Beliefs are orthogonal to proofs. Belief may direct attempted solutions by researchers or rather their main interest but this does not prevent them from checking a proof anyway. The problem with $P \... View answer Accepted answer 31 votes This is Collatz conjecture - still open problem. Conjecture is about proof that this sequence stops for any input, since this is unresolved, we do not know how to solve this runtime recurrence ... View answer 23 votes There is one forgotten thing about optimisation here. There was longish debate about fortran outperforming C. Putting apart malformed debate: the same code was written in C and fortran (as testers ... View answer Accepted answer 22 votes The memory access pattern in Quicksort is random, also the out-of-the-box implementation is in-place, so it uses many swaps if cells to achieve ordered result. At the same time the merge sort is ... View answer 16 votes No it is not, and moreover it does not depend on I/O. Simple counterexample: write a program to find a perfect odd number (this is an open problem: we do not know yet whether one exists) - it does ... View answer Accepted answer 13 votes With equation: not really. Superlinear speedup comes from exceeding naively calculated speedup even after taking into account the communication process (which is fading, but still this is the ... View answer 13 votes There is another interpretation, both$i, j$might be variables, in that case it is double loop: for every$j$in$\{0,\ldots,n-1\}$: for every$i$in$\{0,\ldots,n-1\}$: &... View answer Accepted answer 11 votes I suggest Tree Sort, variant with self-balanced tree. In this case complexity is$O(logn)$(per insertion). In that case you can access sorted structure at any time. If inputs comes in batches, ... View answer 10 votes There are: Elm, Haskell, its predecessor Miranda and its predecessor ISWIM, YAML where spaces are crucial for syntax and tabs are forbidden, OCCAM, Coffee script and Cokescript both are language to ... View answer Accepted answer 10 votes Oblivious means that the control flow is independent of some properties of data. For example Bitonic Sort (also known as sorting net_ is oblivious, because it always compares the same elements ... View answer Accepted answer 9 votes You have introduced$n$and$m$as the order of B-tree, I will stick to$m$. Their height will be in the best case$\lceil log_m(N + 1) \rceil$, and the worst case is height$\lceil log_{\frac{m}{2}}(...

The RE in the Automata Theory are equivalent to FA, but for the programming languages (regexp) this is no longer true. The regular expressions in the programming languages (like PCRE) are far more ...

The constraints of some languages makes it easier to implement faster code (e.g. Fortran vs C and the pointers aliasing) which is a tradeoff between out-of-the-box performance and possibilities). The ...

I would suggest a more detailed explanation of mp3 codec. FFT is applied on the time domain signal, so in fact it does not use the result from the MDCT. The input to the psychoacoustic models is in ...

Human eye is very sensitive to luminance change and order of magnitude less sensitive to chrominance change. MPEG under the hood is based on JPEG transform, so you have 8x8 blocks of DCT. It blurs a ...

Bitonic sequence is defined for example for parallel sort, as non-decreasing and then non-increasing sequence, to allow duplicates. See here: Bitonic sequence. Also Wikipedia article about Bitonic ...

There is hidden linear time to perform merge part of sorting algorithm. Linear is less than loglinear, so it was not visible. $\log1=0$, but it means that you will not e.g. heapify, just merge in $O(n)... View answer 6 votes Hash function calculates array position from given string. If this is perfect hash it means that there are for sure no collisions, the most probably array is at least twice bigger than number of ... View answer 5 votes Build suffix tree using Ukkonen's algorithm, this way in$\mathcal O(n)$you will find all substrings in provided text with indices. In the case of approximate matching, there is also extended ... View answer Accepted answer 5 votes If element appears more than 50% of time, you can use Median of medians algorithm by Blum et. al. It is not deterministic though. Or use specialized algorithm by Boyer and Moore called "Majority vote ... View answer Accepted answer 5 votes The first step is to take$c = a \text{ XOR } b$, this will return$0$if the numbers were equal or some bits set to$1$otherwise. Now to calculate the result the$c$variable should be ORed with its ... View answer Accepted answer 5 votes Let$W$be the number of bits,$A, B$integers to compare.$Result = (NOT((A - B) \text{ OR } (B - A))) >> (W - 1)$. Here NOT negates bits.$A - B$and$B - A$is zero iff numbers are equal ... View answer Accepted answer 5 votes It is not some magic element but$-\infty$, which is because this is min-heap, in max-heap it would be$\infty$. The sole purpose is consistent representation of all elements inserted - it guarantees ... View answer Accepted answer 5 votes Short answer: No, you will not get the same results. It does not matter what coordinate system or what geographic standard you are using, it is not possible to make projection from sphere into ... View answer Accepted answer 5 votes BTrees are used in practice - file systems, database with$k$for example equal 1024 or 4096, so it seems to be bigger than binary. Probably you have not encountered need yet. For example ternary ... View answer Accepted answer 5 votes If it is possible try to exploit banded tridiagonal nature of matrix. Otherwise if the matrix contains only a constant number of distinct values (which surely is being binary), you should try Mailman ... View answer 5 votes Yes, exactly as you said. This is used to decrease the number of multiplications, so it is more efficient than computing it the normal way. Example: You have the polynomial$ax^3 + bx^2 + cx + d$... View answer Accepted answer 4 votes Let me start from correctness check, will this method always generate grids abiding sudoku rules? In fact yes, your shift operator is simply circulant matrix, scattering boxes. Since circulant matrix ... View answer 4 votes Your problem is known as Pancake sorting and it is not true that$f(n) < n$. The minimum number of swaps is between$\frac{15n}{14}$and$\frac{18n}{11}$. Currently we know empirically that$P_{17}...