# Questions tagged [iteration]

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### 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 ...
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 ...
77 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. ...
30 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 ...
143 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 ...
143 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 ...
1 vote
272 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? ...
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 ...
1 vote
143 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, ...
36 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 ...
35 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 ...
162 views

183 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 ...
1 vote
44 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 ...
114 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 ...
133 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 ...
541 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 ...
873 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 ...
48 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 ...
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 ...
1 vote
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 ...
81 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 ...
244 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, ...
302 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 ...
309 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 ...
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 ...
1 vote