A recursive object (e.g. function or data structure) is defined using itself.
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2answers
6 views
Can we create recursive functions only by using if-else statements?
I have to show if a program containing only if-else statements is able to calculate the following type of functions: [f(x)]^n. The function f is applied n times on x, so I guess this is a recursive ...
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votes
1answer
12 views
Time complexity of mutually recursive functions
Suppose I have two mutually recursive functions like this:
...
1
vote
1answer
60 views
Partial recursive function and Turing machine
The wikipedia article about primitive recursion states that
An equivalent definition states that a partial recursive function is one that can be computed by a Turing machine.
My question is how ...
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votes
1answer
89 views
Register Machine code for Fibonacci Numbers
I am not sure whether this is the right place to ask this question.
I would like to write a register machine code which when given an input of n in register
1, returns (also in register 1) the nth ...
0
votes
1answer
39 views
Particularly Tricky Recurrence Relation (Master's Theorem)
Master's theorem is shown below,
The recursive function to be solved is shown below,
I understand that a refers to the number of recursive calls in this ...
9
votes
0answers
150 views
Towers of Hanoi but with arbitrary initial and final configuration
Recently, I came across this problem, a variation of towers of hanoi.
Problem statement:
Consider the folowing variation of the well know problem Towers of
Hanoi:
We are given $n$ towers ...
1
vote
1answer
32 views
Resolving this recurrence equation [duplicate]
I have this recurrence equation:
$T(n) = T(n/4) + T(3n/4) + \mathcal{O}(n)$
$T(1) = 1$
I know that the result is $\mathcal{O}(n \log n)$ but i don't know how to proceed.
0
votes
1answer
46 views
Proving correctness of the algorithm for convex polygon minimum cost triangulation
I have read many solutions for the minimum cost of triangulation problem and intuitively get the idea , however I am struggling to figure out how to prove it formally. I kind of feel that it has to be ...
1
vote
2answers
62 views
Can a recurrence relation be translated to a composite function of itself?
Perhaps this is a question for stackoverflow because its practical nature, but I am not aware of any general method to relate recurrence relations and recursive functions.
Having as an example this ...
0
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0answers
17 views
The use of master theorem appriopriately [duplicate]
I have a recurrence relation and trying to use master theorem to solve it. The recurrene relation is:
T(n) = 3T(n/5) + n0.5
Can i use the master theorem in that relation? If so, can i say that ...
2
votes
2answers
64 views
Need help about solving a recurrence relation
I have a recurrence relation which is like the following:
$T(n) = 2T(\frac{n}{2}) + \log_{2}n$
I am using recursion tree method to solve this. And at the end, i came up with the following equation:
...
2
votes
2answers
87 views
Tasks in which recursion is either the fastest or only way to produce a result [duplicate]
I've just finished studying recursion at university. One thing that stood out for me however was that in both the lectures and in the practical we completed, all the tasks we were asked to do could be ...
1
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1answer
113 views
Why does backtracking work the way it does?
I just recently started learning in a CS context (as opposed to a programming context) about simple recursive functions, along with the combinatorial applications, and techniques such as Backtracking ...
0
votes
1answer
53 views
A Formula For Generalized Josephus problem
There is a formula in wikipedia for the general case of josepus problem
Josephus Problem
But there is no reference for it, I don't know where it came from and I need too find out...
Maybe Donald ...
2
votes
1answer
62 views
Prove $\varphi(x)$ to be primitive recursive
Let $\varphi(x)=2x$ if $x$ is a perfect square, $\varphi(x) = 2x+1$ otherwise. Show $\varphi$ is primitive recursive.
In proving $\varphi$ to be a p.r. function I think it could come in handy the ...
2
votes
1answer
59 views
How to prove “The power set of a countable set must be uncountable”?
I'm not sure if this statement is correct, but my friend said so.
The problem arose from this T/F question:
Let $F=\{f: f$ be a primitive recursive function from $\mathbb{N}$ to $\mathbb{N}\}$, then ...
3
votes
2answers
150 views
Show $x^y$ is a primitive recursive function
As this thread title gives away I need to prove $x^y$ to be a primitive recursive function.
So mathematically speaking, I think the following are the recursion equations, well aware that I am ...
3
votes
1answer
46 views
Clarifications on primitive recursive function definition
I am studying primitive recursive functions and there's something that I don't quite understand: let's take the function that computes $x+y$, then, in order to show that $f(x,y)=x+y$ is primitive ...
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votes
3answers
114 views
Recursive function calculating number of ways to sum $a + 2 b + 3 c = x$
Using python need to code a recursive function with one input and no global integers that calculates the number of options to get $x$ using $a*1+b*2+c*3$.
Say $x=3$, there are four options: $\lbrace ...
2
votes
0answers
83 views
A Recursive Formula For Generalized Josephus problem
The Josephus Problem asks where to start taking out every kth person in the circle consisted of n people, such that you are the last "survivor".
The following recursive formula is given:
...
1
vote
1answer
142 views
Recursion problem involving head, tail and xor
Consider a set of functions:
head(l) returns first bit from list l, e.g.
...
4
votes
1answer
89 views
What is the TAK function for?
We covered this in class today. I understand the mechanics of it, but aside from being a nice example of recursion does it serve any purpose?
Searching the web reveals lots of pages with the ...
1
vote
1answer
133 views
Minimum weight triangulation
I'm just curious about the pseudocode (or real source code, doesn't matter) of the recursive version of this algorithm. In almost every book chapter/paper when describing this topic, they mention that ...
1
vote
2answers
200 views
Need a practical solution for creating pattern database(5-5-5) for 15-Puzzle
I have asked this exact question on StackOverflow. I did not get the answer that I was looking for. Please read this question fully before answering. Thank You.
For static pattern database(5-5-5), see ...
7
votes
3answers
238 views
Do “inductively” and “recursively” have very similar meanings?
Do "inductively" and "recursively" mean very similar?
For example, if there is an algorithm that determines a n-dim vector by determine its first k+1 components based on its first k components having ...
7
votes
4answers
330 views
What is tail recursion?
I know the general concept of recursion. I came across the concept of tail recursion while studying the quicksort algorithm. In this video of quick sort algorithm from MIT at 18:30 seconds the ...
2
votes
1answer
130 views
How to show that f(x) is primitive recursive?
Let
$$f(x)=\begin{cases} x \quad \text{if Goldbach's conjecture is true
}\\ 0 \quad \text{otherwise}\end{cases}$$
Show that f(x) is primitive recursive.
I know a primitive recursive ...
3
votes
3answers
134 views
Optimize a linear recurrence
$$\begin{align*}
T[1] &= 1 \\
T[2] &= 2 \\
T[i] &= T[i-1] + T[i-3] + T[i-4] & \text{for \(i \gt 2\)} \\
\end{align*}$$
I have to calculate $T[N]$, but $N$ is too big ($\approx ...
3
votes
3answers
411 views
How to write a recursive function that with certain time complexity
I'm now doing exam revision, and from some past year exam papers, I noticed some questions that ask to write a recursive method with signature like
...
1
vote
1answer
178 views
Recursion for runtime of divide and conquer algorithms
A divide and conquer algorithm's work at a specific level can be simplified into the equation:
$\qquad \displaystyle O\left(n^d\right) \cdot \left(\frac{a}{b^d}\right)^k$
where $n$ is the size of ...
11
votes
5answers
1k views
When to use recursion?
So we are covering recursion in a C++ class I am taking. I understand what it is, a function that calls itself (a very basic explanation), I am just having trouble coming up with a lot of instances ...
10
votes
6answers
803 views
Examples of sophisticated recursive algorithms
I was explaining the famous deterministic linear-time selection algorithm (median of medians algorithm) to a friend.
The recursion in this algorithm (while being very simple) is quite sophisticated. ...
6
votes
3answers
856 views
Algorithm to test whether a binary tree is a search tree and count complete branches
I need to create a recursive algorithm to see if a binary tree is a binary search tree as well as count how many complete branches are there (a parent node with both left and right children nodes) ...
8
votes
2answers
259 views
Recursive definitions over an inductive type with nested components
Consider an inductive type which has some recursive occurrences in a nested, but strictly positive location. For example, trees with finite branching with nodes using a generic list data structure to ...
