Questions tagged [recursive-algorithms]
Questions dealing with recursive algorithms. Their analysis often involves recurrence relations, which have their own tag.
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Generate set of numbers containing 3 consecutive 1, but without the elements of the previous set
So I have this specific problem that I couldn't figure out. I want to create a set $F_n$ containing all bitstrings that has 3 consecutive 1s, but not those that are already contained in all the ...
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Division based recurrences instead of subtraction based: $F(x)=F(x/2)+F(x/3)$
The most famous (and simplest non-trivial) recurrence is the Fibonacci recurrence $F(n)=F(n-1)+F(n-2)$ with $F(0)=0, F(1)=1$. What if we consider instead division based recurrences, the simplest non-...
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How to best approach a numerical computational solution towards matching $e^{-r}$ and $k_2\sin(k_1\,r)$ as well as their derivatives $\frac{d}{d\,r}$?
In my question, "Why does it seem like two parameters $k_1$ and $k_2$ are needed to match $e^{-r}$ and $k_2\sin(k_1\,r)$ as well as their derivatives $\frac{d}{d\,r}$?", it was identified ...
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Why doesn't this diagonal argument work?
I have a question about the standard rules for computing p.r. terms (see below). It seems pretty clear that these rules could be used to define a p.r. operation that evaluates any p.r. term of the ...
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How to Prove Division of One Bezier Curve into Two using de Casteljau Algorithm
$\newcommand{\brstbasis}[2]{b^{#1}_{#2}}$
$\newcommand{\posintset}{\mathbb{Z}^{+}}$
$\newcommand{\intset}{\mathbb{Z}}$
$\newcommand{\realset}{\mathbb{R}}$
$\newcommand{\domain}[1]{\operatorname{dom}\...
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Recursive approximations of inverse square law
I have a toy electrostatics simulation that consists of some number of 2D point particles that each have a real-valued "charge" $q_i$, which then exert forces on each other proportional to $...
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Tried finding an efficient algorithm for a 4-digit number guessing game, knowing only the number of digits on correct positions..
I've been playing a game similar to Bulls and Cows, but it goes like this: one player has to pick a random $4$ digit number. Digits can repeat, any digit between $0$ to $9$ and, you only get the ...
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Find limit of Decrementing Recursive Series
I want to find a formula to find the lower limit part of this recursive or geometric series
$$
x_{n} = \left( x_{n-1} + p \right) \times \left( 1 - \frac{t}{100} \right)
$$
I was just wondering what ...
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Prove that $x_{n+1} = \frac{1}{3}(2x_n + \frac{a}{x_n^2})$ is decreasing
Prove that $x_{n+1} = \frac{1}{3}(2x_n + \frac{a}{x_n^2})$ is decreasing where $x_1$ $> 0$.
I have been asked the above question and the working out given to me skipped some steps in between.
It ...
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create a recurrence relation for the number of ways of creating an n-length sequence with a, b, and c where "cab" is only at the beginning
This is similar to a problem called forbidden sequence where you must find a recurrence relation for the number of ways of creating an n-length sequence using 0, 1, and 2 without the occurrence of the ...
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Lemma 6.2. in Scaling Algorithms for the Shortest Path Problem
I have a question regarding the proof of Lemma 6.2. in this paper: https://www.cs.princeton.edu/courses/archive/fall03/cs528/handouts/scaling%20algorithm%20for%20the%20shortest.pdf.
The simplified ...
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Let $x_0 = 3;\ x_{n+1}=3x_n\ $ if $\ \frac{x_n}{2}<1;\ x_{n+1}=\frac{x_n}{2}\ $ if $\ \frac{x_n}{2}>1.\ $ Is $\ \liminf_{n\to\infty} x_n=1?$
This is a natural follow-up question of this previous question of mine.
Let $x_0 = 3.$ Let $\ x_{n+1} = 3x_n\ $ if $\ \frac{x_n}{2}<1;\quad x_{n+1} = \frac{x_n}{2}\ $ if $\ \frac{x_n}{2}>1.\quad ...
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Further explain natural language explanation for statements deduced from master theorem for solving recurrences
This content is taken from from Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest and Clifford Stein, Introduction to Algorithms, The MIT Press, 2022, Chapter 4.
Given the following recurrence ...
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Guaranteed graph labyrinth solving sequence
Starting from a vertex of an unknown, finite, strongly connected directed graph, we want to 'get out' (reach the vertex of the labyrinth called 'end'). Each vertex has two exits (edge which goes from ...
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Finding an algorithm that goes through all the possible permutations of a set only by swapping 2 elements
I recently came across a problem when trying to deal with a set of numbers with n elements.
The problem is as follows:
Starting with a set of n distinct elements, how would one generalize a unique ...
