)+(n cdot lg(n))^{1/2}$$ I started with $a=9,b=27$ and $f(n)=(ncdot lg n)^{1/2}$ for using the master theorem by $n^{log_b(a)}$, and if Read More …
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Computational power of deterministic versus nondeterministic min-heap automata
Problem Detail: This is a follow-up question of this one. In a previous question about exotic state machines, Alex ten Brink and Raphael addressed the computational capabilities of a peculiar kind of state machine: min-heap automata. They were able to show Read More …
NFAs with more than one initial state
Problem Detail: I’m trying to give a meaningful definition for NFAs with more than one initial state. I know from the formal definition in Wikipedia that it is possible to have more than one initial state, it mentions that “There is Read More …
Minimum cost closed walk in a graph
Problem Detail: Is there an efficient algorithm which gives the minimum cost closed walk in an undirected graph, which visits all vertices? Does this problem have a name? I tried to reduce this to similar problems (in particular the traveling salesman Read More …
If $L$ is a subset of ${0}^*$, then how can we show that $L^*$ is regular?
Problem Detail: Say, $L subseteq {0}^*$. Then how can we prove that $L^*$ is regular? If $L$ is regular, then of course $L^*$ is also regular. If $L$ is finite, then it is regular and again $L^*$ is regular. Also I Read More …
How to get expected running time of hash table?
Problem Detail: If I have a hash table of 1000 slots, and I have an array of n numbers. I want to check if there are any repeats in the array of n numbers. The best way to do this that Read More …
Why should one not use a 2^p size hash table when using the division method as a hash function?
Problem Detail: I don’t understand what is meant by: “m should not be a power of 2, since if m = 2^p, then h(k) is just the p lowest-order bits of k.” (pg. 231 of CLRS) Terms defined: m: size of Read More …
Calculating the Transfer Time for a Hard Disk
Problem Detail: I know that transfer rate is data size over transfer speed – but according to the information given, I don’t know what the data size is to calculate the transfer rate. Am I missing something or was I really Read More …
Proofs using the regular pumping lemma
Problem Detail: I have two questions: I consider the following language $$L_1= { win {0,1}^* mid not exists uin {0,1}^* colon w= uu^R}.$$ In other words $w$ is not palindrome with even length. I proved that this language is NOT regular Read More …
tightest upper bound on binary search tree insertion?
Problem Detail: The upper bound on the runtime of binary search tree insertion algorithm is O(n) which is if it is not balanced What will be the tighter upper bound on this,will it become O(logn) I have read that tighter upper Read More …
