FAQ Database Discussion Community

## Sorting algorithm times using sorting methods

python,algorithm,sorting,time-complexity,computation-theory
So I just learned about sorting algorithm s bubble, merge, insertion, sort etc. they all seem to be very similar in their methods of sorting with what seems to me minimal changes in their approach. So why do they produce such different sorting times ie O(n^2) vs O(nlogn) as an...

## How to match a set against a set of sets, completely

mapping,combinatorics,computation-theory,np-complete,set-theory
This problem is similar to the "Exact Hitting Set" problem (http://en.wikipedia.org/wiki/Exact_cover#Exact_hitting_set) but with slightly different constraints. I am looking for libraries, implementations, or papers that solve the following. Say I have a set of sets S, and is initialized as follows: S = {N, O, P, E}; N = {1,...

## Fastest Way to Generate x Number of Random Variables

matlab,vectorization,computation-theory
index = [10 100 1000 10000 100000] Let's say I wanted to generate 10, 100,...,100000 (corresponding to index above) exponential random variables with parameter 1/10. I of course did this with a for loop and with the command for example x = exprnd(0.1,100,1) One can also generate the exponential random...

## NP and 3-SAT and One Facts

computation-theory,turing-machines,np-complete,np,decidable
any expert could help me why this sentence is True? if L ∈ NP and L ≤p 3−SAT (i.e: reduce L to 3-SAT in poly time) then L is NP-Complete. ...

## expressions in lambda calculus

lambda,functional-programming,computation-theory
am trying HARD AND FAILING to find how to express a question in Lambda.. Perhaps am mistaken in the search? As far as I understand, in Lambda calculus, we get to define the parameters, operations, etc. eg: TRUE := λx.λy.x FALSE := λx.λy.y AND := λp.λq.p q p OR :=...

## Guidance on Algorithmic Thinking (4 fours equation)

algorithm,computation-theory
I recently saw a logic/math problem called 4 Fours where you need to use 4 fours and a range of operators to create equations that equal to all the integers 0 to N. How would you go about writing an elegant algorithm to come up with say the first 100......

## Language class compilable to heapless runtime

compiler-construction,programming-languages,computation-theory,memory-model,turing-complete
So in the general case, a program uses both memory in the stack (automatically managed) and heap (garbage collected or manually managed). What is the class of programs that can be compiled to use memory in a stack-like fashion only and no heap allocation? Is it still Turing-complete with some...

## Is finding a subset with exact cut with other given subsets NP-hard?

algorithm,complexity-theory,combinatorics,computation-theory
I am trying to figure out whether the following problem is NP-hard: Given G_1,..,G_n subsets of {1..m} c_1,..,c_n non-negative integers in {0..m} Find T subset of {1..m} S.T. for all i=1..n, T intersects G_i in exactly c_i elements I tried to find reductions to NP problems such as coloring, or...