instruction stringlengths 35 29.1k |
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I have an unknown $n$-dimensional vector $x$ whose analytical expression depends on the following sum $x = z + Ba$ where the vector $z$ and the matrix $B\in \mathbb{R}^{n\times s}$ are given. So the $s$-dimensional vector $a$ is to be computed to find $x$.
The only assumption that we have is $x=0$ when we project $x$ o... |
The complexity class $\Sigma_{k}^{p}$ is recursively defined as follows:
\begin{align}
\Sigma_{0}^{p} & := P, \\
\Sigma_{k+1}^{p} & := P^{\Sigma_{k}^{p}}.
\end{align}
Why is every language that is reducible to a language in $\Sigma_i^p$ also in $\Sigma_i^p$?
This comes in the proof of the theorem: If there is a PH-comp... |
I've stumbled at the first OralMessage algorithm in Lamport, et al's paper.
I've searched the web and there are dozens of sites, restating in exactly the same terms and examples, which isn't helping me.
Lamport claims the algorithm can handle (n-1)/3 traitors, and works when the commander is a traitor.
My restatement o... |
I am working on a pumping lemma question and trying to prove that the following is not regular, but I can't finish the proof, if someone can help me it will be great.
So I am given this language:
$L = \{ a^n | n = 3^k , k≥0 \}$ .
Ok. I choose $w = a^{3^m}$. I know for sure that $y = a^t$ ($y$ must be any number or $a$... |
What is a good metaphor or example to explain to an English major the difference between classical computer science and "being good with using MS-Windows"
computer science
computer programming
using computers
3 profoundly different things. Most people have no idea what Computer Science even is. They just see t... |
I'm looking for formal statements and proofs that I can make when using SCXML statecharts. As such, I'm trying to categorize it properly.
SCXML supports hierarchical states. I believe that any hierarchical state machine can be converted into an equivalent non-hierarchical state machine. And I believe that a "simple" no... |
The Chomsky hierarchy is a guideline on language expressive power. The linear feedback shift register is a very interesting "element" to structure a language and there is a large theoretical literature.
In reference to the Chomsky hierarchy (and automata), which is the linear feedback shift register languages/automato... |
I'm trying to prove that the set of even-length strings with the two middle symbols being equal cannot be accepted by finite automata. I can explain why it cannot be accepted intuitively, but I'm having trouble with the proof. Our symbols are {a, b}.
I allowed L = $\{(ab)^{*{\frac{n}{2} - 1}} aa (ab)^{*{\frac{n}{2} -... |
What I'm trying to do is to show a problem in NP can be reduced to the min weight vertex cover problem
I've chosen the max independent weight problem =
input: A graph G with weights on each vertex,
output: An independent set with the max total weight
Before reducing, I've tried to show that the max indep. weight prob... |
In the book Type Theory and Functional Programming [Thompson, S 1999] the author explains the relationship between specifications, types and proofs of functions:
The equivalent specifications can be thought of as suggesting different program development methods: using the ∃∀ form, we develop the function and its proof... |
Which one is better approach do data compression before encrypting it or Encrypt data before compression ? I think it is biased towards the application requirement. Please share your views.
|
To clarify, in haskell, there is an ord function that gives the byte integer of a character (i.e. ord 'a' yields 97); and there is a char function that takes the byte integer of a character and returns the character (i.e. char 97 yelds 'a'.
What is the name of a collection of such functions? I'm not very mathematically... |
Given the algorithm above (taken from the slides (p. 35) of the Coursera course “Algorithms Part I” by Robert Sedgewick and Kevin Wayne), look at the scenario where i is at "X", the following happens:
Scenario: i -> "X", "X" > "P"
1. swap("X", "Z"), gt--; // the value at i is now "Z", which is still > "P"
2. swap("Z... |
The Stable Roommates Problem matches 2n participants into n sets of roommates based off of each participant's list of preferences. I was wondering if there was a variant of this problem where the number of roommates is different. For example, matching 10n participants into n sets. Thanks for the help.
Edit: The Hospita... |
I'm not sure if this is the correct place to ask this kind of a question, but here goes:
I'm doing my own reading of the Principles of Program Analysis book, and i'm having trouble understanding some priciples from Chapter 5 - Type and Effect Systems.
In the book (page 286) there is an example:
I can not understand, w... |
The 3-Partition problem (wiki) is a $\text{NP}$-complete problem which is to decide whether a given multiset of integers can be partitioned into triples that all have the same sum. It is well-known that the 3SAT problem has a plenty of variants. Are there some variants of the 3-Partition problem discussed in the litera... |
I had a debate with my friend. He argued that $o(1)\subseteq O(1)$, so if a function converges to 0, then it belongs to both $o(1)$ and $O(1)$. However I imagine that $O(1)$ represents a constant time, in essence, a non-zero constant time. Is there a broad acceptance that a function converging to zero belongs to $o(1)$... |
There is a shop which consists of N items and there are M buyers. Each buyer wants to buy a specific set of items. However, the cost of all transactions is same irrespective of the number of items sold. So, the shopkeeper needs to maximize the number of buyers. The buyers will buy only if all the items are being sold. ... |
I want to try to create my own very simple programming language and it's compiler or interpreter.
The programming language I use is Java.
My idea was to create a compiler which will compile source code of my created language to some kind of intermediate code (nothing binary or complex, just plain text), and then have a... |
I want to find a context-free grammar for $L = \{a^n : n\leq2^{20}\}$. There's one for sure. I approached it by two ways and both seemed dead end. One was to set a limit during the production of the new strings. But I don't think there's such a thing in CFGs. Second approach was to produce the strings of the language t... |
I have a data set with two classes: one class has at most 2000 members while the size of the second class is unlimited, though it is typically in the hundreds of thousands. I have read that it is problematic to use a decision tree to naively classify this data. My question is, how how I modify the data or the classif... |
I am wondering what is the difference between Bottleneck Travelling Salesman Problem and normal Travelling Salesman Problem?
Thank you
|
Currently I am studying Turing machines and I understand that a Turing machine can produce all the strings of the language accepted by that particular Turing machine. We call such a Turing machine an enumerator. I have studied the formal definition of enumerators that have no input. But I am unable to realize how a Tur... |
Consider
the language $L = \{w, w \in \{a,b,c\}^*, n_c(w) = n_a(w) + n_b(w)\}$, where $n_q(\omega)$ is defined to be "the number of $p \in \omega$.
I have tried a couple of PDA's that follow this whole idea of a stack-replacement kind of algorithm, but the reasoning behind it is incorrect. I know it is not the right ... |
I find binary confusing. I have watched minecraft redstone videos on binary adders, real binary adders, diagrams, etc and yet I have not learned much at all. How does electrons flowing through wires made of gold "add/subtract" to make numbers through some logic gates?!
|
In algorithm analysis, we assume a generic one processor Random Access Machine (RAM). As far as I know, the RAM machine is no more efficient than the Turing machine. All algorithms can be implemented in the Turing machine. So my questions are:
If the Turing machine is as efficient as the RAM machine, then why are we n... |
All problems solved by standard today's general purpose computer can be solved by standard Turing machine.As general purpose computer can't do more than Turing machine so The Turing machine halting problem must also be unsolved by today's general purpose computer.How can I realize the fact that halting problem can't b... |
I want to find a minimal vertex in a tree from which we can traverse some edges exactly twice then come back to that vertex then do it with the rest of edges. By minimal, I mean that the difference of numbers of two subsets of edges have to be minimum.
|
I need to reduce the vertex cover problem to a SAT problem, or rather tell whether a vertex cover of size k exists for a given graph, after solving with a SAT solver. I know how to reduce a 3-SAT problem to vertex cover problem, by constructing the subgraphs for each variable (x, !x) and for each clause (a triable). Bu... |
I want to implement various Randomized Distributed algorithms for MIS, Broadcast, Coloring in Radio Networks. I want use very high level language or any simulator for this. Please suggest on this.
|
I know math is necessary for application development in simulation software and else.
But I'm learning Python and trying to go deep in PHP, and like to develop applications and extends web servers' capability.
I'm before a big dilemma that whether to learn math professionally or not. I have tried my best to avoid being... |
We're accessing an API of a web system for obtaining product information. We require some additional information, which is not available through the API. This information is publically available for each product visually - through the source code for each item on its item page. We've written an algorithm which parses t... |
I am interested in the time complexity of a compiler. Clearly this is a very complicated question as there are many compilers, compiler options and variables to consider. Specifically, I am interested in LLVM but would be interested in any thoughts people had or places to start research. A quite google seems to bring l... |
I am trying to find a way to solve Euclidean TSP in a polynomial time. I looked at some papers but I couldn't decide which one is better. What is the general approximation algorithm for solving this problem in polynomial time?
|
In the Shamos-Hoey algorithm for finding whether or not any two of $n$ line segments intersect, which is available at this site: http://geomalgorithms.com/a09-_intersect-3.html, there is use of "nearest line above" and "nearest line below". The algorithm is supposed to run in time $O(n\log n)$. Here is their pseudocode... |
I was going through a deterministic PDA that accepts $wcw^R$ (described in Ullman's textbook), in which the last transition is given as $(q_1,\epsilon, Z_0)\to(q_2,Z_0)$, where $q_2$ is the final state.
In DFAs we don't consider $\epsilon$ transitions, while in PDAs we do include them. Why?
|
I'm wondering why the following argument doesn't work for showing that the existence of a Las Vegas algorithm also implies the existence of a deterministic algorithm:
Suppose that there is a Las Vegas algorithm $A$ that solves some graph problem $P$, i.e., $A$ takes an $n$-node input graph $G$ as input (I'm assuming th... |
Let $G$ be a DAG. We know that some nodes in $G$ are "bad", while the others are "good"; a descendant of a bad node is bad while the ancestors of a good node are good. We also know that bad nodes have a unique minimal element in $G$ which we'd like to find querying as few nodes as possible with queries of the type "Are... |
Given a set of buyers, houses, agents with the following constraints:
Agents only know a subset of buyers
Agents only know a subset of houses
Agents can only do some amount of transactions
Construct a flow network to model the problem.
Disclaimer this is homework
I have put together some thoughts on a solution to th... |
Consider the following Huffman trees:
I was asked if those trees can have the same corpus. My answer was no, based on these calculations:
For the right tree:
$a_1 \le a_2$
$a_1 + a_2 \le a_5$
$a_3 \le a_4$
$a_1 + a_2 + a_5 \le a_3 + a_4$
For the left tree:
$a_1 \le a_2$
$a_3 \le a_4$
$a_1 + a_2 + a_3 + a_4 \le a_5$ ... |
This is a question I have stumbled upon in my textbook, and didn't really know how to approach:
Given a $k$-bit binary counter.
We have an operation Increment, which adds 1 to the counter.
We add a new operation Decrement, which subtracts 1 from the counter.
Prove that the cost for executing $n$ operations is $\Theta(n... |
Deterministic context-free languages are not in general closed under substitution. I have been looking at the DK-test (it is described in the 3rd edition of Sipser's Intro. to Theory of Computation, 2012) which can be used to check if a given CFG is deterministic, and it seems to me this can be used to show that DCFLs ... |
For probabilistic algorithms such as PageRank and EigenTrust, the stopping case is given as $|R_{t+1} - R_{t}| < \epsilon$ (i.e. convergence is assumed). Neither the papers on EigenTrust or PageRank, or the PageRank wiki page, give any clear indication of what $\epsilon$ should be.
I believe it might be something to d... |
Periodically I come across sentences like
"Winograd's variant [20] of this algorithm, whose asymptotic complexity is
also $O(n^{2.81})$ are considered" (from https://www.cise.ufl.edu/~sahni/papers/strassen.pdf)
I understand intuitively how we end up with complexities like $O(n^2)$ and $O(n \log n)$ because I can see ... |
An automaton is an abstract model of a digital computer. Digital computers are completely deterministic; their state at any time is uniquely predictable from the input and the initial state.
When we are trying to model real systems, why include nondeterminism in Automata theory?
|
If we have a FPRAS for approximating the quantity c, can we get another FPRAS for estimating (c-1) using the estimation of c?
|
I'm wondering which is a better scheduling algorithm to use. The only real difference I can see is that in FSCAN there are two queues, and when a scan begins all requests are put in one queue and the other left empty. Then during the scan the other queue is used to store new requests and deferred until all the old requ... |
I'm having a lot of trouble solving problems in my Comp Theory class. I just have no idea how to formulate arguments for certain things like proving the concatenation of two non reg langs can have reg languages, or whatever. I know it sounds cliche and really corny, but I don't want to just google the answers. It may b... |
How different are string matching and integer matching in terms of time complexity?
I'm asking this especially in relation to Rabin Karp algorithm. Why is it faster to compute hash code for every substring and check for equality of hashcode with the hashcode of the given string than the naive method of just checking if... |
Consider the following soft margin loss function: $\max(0, 1-yf(x))$. I have the problem of needing to compute the conditional probability $p(y|x)$ corresponding to this function and am having trouble making the connection between conditional probability and this function. I have come across a few papers (e.g. http:/... |
Let f be a polynomial-time reduction of a decision problem A to a decision
problem B. We know that, if B $\in$ P then A $\in$ P. Similarly, if B $\in$ NP then
A $\in$ NP. However, what about the other direction? Assume that A $\in$ NP and
consider the following non-deterministic algorithms to decide whether y $\in$ B:
... |
I was watching the lecture by Jim Weirich, titled 'Adventures in Functional Programming'. In this lecture, he introduces the concept of Y-combinators, which essentially finds the fixed point for higher order functions.
One of the motivations, as he mentions it, is to be able to express recursive functions using lambda ... |
Assume $P\neq NP$.
What can we say about the runtime bounds of all NP-complete problems?
i.e. what are the tightest functions $L,U:\mathbb{N}\to\mathbb{N}$ for which we can guarantee that an optimal algorithm for any NP-complete problem runs in time of at least $\omega(L(n))$ and at most $o(U(n))$ on a input of length ... |
I'm writing a small program that implements a trigram HMM model and apply it by using Viterbi Algorithm. It's very standardized. However, I have never written anything like this before, and I get confused of what I should use as the START (*) and STOP symbols.
I tried to search for the answer online but apparently peop... |
Can $R$ be inferred from $P$, $Q$, and $(P \to Q) \to R$ using only modus ponens?
My understanding is that it can, as shown below, but I was told this was incorrect.
Proof of ${P, Q, (P \to Q) \to R} \vdash R$ using modus ponens:
P, Q, (P->Q)->R : Given
Q, (Q)->R : By Modus Ponens
R : By Modu... |
Quicksort is described as "in-place" but using an implementation such as:
def sort(array):
less = []
equal = []
greater = []
if len(array) > 1:
pivot = array[0]
for x in array:
if x < pivot:
less.append(x)
if x == pivot:
equal.appen... |
What does superscript + mean in relational algebra? Suppose $A$ is a subset of attributes of all attributes in a relation $R$. What does $A^+$ mean?
|
Is there already a worst case time complexity proof for the sum of all elements in a power set? I would assume, naively, you have to just add everything, which would run in about 2^n, where n is the size of the set.
For example: A = {1,2,3} Powerset(A) = {{}, {1}, {2}, {1, 2}, {3}, {1, 3}, {2, 3}, {1, 2, 3} } Sum(Power... |
I implemented dependently typed lambda calculus in the spirit of this article: http://www.andres-loeh.de/LambdaPi/LambdaPi.pdf
The calculus, works and I experimented with it and like it. However, I want to add inductive types to do more complex stuff. What are the options for doing this?
I am thinking about two ways of... |
Let's say we have a directed graph $G = (V, E)$ for which $(v, w) \in E$ and/or $(w,v) \in E$ holds true for all $v, w \in V$. My feeling is that this graph most definitely is Hamiltonian, and I want to find a Hamiltonian path in it (from any vertex to any other vertex, I don't care where to start or stop).
I wanted to... |
Does anybody know any toy database / relations that are particularly good and also complete to demonstrate and test relational algebra concepts? I'm hoping some database researchers should have already made that and improved over long time from pedagogical practices.
|
I'm curious to know if this problem is NP-Hard / NP-Complete, which I believe would mean I'm unlikely to find a polynomial-time algorithm to solve it.
I have written a program which randomly generates a tournament fixture, and I call it many times to try to pack the matches into the smallest number of rounds.
When it c... |
In a given cellular automaton, such as Conway's Game of Life, is there anything known about how many Garden of Eden patterns there are by pattern size? Say, pattern size is n x n, what's the likelihood that a random pattern is a GoE as n increases?
Also, by the Garden of Eden-theorem, only cellular automata which are ... |
How would about proving this is not regular with the pumping lemma. Please include all steps and explain all steps. I am really new with this.
$1^{2x}0^y$ and $y>= x$
Does it matter which side you pump? How do you pick which side to pump?
This is what I was thinking:
$$u = 1^{2x}$$
$$v = 0^y$$
$$w = 1^{2x}0^y$$... |
I am trying to prove this expression but don't have an exact idea about what to do:
If $E$ is any alphabet and $L$ is any language $L \subseteq E^*$. Prove that $L^*L^* = L^*$.
|
I have a variant of bidding problem at hand.
There are N bidders(~20) who bid for items from a pool of many items(~10K). Each bidder can bid many items. I want to maximize the number of bidders who are satisfied. A bidder is satisfied if he gets all the items that he bid for in the first place. For eg-
Bidders = A,B,C
... |
$ALL_{REGEX}$ is the computational problem of determining for regular expression x if $L(x) = \Sigma^*$. In a proof for $ALL_{REGEX} \in PSPACE$, the following non-deterministic turing machine $M(R)$ on regular expression $R$ is given
Convert R to an NFA $N = (Q,\Sigma,\delta,S,F)$; $K = S$;
While $K \cap F \neq \... |
I am trying to solve a given problem: Find an algorithm to determine if a graph has a clique of size 3 in $O(n^{2.81})$ steps. The hint given is that $2.81 > \log 7$. In order to solve this I came up with a conjecture: if $m > n^{\log 7}$ then the graph has $K_3$ as a subgraph. This will easily solve the problem if the... |
For a proof I need to use the fact that every word in the language of an enumerator occur on the output paper in finite time. Is it true?
For example, the language of the natural numbers in decimal representation. Can the enumerator print the odd numbers first and then the even numbers? (if yes, I am wrong)
$1, 3, 5, 7... |
Basically, I believe that if you have something like a .dmg file the OS opens it with a certain program which takes the code behind it and does things to it. So why couldn't you then take the program that runs the .dmg file on Mac and put it on window to run the program? I know I'm probably missing some key component h... |
(This is based on my earlier MSE question that has been stagnant for just over a week, since the
best answer only addresses the case of two mines and does not even completely resolve that.)
What is the computational complexity of playing 1-dimensional Minesweeper in a way that
maximizes the probability of winning, wh... |
Can a Turing Machine decide whether an arbitrary real number is computable or not? Does this even follow from the solution of the Halting problem? If not, who proved it?
|
I'm an undergraduate just beginning to read about reversible computing. I know that, because of Landauer's principle, irreversible computations dissipate heat (and reversible ones do not). I brought it up with my professor, who had never heard of reversible computing before, and he was having difficulty understanding w... |
In the plot squared length of Fourier coefficients vs frequency, the peak gives the strongest frequency. does it give the accurate value of period??
Is it like a single frequency in frequency domain corresponds to a range of periods??
|
I am trying to work out centrality in a network using Freeman's network centrality. I have an in degree of 83 and an out degree of 110. I want to work out the network centrality using my out degree using the following formula:
$$
\frac{\sum_{i=1}^{g}[{C}^d ({n*})-C^{d}]}
{[(N-1)(N-2)]}
$$
This is where
$$
{n}
$$
is ... |
Suppose one wanted to build a tree at random. Let the first insertion at step $i = 1$ be the root node. From here, nodes are inserted into the tree at random one at a time. How would one go about calculating the expected number of nodes $E(d)$ at depth $d$ after $i$ insertions?
For example, At $i = 1$, it's just the... |
Can there be any relations regarding the number of nodes available in a digraph so that to qualify it as NP-Complete problem.
If we consider this problem for instance:
Input: A digraph $G=(V,E)$ and two nodes $u,v \in V$
Question: Is there a path in $G$ from $u$ to $v$?
Can we say this problem is NP-Complete problem... |
I've always wondered why processors stopped at 32 registers. It's by far the fastest piece of the machine, why not just make bigger processors with more registers? Wouldn't that mean less going to the RAM?
|
What will happen if sequence number is not used in an ARQ protocol (e.g, Go-back-N, selective repeat)?
|
Hi I am trying to solve a LL(1) form question for first n follow rule The question is
A::=BC|C
B::=Bd|ef
C::=gh|j
What I have done to eliminate left recursion
A::=CA’
A’::=CB’
A’::=ϵ
B::=efB’
B::=dB’
B’::=ϵ
C::=gh
C::= j
Is it correct?
Thanks guys, it has been solved.
|
This is a problem from 'Concrete Abstractions' which is available free on the web[1]. It's a book similar to SICP. The problem:
Exercise 2.16
Consider the following procedure foo:
(define foo
(lambda (x n)
(if (= n 0)
1
(+ (expt x n) (foo x (- n 1))))))
Use induction to prove that (foo x ... |
Hello everyone just like the title says I want to prove that $H(x) = \mu y T(x,x,y)$ has no total computable extension such that if we had a function $BIG(x)$ that is both total and agrees with $H(x)$ whenever $H(x)$ is defined, then $BIG(x)$ is not computable. This is a homework question so I don't want a full solutio... |
I meant that that the game programmer can just add its own code to the game to manipulate its own low level function as the operating system does provide in a common executables,and load it into the boot mode using its own bootstrap
|
I am reading the paper: "Maximum Weight Independent Set Of Circular-Arc Graphs and It's Applications" (http://link.springer.com/article/10.1007%2FBF02832044). And I had a question regarding the proof of Lemma 3 in the paper. It is stated as follows.
If $X$ is the maximum weight independent set of the circular-arc graph... |
As we all know, Matrix Factorization is an effective method to do rating prediction jobs in recommender systems. Thanks to the work of Yahuda Koren. My question is why MF can do this job? What's the physical meaning behind it?
|
I'm looking for examples of loops that have running time $O(nm)$, $O(n+m)$ and $O(n\log m)$ to help me understand these concepts. Could anybody give some examples and explain why they have the given running time?
|
I made a method that appends a sequence to another sequence.
So: (append [1,2,3] [4,5,6]) = [1,2,3,4,5,6]
CODE In C#
IEnumerable<int> Append(IEnumerable<int> xs,IEnumerable<int> ys)
{
using(var iteratorX = xs.GetEnumerator())
using(var iteratorY = ys.GetEnumerator())
{
bool isTrueForX = false;
... |
Union-By-Rank and Path Compression is supposed to improve the performance of a tree implementation of a disjoint set.
However, in looking at the UNION(x, y) operation, I noticed that if x and y are actually the roots of the 2 trees being merged, no path compression actually takes place. The resulting tree would simp... |
Bloom filters are a variant of hash tables except it is much more space efficient at the cost of a low probability of false positives .
How it works : Assume there are 10000 bits , 3 hash functions and an object Foo is to be inserted into the Bloom Filter .
Insertions : Foo will be hashed by the 1st hash function and t... |
I am reading the proof of PCP theorem in Proof Verication and Hardness of Approximation Problems. The following paragraph appears in section 3 (page 4), "Outline of the Proof of the Main Theorem".
The results of these sections show that $NP \subset OPT (poly(n), 1)$ (Theorem 5) and $NP \subset OPT (\log n, poly \log n... |
When using 2's complement with 4 bits, the largest positive int I can represent is 0111. The smallest negative one is 1000.
The smallest int should intuitively be the negative of 0111 - 1 = 0110 since we can represent one more positive than negative int.
If we invert the bits of 0110 and then add 1, however, we get 101... |
We all know how to use “Big O” notation to show how CPU instructions run increase as the size of the dataset increases. E.g. a quick sort is O(n log n).
However for the last few years, instructions that don’t access any data outside of the level 1 cache have been close to free compared to instructions that hit main ... |
Garbage collections have to visit all objects that are alive, so as to find the memory that can be reclaimed. (Having many generations’ just delays this a bit)
All things being equal, it is clearly better to first visit the object that are already paged into RAM, before paging other block in and therefore paging out... |
To prevent collisions in Hash table , seperate chaining with linked list is used . Hash table works by hashing the key and storing the value in the bucket.
Assuming 4 keys hash to the same bucket , and the bucket has a linked list which has 4 nodes , how would we know which value belong to the key when we try to searc... |
I need an efficient data structure for maintaining a set of values.
Here, $n_1$ is the number of insertions per unit time; $n_2$ is the number of deletions per unit time; $k$ is the number of searches per unit time.
I have 4 possible use cases:
$k \gg n_1,n_2$ with limited memory
$n_1 \gg k,n_2$ with limited memory
$... |
I am trying to wrap my head around recursion and divide and conquer algorithms. Can someone provide a proof and explanation of how many times a list of n elements can be divided in 1/2 on both sides.. In other words the total number of half divisions in a recursive divide procedure on a list of size n.
|
I have a problem with an exercise asking me to solve the following recurrence:
$$f(n+1)=f(n)^2, \quad f(0)=2$$
Can someone explain how to solve this? I tried but couldn't.
|
I have been learning about Big O, Big Omega, and Big Theta. I have been reading many SO questions and answers to get a better understanding of the notations. From my understanding, it seems that Big O is the upper bound running time/space of the algorithm, Big Omega is the lower bound running time/space of the algorith... |
I start to suspect this problem is very hard now that I cannot find a single relevant literature on the subject, but it's too late to change the class project topics now, so I hope any pointers to a solution. Please pardon the somewhat artificial scenerio of this question, but here goes:
Technical version:
Let $\Sigma... |
I need to use discrete differential evolutionary algorithm for assigning discrete values from set size $L$ to vectors of size $D$ where $L$ could be smaller, equal or larger than $D$. Elements of vector $X$ could take the same values of other elements. My question is if we have a population of size $NP$ with each vect... |
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