# 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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### Complexity and Recurrence relation for Lowest Common Ancestor Binary Tree

I have written this solution for finding the Lowest Common Ancestor in a Binary Tree. Now I wanted to find the time complexity of this problem by solving via recurrence relation. Can someone suggest ...
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### Print Binary Tree Diameter Path [duplicate]

Diameter of the tree is defined as a long path or route, between any two nodes in a tree. The path may or may not goes through the ROOT. Print the Longest leaf to leaf path in a binary tree and its ...
420 views

### primitive recursion in the lambda calculus

I am having trouble finding out what a primitive subset of the lambda calculus would look like. I reference primitive recursion as shown here: "https://en.wikipedia.org/wiki/...
338 views

### What is the running time of this recursive algorithm?

I made the following (ungolfed) Haskell program for the code golf challenge of computing the first $n$ values of A229037. This is my proposed solution to compute the $n$th value: ...
1k views

### Recurrence relations when function call is made inside loop

int fun (int n) { int x=1, k; if (n==1) return x; for (k=1; k<n; ++k) x = x + fun(k) * fun(n – k); return x; } What is the value of fun(5)? I ...
20 views

### What would be the time complexity if a recursive function is inside a loop? [duplicate]

I am confused in calculating the time complexity for a recursive function inside a loop. ...
520 views

### How many recursive calls does it take to compute binomial probability weights?

I was given an algorithm and I was asked to estimate how often it would be called if I was trying to calculate ${100 \choose 50}0,25^{50}0.75^{50}$, the Binomial distribution of $50$ elements chosen ...
215 views

### How can the class of tail recursive functions be compared to the classes of PR and R?

How can the class of tail recursive functions (TR) be compared to the classes of primitive recursive functions (PR) and recursive functions (R)? The computation of a PR function always halts. This ...
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### Help needed with lesson on recursion

I'm studying CS online, and I'm reading this lecture on recursion, see "3.2. A Mathematical Example". I understood the beginning and I even made a program that calculates $X$ to the power of $N$ ...
121 views

### 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 ...
1k views

### If recursive Fibonacci is $O(2^N)$ then why do I get 15 calls for N=5?

I learned that recursive Fibonacci is $O(2^N)$. However, when I implement it and print out the recursive calls that were made, I only get 15 calls for N=5. What I am missing? Should it not be 32 or ...
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### Undecidable definition of pure function?

I am trying to come up with a formal definition for functional purity in a simple programming language (think JavaScript). What I've got so far is this: DEFINITION: A statement is impure if ...
162 views

### What is the complexity of this recursive merge of two ordered Python lists?

This is not an assignment, but it is related to my Data Structures class. I just wrote this Python code to merge two ordered python lists. I do know that I could do something like this: list1 + list2....
526 views

### Time complexity of linear program? [closed]

I have built a heuristic algorithm for approximately solving an NP complete graph problem by recursive linear relaxations. In each recursion, the algorithm returns a reduced graph, with number of ...
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### Why is $X_m$ and $Y_m$ not included in the shaded region(where median can lie)?

This problem is from Algorithms, problem 2 The Problem Given two sorted list of numbers $X$[1..$n$] and $Y$[1..n]. we need to come up with a O($log n$) time algorithm to find the median of the 2$n$ ...
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### Finding the $k$th smallest element in union of two sorted arrays

I know that this problem is solvable in linear time with a merge but I want to get a sub-linear algorithm. What I came up is that, if a[k] < b[k] then the $k$th ...
280 views

### Reccurence of recursive function with unequal sizes of subproblems [duplicate]

Given pseudocode: ...
693 views

### Algorithm to decide the Kleene Star of a Language A

Assume $f$ decides a language $A$ in $O(g(n))$ time, where $n$ is the length of the input string. How to write a recursive algorithm to decide $A^*$ (recursive)? Moreover, can an $O(n^2g(n))$ ...
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### Something wrong with this definition of factorial with structural recursion? [closed]

In The Algebra of Programming page 5, the authors defined structural recursion foldn (c, h) over natural numbers: ...
7k views

### Finding the time complexity of fibonacci sequence [closed]

I tried it as follows and would like to know if it is correct.
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### Runtime of a recursive algorithm

I have a simple recursive solution as below: ...
42 views

### What is the name of this size method calculating the size of a node?

My confusion is that if the recursive call calls the left nodes, and then adds with the right nodes, how are the nodes that are to to right of the left nodes and vice versa being called? ...
163 views

### Time-complexity of recursive defined code [duplicate]

How would I set up a recursive formula for time-complexity for this code: ...
394 views

### Find one-variable recursive formula for running time of Karatsuba multiplication

I'm currently trying trouble to set up the recursive expression for the Karatsuba multiplication of two integers with $n$ and $m$ bits (both having a different number of bits). Usually, the recursion ...
91 views