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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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Write the Brute Force Recursive Code to generate the longest substring containing k distinct vowels

Given a string s we have to find the length of the longest substring of s which contain exactly K distinct vowels. This is the problem statment given on geeksforgeeks Input : s = “artyebui”, k = 2 ...
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1answer
45 views

Avoiding “side effects” in recursive functions

I am writing a function to find the intersection between two sets. The non-functional requirements of the assignment include avoiding "side effects". ...
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T(n) = T(n-1) +3n^2 - 2n +1 [duplicate]

I was wondering how do I solve this, I've been trying any possible way to but I've failed: $$\begin{align*} T(n) &= T(n-1) +3n^2 - 2n +1 ,& n \ge 1 \\ T(0) &=2 &\\ \end{align*}$$
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1answer
130 views

Worst-case input for median-of-medians with groups of size 3

Typically, median of medians algorithm is written with groups of size $5$ or $7$ to ensure worst-case linear performance. The argument against groups of size $k=3$ is typically that we get a ...
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2answers
91 views

prove by induction that the complete recursion tree for computing the nth Fibonacci number has n leaves

I have referenced this similar question: Prove correctness of recursive Fibonacci algorithm, using proof by induction *Edit: my professor had a significant typo in this assignment, I have attempted ...
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Sketch Recursion Tree

Can somebody sketch the recursion tree for the execution of f(0,3) and compute T(3) where T(n) denotes the total number of calls of f in the execution of f(a, b), where n = b-a ? Java Function: ...
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0answers
34 views

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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1answer
28 views

Whether it's necessary for a grammar to be ambiguous when it is both left recursive and right recursive

I read somewhere that if a grammar is left recursive as well as right recursive, then it is not necessarily ambiguous. I couldn't make up my mind on this statement. How can a grammar which is both ...
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1answer
91 views

Can memoization be applied to any recursive algorithm?

I am new to the concepts of recursion, backtracking and dynamic programming. I am having a hard time understanding if at all I can apply memoization to a particular recursive algorithm and if there ...
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0answers
41 views

Dynamic Programming solution for finding shortest distance to travel between points

So consider a person located at point $c$ (let's say $c=140$). Given a set of other points, for example, $P = \{100, 50, 190\}$. The cost of traveling to a point $P_i$ is then $|c-P_i|$. Points can be ...
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1answer
40 views

Recursively edit 2-D array using backtracking

I have a 2-D array which contain 3 types of elements: C (Contaminant) R (Rock) W (Water) The rule is that: contaminant can seep through water but not through rocks. Let's say I have the ...
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2answers
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Recursion to DP Solution

There's a problem in Kleinberg & Tardos's Algorithm Design (Chapter 6, Question 4) where you are running a lightweight consulting business that has two offices: NYC and SF. In month $i$, you'll ...
2
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1answer
31 views

Maximum Expected Fishing Day (Recurrence Relation)

John joined a meetup where organize day long fishing trip once a month. The organizers are vary poor at planning, so will organize fishing on a random day of the month without any advance notice. ...
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4answers
125 views

What is the depth of recursion if we split an array into $\log_2(n)$ with each recursive call?

We have a function which takes an array as input. It breaks an array into $\log_2(n)$ parts with equal sizes where $n$ is the size of the subarray. It keeps breaking each of the subarrays until there ...
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1answer
38 views

Is there a relation between the size of the domain/range of a function and its computability?

This was a question given in a course, without answer. The referenced literature (just a few books) do not cover it, unfortunately. I think there is no relation with the range as the range of the ...
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1answer
55 views

Recursive factorial algorithm

I'm struggling to understand this factorial algorithm. ...
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1answer
70 views

Merge sort and quciksort recursion tree depth

1) I need to determine recursion tree depth for strings composed of 10, 100 and 1000 elements when using merge sort. For the 10 elements one I can do it on a paper, just drawing tree, but what about ...
2
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1answer
89 views

Induction to prove equivalence of a recursive and iterative algorithm for Towers of Hanoi

Using induction how do you prove that two algorithm implementations, one recursive and the other iterative, of the Towers of Hanoi perform identical move operations? The implementations are as follows....
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3answers
51 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 ...
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0answers
90 views

Shortest Uncommon Subsequence

Here is another GeeksforGeeks problem that asks how to find the shortest Uncommon Subsequence of 2 strings? For example, Input : S = “babab” T = “babba” Output : 3The subsequence “aab” of ...
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0answers
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Is there a specific search paradigm for finding pairs in a set?

I'm dealing with a very common problem in computer programming that involves, for example 4 people to be divided into 2 pairs. Mathematically, this is just a permutations problem, and the number of ...
2
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2answers
108 views

Technique for converting recursive algorithm to DP

I'm new to Dynamic Programming and before this, I used to solve most of the problems using recursion(if needed). But, I'm unable to convert my recursive code to <...
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2answers
59 views

Algorithm for generate all solutions to a linear Diophantine equation

Consider the linear Diophantine equation of the form: $$\sum_{i=1}^{k}a_ix_i=n.$$ My goal is to list all the non-negative solutions to this equation. I wrote the following recursive algorithm, but I ...
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1answer
34 views

Polynomial time algorithm - Matching pairs of vertices

Let T be a tree with root r and S a set with an even number of vertices of T. Design a polynomial time algorithm that finds |S|/2 simple and disjoint paths in edges matching pairs of vertices in S. ...
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3answers
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Write a routine to print the numbers 1 to 6 and back to 1 again without using any loops [closed]

Can anyone help with this question? I currently have this solution that prints 1 2 3 4 5 6 but I'm having trouble going back down to 1. ...
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1answer
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Few questions about Mergesort and Recirsion algorithms

Can we use recursive algorithm to find the greatest element of a finite list when numbers are unsorted. How to use recursive algorithm to find the least element of a finite list of unsorted numbers ...
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1answer
119 views

How to solve F(n)=F(n-1)+F(n-2)+f(n) recursive function?

Like in the title the following equation: F(n)=F(n-1)+F(n-2)+f(n) F(0)=0, F(1)=1 ...
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2answers
48 views

Possible to use Master theorem? $T(n) = aT(\lfloor \frac{n}{b} \rfloor) + g(n)$

The master theorem can be used in case of a recurrence relation of the form $T(n) = aT(\frac{n}{b}) + g(n)$ But is it possible to use the master theorem for recurrence relations of the form $T(n) = ...
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1answer
102 views

Handling epsilon productions in recursive descent parsing

I am working on a recursive descent parser for lambda calculus. In my grammar, after removing left-recursion, I am left with the following two productions: ...
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1answer
591 views

Complexity of finding a majority element

I was given a question that is stated that; Suppose you’re consulting for a bank that’s concerned about fraud detection, and they come to you with the following problem. They have a collection ...
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2answers
45 views

Using Iterative method to find recurrence relation vs Master Theorm

I'm trying to solve this recurrence relation using the iterative method and i keep getting the different answer from using the master theorem. $$\begin{aligned} T(n) &= 5T(n/2) +n^2 \\ &=...
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1answer
28 views

Is any State Space Tree always Binary Tree?

A backtracking algorithm generates, explicitly or implicitly, a state-space tree. Introduction to the design & analysis of algorithms / Anany Levitin I wonder that whether the saying ...
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1answer
82 views

Answering questions about the recurrence of certain aspects of an algorithm

I am thoroughly confused by a problem that was brought up in class: Given the following pseudocode for a function RANDOM which generates a random number based off of recursion: ...
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2answers
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Pancake Sorting Graph Recursive Definition

I'm having trouble understanding exactly how the graph for Pn (where n = number of pancakes) is defined recursively for n>= 4. I can see obviously that, in the case of n=4, there will be 4 rough ...
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3answers
98 views

Time complexity of function vs return value

I came across following problem: Find the time complexity of below recurrence relation: $T(n)=\begin{cases} & 2T(n/2)+C; & n>1\\ & C;&n=1 \\ \end{cases}$ The solution ...
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1answer
183 views

Finding recurrence equation for a variant of insertion sort [closed]

I have a variant of Insertion sort (recursive version) that we call split insertion sort because there are two kinds of input. The input array has both numbers and alphabets, hence we have to sort ...
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1answer
35 views

How to implement recursive solution with large number or parameterized possible next steps

I was looking at a recursive solution for the robot on a grid problem which basically states that there is a robot on the top left corner on a grid and you are supposed to find a path to the bottom ...
2
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1answer
516 views

What's the Big O runtime of a DFS word search through a matrix?

The problem is to try and find a word in a 2D matrix of characters: Given a 2D board and a word, find if the word exists in the grid. The word can be constructed from letters of sequentially adjacent ...
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0answers
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Is this solution is bad for the coin change problem? [closed]

was doing coin change problem as an assignment(didnt know before), after came with this solution i checked the solutions available couldnt find a similar one like this, just curious. removing the ...
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1answer
82 views

Asymptotic bound of a recursive function

Consider the following procedure computing a dummy function. Which one is a correct asymptotic bound for the running time of F(N) expressed in terms of N? ...
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2answers
79 views

Time Complexity of the code

I am having trouble finding the time complexity of the below code. ...
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0answers
35 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 ...
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2answers
4k views

Will this program terminate for every Integer?

In a Part Test for GATE Preparation there was a question : f(n): if n is even: f(n) = n/2 else f(n) = f(f(n-1)) I answered "It will terminate for all ...
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1answer
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Water Jug Problem

I was reading an article on Water Jug Problem. The problem is -You are given a m litre jug and a n litre jug where 0 < m < n. Both the jugs are initially empty. The jugs don’t have markings to ...
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1answer
51 views

Solving double recurrence relation

How to calculate the rate of growth of the below function $f(x)$? $$ \begin{align*} f(x) &= \begin{cases} f(x-1) + g(x) & \text{if } x > 1, \\ 1 & \text{if } x \leq 1. \end{cases} \\ g(...
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0answers
28 views

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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1answer
421 views

Prove Recursive formula (Dynamic programming) N(C,i)

I've been asked to prove the correctness of the following recursive formula. The formula is trying to define, how many ways you can spend your money C on the i amount of beers. I did the following ...
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2answers
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Recursive relations in binary trees

I have an exercise in my algorithm's Course for which I have the correction but do not understand it. 1.Exercise . Let Th be a full binary three of height h(meaning all the levels all completely ...
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726 views

Longest increasing subsequence (Dynamic Programming)

I have written the following recursive structure for finding length of longest increasing subsequence. ...