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Questions tagged [iteration]

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SCoP, Iteration Domain in Polyhedral Optimization and use of Presburger arithmetic

Context: While exploring the fundamentals of polyhedral optimization and attempting to explore a connection from the input Static Control Part (SCoP) to the iteration domain from birds eye view, I am ...
F.C. Akhi's user avatar
  • 123
1 vote
1 answer
88 views

Loop Bounds vs. Iteration Domain in Polyhedral optimization

Context: I was reading a tutorial on polyhedral optimization. But got confused while trying to translate the iteration domain (i.e. loop bound) to set builder notation. Problem Description: A code ...
F.C. Akhi's user avatar
  • 123
2 votes
1 answer
125 views

Iterate over a range randomly without any duplicate or storing the full range in memory

I'm trying to create (or find) an algorithm to iterate over a range (e.g.: 1-100, etc) but randomly, without any duplicate values (similar result to random sort, etc) but without actually storing the ...
Nordine Lotfi's user avatar
0 votes
0 answers
14 views

Periodicity of substitution system

I’m interested in substitution systems: maps which use a set of rules to transform elements of a sequence into a new sequence. For simplicity we will consider here only binary 1-D arrays. Unlike the ...
lesobrod's user avatar
  • 111
0 votes
0 answers
79 views

Iterate through all values of a certain subset of all permutations

Let's say we've got $n$ numbers to multiply together. But the multiplication operation, like in computer floating-point arithmetics, is not associative. Thus the order of multiplication matters. ...
user2373145's user avatar
0 votes
0 answers
34 views

Symmetry group of the acyclic oriented L-cube using the Hyperoctahedral group

I'm trying to figure out all elements of a symmetry group for the acyclic oriented $L$-cube. I do have an algorithm, but its complexity is not suitable for larger $L$. I computed $L=5$ on my old ...
Dan's user avatar
  • 51
0 votes
0 answers
172 views

Iterative version of depth-first-search code to detect cycle in a directed graph [duplicate]

I have solved a problem that required me to find if the given directed graph had a cycle or not. The deal is, I used a recursive approach to solve it in the depth-first-search method. I was just ...
Siddharth VS's user avatar
2 votes
1 answer
164 views

Iteration Vs Induction Method

I am working on different methods to solve Recurrence Relations. I am using Iteration method and substitution method, which involves Induction, but I feel that sometimes Induction method creates a bit ...
محمد صلاح الدین جمیل's user avatar
1 vote
2 answers
277 views

Why is there no "traditional"-mathy way to describe the general algorithm and give a more math-friendly definition of algorithm?

Why is there no algebraic definition of algorithm besides recursive functions? If I'm wrong, what is the matheist definition of algorithm that you've ever seen in a paper and can you provide a link? ...
HighAsAKiteOnMath's user avatar
20 votes
3 answers
7k views

Time complexity $O(m+n)$ Vs $O(n)$

Consider this algorithm iterating over $2$ arrays $(A$ and $B)$ size of $ A = n$ size of $ B = m$ Please note that $m \leq n$ The algorithm is as follows ...
Shylajhaa's user avatar
  • 301
1 vote
1 answer
145 views

How to use Runge–Kutta methods in a second order ODE

Consider a second order equation $F=ma=m\ddot{x}$. In the language of Euler's method $\ddot{x}(t+dt)=F(t,x(t),\dot x(t))$ $\dot{x}(t+dt)=\dot x(t)+\ddot x(t)dt$ $x(t+dt)=x(t)+\dot x(t)dt$ Basically, ...
ShoutOutAndCalculate's user avatar
0 votes
0 answers
38 views

Is it possible to determine an instance of an NP-hard problem is easy or hard by the optimization?

I have an NP-hard problem and an optimization to deal with the problem. I want to know that is it possible to distinguish between easy and difficult instances of the problem by the parameters of the ...
samie's user avatar
  • 21
0 votes
1 answer
36 views

What parameter of optimizations, like time solving, can be used to show a phase transition in NP-hard problems?

Before asking the question, I should say that I am not sure here is a proper community to ask this question or not. I have an NP-hard problem and an optimization to deal with the problem. Recently, I ...
samie's user avatar
  • 21
2 votes
2 answers
171 views

How to iterate the Hardy-Ramanujan integers quickly

The Hardy-Ramanujan integers, A025487 - OEIS, are integers which when factorized, have their exponents for all the primes starting from 2, in decreasing (not strictly) order. The first few terms are: $...
simonzack's user avatar
  • 313
1 vote
1 answer
203 views

Iterate unique sets of integers

I'm trying to figure out of if there's a way to generate all unique sets of integers of length K, where each member has an upper bound of N, and a lower bound of M, without tracking which sets have ...
thephpdev's user avatar
  • 113
1 vote
1 answer
406 views

Computation of iterated logarithm function

I recently came across the iterated algorithm function denoted as $\lg^* n$. But I am having a hard time understanding this statement: $\lg^* n = \min \{i \ge 0: \lg^{(i)} n ≤ 1\}$ I could not ...
Sachin Bahukhandi's user avatar
1 vote
1 answer
1k views

Arbitrary depth nested for-loops without recursion

Suppose I have an array of n values I want to apply nested for-loops over to an arbitrary depth m. ...
dx_over_dt's user avatar
1 vote
0 answers
296 views

Can every problem that uses recursion be solved using iteration? [duplicate]

We all know iterations and recursions are a powerful thing in programming. But this doubt always troubles me whenever I write an iteration or recursion. Can every recursive problem solved using ...
J Arun Mani's user avatar
3 votes
0 answers
51 views

What is the name of visiting an array starting at first element, then last element, then second, then last but one, then third, etc

For example if I have an array [0, 1, 2, 3, 4, ..., n] and I want to iterate over it in an order like ...
Azat Ibrakov's user avatar
0 votes
1 answer
39 views

Search Algorithm with two areas of solutions [closed]

I need some help with a problem. I have currently an algorithm. This algorithm gives me a true or false for a variable which I need to iterate( e. g. From 0 to 100} . Till now I solved it with a brute ...
Ildon's user avatar
  • 3
2 votes
2 answers
105 views

Is there a formal definition for iteration?

I wanted know if there is a formal definition of iteration. In the sense that, this definition will say that after the 4th iteration is termination or the 5th iteration and not the 2nd iteration. ...
rert588's user avatar
  • 261
0 votes
2 answers
245 views

Iteration vs Recursion question in Lisp method

I am curious if the following method would be called iterative or recursive: ...
subjectsphinx's user avatar
0 votes
1 answer
31 views

How does a=2 twice in this code sample? [closed]

I am just starting out learning code. The output of the following code is OOOXOXOO, but I don't see how X can be printed twice. How does a=2 more than once? ...
BenG's user avatar
  • 3
0 votes
0 answers
36 views

Application of iterative algorithm $(\theta_n,w_n)$ converging to $\{(\theta,\theta):\theta \in \Bbb R\}$

I have a iterative algorithm $(\theta_n,w_n)$ which I am showing converges to $\{(\theta,\theta):\theta \in \Bbb R\}$. The iterative algorithm is of the form : $\theta_{n+1} = \theta_n + a(n)[h(\...
applied_math's user avatar
0 votes
3 answers
187 views

Which is better ? Iterations or Recursions?

I've heard that any algorithm using iterations can be changed into one that uses recursions and vice-versa. But which type of repetition is preferable for minimum amount of computational effort and ...
Demis's user avatar
  • 119
1 vote
0 answers
49 views

Nested Function stuck on iteration update

I want to solve the Sparse Extended Information Filter Slam described by Dr. Sebestian Thrun in Probabilistic Robotics.I stuck in some nested function. The algorithm is described in page 309 in this ...
Encipher's user avatar
  • 167
0 votes
2 answers
125 views

If it's Possible to Create the If-Statement from Simpler Primitives

This question is about how to create an if statement (one of the control-flow statements) from scratch. An if-statement is typically a built-in construct in ...
Lance's user avatar
  • 2,243
0 votes
0 answers
139 views

Understanding How to Flatten a Nested Function System

There are at least two ways to flatten out a nested function. Both of them need to keep a certain amount of state to accomplish this. The two ways are: By creating several boolean variables for each ...
Lance's user avatar
  • 2,243
4 votes
1 answer
557 views

Prove correctness of the iterative algorithm

Description: Given an array nums and a value val, remove all instances of that value in-place and return the new length. Do not allocate extra space for another array, you must do this by modifying ...
CodeYogi's user avatar
  • 281
7 votes
0 answers
1k views

Understanding the Polyhedral Model

I am wondering at a high level the mathematics of the Polyhedral Model. The polyhedral model (also called the polytope method) is a mathematical framework for programs that perform large numbers of ...
Lance's user avatar
  • 2,243
2 votes
1 answer
50 views

Generating all words of length $n$ avoiding $A^2$ and $B^3$

I need to find a way to iterate over all sequences of words in two letters $A,B$ avoiding the sequence $A^2 = AA$ and $B^3 = BBB$. First of all, what is the regular expression for such a thing? I ...
john mangual's user avatar
  • 1,951
2 votes
1 answer
99 views

Calculating $\sum_{i=1}^a \lfloor a/i \rfloor i^2$

I have a sum: $$S = \sum_{i=1}^n{\lfloor a/i \rfloor i^2},$$ where $a$ is a constant. Is there a way to speed this up? That is, can we avoid iterating overl all $i$s, possibly calculating it in ...
Robert Hanigan's user avatar
1 vote
1 answer
3k views

Find Number of even subarrays $O(n)$ [explanation needed]

So I found a solution to this problem here http://marcodiiga.github.io/number-of-even-sum-subarrays but I am unsure of exactly how it works. I get the premise that in order to have an even sum it must ...
wieiooof's user avatar
0 votes
0 answers
82 views

How is this defined in an iterative style?

This is the so-called recursive style: And this is the so-called iterative style: It seems like it is defined recursively to me. The function doesn't hide the next call of the function defined in it ...
Jack Pan's user avatar
  • 133
0 votes
1 answer
255 views

How to convert this recursive algorithm to an iterative form?

Let us assume there's a folder structure as shown below: The letters a-d represent folders and the number 1-5 represent video files where for the file n, ...
Somenath Sinha's user avatar
5 votes
1 answer
321 views

Finding the largest linear combination that is not possible

Regarding the problem: What is the largest bet that cannot be made with chips worth $\$7.00 $ and $\$9.00$? Verify that your answer is correct with both forms of induction. I need to find an ...
jiten's user avatar
  • 187
0 votes
0 answers
318 views

Iteration vs. recursion: what do these terms really mean?

Most of us know the typical answer to this question: if a function calls itself, it's recursion, if it's a loop, it's iteration. We also know that recursion can be simulated using iteration (by ...
John Doe the Righteous's user avatar
0 votes
2 answers
59 views

Is linked list a preferable underlying basic DS for a collection mutable through an iterator

I need to implement a collection DS that exposes an iterator which can be used to iterate an underlying collection and possibly remove the current item. I can use either a vector (dynamic array) or a ...
Max Koretskyi's user avatar
1 vote
0 answers
27 views

Basic Determine exact amount of iterations

How exactly do you track the exact amount of iterations? I know its probably basic but can't figure out how so was hoping someone could explain to a complete beginner how you arrive at an answer. <...
yige's user avatar
  • 11
46 votes
5 answers
12k views

Iteration can replace Recursion?

I've been seeing all over stack Overflow, e.g here, here, here, here, here and some others I don't care to mention, that "any program that uses recursion can be converted to a program using only ...
Tobi Alafin's user avatar
  • 1,617