# Questions tagged [recursion]

Questions about objects such as functions, algorithms or data structures that are expressed using "smaller" instances of themselves.

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### The evolution of the term “recursive” from Goedel to Church to present day

I'm currently studying some of the history of computation / computability, in the early days known as recursion theory. I see Goedel's definition of recursive functions seems significant in his paper,...
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### Why can't a programming language be both fully recursive and polymorphic

In my theory of computation class last Spring my professor said in passing that a programming language cannot be both fully recursive and polymorphic. I didn't think much of it till now? What does it ...
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### Termination of deterministic term rewriting

Consider a simple language: $$t ::= plus ~ t ~ t ~ | ~ gen ~ t ~ | ~ except ~ N ~ t ~ | ~ N$$ with N constructors plus, gen and except, N being the natural numbers, and $G = \{t_n\}$ a finite, ...
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### Axiomatisation in the presence of recursion

I read Klaus Havelund's thesis on the Fork Calculus: http://havelund.com/Publications/thesis.ps He develops the Fork calculus for reasoning about concurrent functional programs, the motivation being ...
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### Reference request: Leaf-heavy master theorem algorithms

I know many algorithms that can be analyzed using master theorem, but the only algorithm I know where the time is dominated by the leaves is fast matrix multiplication. Are there other recursive ...
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### number lesser than a given number composed of only binary numbers

Give a decimal number, such as 123. Need to figure out all smaller numbers lesser than 123 made up by ...
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### Complexity of iterative exponentiation

I've watched multiple videos and read articles about recursion but I'm still confused. I've got this problem here but I'm unsure how to answer it: The following function calculates $x^n$ ...
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### Recursion Time Complexity (Half n' Half)

This is my solution for Leetcode 395, and I'm wondering how I can come up with its time complexity: Input: string $s = s_1,\ldots,s_n$, integer $k$ Go over all symbols $s_1,\ldots,s_n$, one by one ...
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### How to find the Big-O for finding combinations of balanced parentheses?

Given n pairs of parentheses, a function which returns the total number of all combinations well-formed parentheses could be: ...
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### How to solve 2 variable recursion?

T(m,n) = T(m-1,n) + T(floor(m/2), n-1) Base conditions T(m,n) = 1 when n = 0 T(m,n) = 0 when m < n Edited: Below is the code for which I want to know the time complexity in terms of m and n. <...
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### Is McCarthy Formalism first ever formalism for defining functions recursively in computer science?

McCarthy formalism is a formalism for defining functions recursively, first introduced in classic paper Recursive Functions of Symbolic Expressions and Their Computation by Machine, Part I (1960). ...
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### Longest increasing subsequence (Dynamic Programming)

I have written the following recursive structure for finding length of longest increasing subsequence. ...
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### Understanding Martin Farach's suffix tree algorithm

I feel stuck at this point. I have spent several days trying to get my head around the algorithm, but both resources I have   seems to skip over whatever details that would make me comfortable ...
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### Knight's Tour Parberry algorithm: 4 knight's tour merge procedure

I'm implementing Parberry's algorithm for closed Knight's tour problem. Brief idea of the algorithm: split the board in $4$ parts, find the tour on them recursively then delete $1$ edge in each part ...
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### Help with deterministic selection algorithm

All we know what is Deterministic Selection Algorithm: Line up elements in groups of five (this number $5$ is not important, it could be e.g. $7$ without changing the algorithm much). Call each group ...
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### Creating a self-affine fractal on L-systems

Hi I would like to create a self-affine fractal on L-Systems. The axiom I have created is FF-GGG-GG-GGG++GGG+GG-GGG+GG+GGG+FF++ffGG+GGG+FF+GGG which creates the image below At each stage I would like ...
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### Why do we count the ceils and floors in recursive functions?

When we solve the recursive functions using substitution method, the impact of ceil and floor functions is trivial when the size of the input is large enough. For example the answer of  T(n) = T(\...
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### Understanding Dynamic Programming through this example

I have trouble understanding The classic Mailbox Manufacturers Problem. You can read it here: https://open.kattis.com/problems/mailbox I have also found a solution text: http://www.ida.liu.se/projects/...
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### Recursive algorithm for counting pairs of ancestor and child, where sum =n

Hey, this is a question from my handouts, but how would I go about writing a recursive program that would return the number of pairs of an ancestor and a child, whose sum equals to n, given that the ...