Recursion problems. 3 Calculating the Sum of a List of Numbers; 5.

Recursion problems Dec 24, 2024 · Recursion breaks the problem down into smaller subproblems then aggregates the result. Mock AIME 2 2006-2007 Problem 8 (number theory) 1994 AIME Problem 9; A combinatorial use of recursion: 2006 AIME I Problem 11; Another combinatorial use of recursion: 2001 AIME I Problem 14; Use of recursion to compute an explicit formula: 2006 AIME I Problem 13; Use of recursion to count a type of number: 2007 AMC 12A Problem 25 Jul 12, 2024 · The advantages of recursive programs are as follows: Recursion provides a clean and simple way to write code. Start My Journey. 10 Dec 21, 2024 · Write a Python program to calculate the sum of a list of numbers using recursion. 6 Stack Frames: Implementing Recursion; 5. Disadvantages of Recursive Programming. e. Using recursive algorithm, certain problems can be solved quite easily. c_str(), search. 10. Introduction to Recursion. c_str()) Recursion method: Dec 21, 2024 · Write a Java recursive method to calculate the factorial of a given positive integer. This series is dedicated to explaining Python problems. Medium Problem Solving (Intermediate) Max Score: 20 Success Rate: 89. Base cases often correspond to emptiness – the empty string, the empty list, the empty set, the empty tree, zero, etc. ” It just means “solving a problem by solving smaller copies of that same problem. I have been trying to solve this problem for a while now but it's bested me so far. However, as we saw in the analysis, the time complexity of recursion can get to be exponential when there are a considerable number of recursive calls. Try using "regular" iteration like do-while or for. Jul 28, 2014 · I am relatively new to python and especially recursion. Test Data: Input the base value : 5 Input the exponent : 3 Recursion - Recursion is the process of repeating items in a self-similar way. Use the solutions of the smaller problem to solve the larger problem. Recursion in computer programming is exemplified when a function is defined in terms of simpler, often smaller versions of itself. The best way to figure out how it works is to experiment with it. 7 Introduction: Visualizing Recursion; 5. Recursion is extremely useful in the cases of tree-based and graph-based problems Recursion is a technique for solving a large computational problem by repeatedly applying the same procedure(s) to reduce it to successively smaller problems. 4 The Three Laws of Recursion; 5. Dive into the world of recursion challenges at CodeChef. > Test Data : Input a string to including one or more capital letters : testString Expected Output: The first capital letter appears in the string testString is S. Let’s consider the example of factorial of number: Mar 13, 2023 · The primary property of recursion is the ability to solve a problem by breaking it down into smaller sub-problems, each of which can be solved in the same way. The examples aim to understand the power and usage of recursive functions in solving problems, both simple and complex. Ensure that you are logged in and have the required permissions to access the test. It is a powerful tool for solving problems and is often used in Recursion practice problems: Here, you will find the various recursion practice problems with solutions that are commonly asked in the various interview rounds of the companies. Some problems are inherently recursive like tree traversals, Tower of Hanoi, etc. The disadvantages of recursive programs is as follows: Recursion isn't very advisable method of solving the problems because its implementation is inefficient. . For example, the Fibonacci sequence is defined as: F(i) = F(i-1) + F(i-2) Je rey Chen and Dylan Yu (May 13, 2020) Recursion in the AMC and AIME §3First Counting Problem While recursion might seem like a purely algebraic idea at rst and something that looks fun but not useful, it can help solve many di cult counting problems (as well as certain computer science problems). • Recursion doesn’t mean “the absence of iteration. > Test Data : Dec 20, 2024 · Write a C++ program to implement a recursive function to check if a given string is a palindrome. Lets see an example of recursive code in JavaScript. It is frequently used in data structure and algorithms. One example application of recursion is in parsers for programming languages. Jun 2, 2024 · In Java, Recursion is a process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. Recursion in C++ is a technique in which a function calls itself repeatedly until a given condition is satisfied. Loops likely have better time & space complexity for Fibonacci and similar sequence problems. I have to create a function that takes in 2 strings and uses recursion to see if elements from the first string are in the second string if so it returns true if not than it returns false say "Carpool" and "prlo" or "elephant" and "xph" in the first case Jul 28, 2023 · A recursive function is a function that calls itself with a failure condition. A palindrome is a word, number, phrase, or other sequence of symbols that reads the same backwards as forwards, such as the words madam or racecar, the date/time stamps 11/11/11 11:11 and 02/02/2020, and the sentence: "A man, a plan, a canal Dec 1, 2024 · Backtracking algorithms are like problem-solving strategies that help explore different options to find the best solution. 2 What Is Recursion? 5. This is a simple example that demonstrates recursion. That can save a lot of money (development, validation, maintenance, …) Apr 15, 2011 · I'm grabbing links from a website, but I'm having a problem in which the higher I set the recursion depth for the function the results become stranger for example when I set the function to the Sep 9, 2021 · Problems : 00:05 - Tower of Hanoi26:40 - Print string in reverse32:06 - Find first & last occurrence of element41:11 - Check if the array is sorted (strictly Jan 22, 2015 · Try not to use recursion to solve this problem, even with memoization. This can be a very powerful tool in writing algorithms. 1. Our only task is to reduce the problem instance we’re given to one or more simpler instances, or to solve the problem directly if such a reduction is impossible. This is why we use recursive solutions. But recursion leads to more elegant code if the data aligns with hierarchies/trees. The examples of recursion above display the concept simply, but it‘s not a real-world problem and our “code” is only pseudocode. This is the best place to expand your knowledge and get prepared for your next interview. 6. It also has an For some problems, a recursive solution, though possible, will be awkward rather than elegant. We introduce 5 simple steps to help you solve challenging Recursion is solving a problem with a function that calls itself. be able to implement some well-known recursive algorithms. I think finding a list for recursion might be difficult because it's more of a meta topic. This was a massive fail. Hence, usage of recursion is advantageous in shorter code, but higher time complexity. , tree traversals, dynamic programming problems). For such problems, it is preferred to write recursive code. A recursive function must have a base case or stopping criteria to avoid infinite recursion. Aug 14, 2022 · Earlier, I have shared frequently asked programming interview questions, books, and courses and here, I will share 25 to 30 Recursion practice problems and exercises you can do to learn Test your coding skills and improve your problem-solving abilities with our comprehensive collection of Recursion problems. Solve company interview questions and improve your coding intellect We use cookies to ensure you have the best browsing experience on our website. be able to estimate the complexity of recursive processes. Super powerful programming tool Not always the perfect choice, but often a good one; Some beautiful problems are solved recursively. That being said, recursion is an important concept. List of the recursion practice problems Basic recursion problems. Write a Java recursive method to calculate the sum of all numbers from 1 to n. Recursion strategy: first test for one or two base cases that are so simple, the answer can be returned immediately. Write a Python program to sum recursion lists using recursion. Recursion may be a bit difficult to understand. 9 Complex Recursive Problems; 5. 21. Recursive algorithms typically have two parts: Base case: Which is a condition that stops the recursion. 3. Learn recursion, a problem-solving technique that involves breaking a problem into smaller and simpler problems of the same kind. If it makes it easier for you to follow, save the solutions to the smaller problems to local variables (e. Medium Problem Solving (Basic) Max Score: 30 Success Rate: 73. 1 Objectives; 5. Write a program in C# Sharp to calculate the power of any number using recursion. Update: more context on why I graduated without without fully understanding recursion. For example, it is common to use recursion in problems such as tree Oct 9, 2024 · Many problems have a simple recursive solution. Recursive Digit Sum. Types of Recursion. I would recommend going through the easy-med LC tree problems the majority can be solved with recursion/dfs. Write a C++ program to implement a recursive function to find the greatest common divisor (GCD) of Dec 30, 2024 · Recursion is a programming technique where a function calls itself to solve problems by breaking them into smaller subproblems, requiring a base case to prevent infinite loops, and is widely used in algorithms like sorting, tree traversal, and dynamic programming. , the same problem but for a smaller input size. On top of recursion, I found that bit manipulation questions can take your problem-solving skills to another level. The solution to the problem is then devised by combining the solutions obtained from the simpler versions of the problem. Recursive Sum from 1 to N. Usually recursion involves a function calling itself. Recursion is a programming technique in which a function calls itself. Recognizing the divide-and-conquer nature of a problem is a key Nov 6, 2024 · Recursion is considered difficult to understand by many people but once you understand the working of recursion, it becomes a powerful weapon in your arsenal to battle complex problems. You have not created any collections yet. 1 Fred wants to climb a 10 step Sep 20, 2008 · Recursion is appropriate whenever a problem can be solved by dividing it into sub-problems, that can use the same algorithm for solving them. b^0 Every recursive method has one (or more) recursive cases ⬜The function calls itself on inputs that are “closer” to the base case ⬜n! = n x (n-1)! . In some problems, after conditioning we get a recursive relation that can help us solve the problem. Three Musts for Recursion: Your code must have a case for all valid inputs Feb 20, 2023 · In Java, Recursion is a process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. A recursive procedure has two parts: one or more base cases and a recursive step. Oct 31, 2020 · So, I need to write a code that solves this problem for me using recursion. AP Computer Science A Practice Test 17: Recursion. int: the factorial of ; Note: If you fail to use recursion or fail to name your recursive function factorial or Factorial, you will get a score of . In this tutorial, we will talk about recursion and how we can use it to divide and conquer! 💪💪💪We will also see which is faster - recursive functions or f Dec 7, 2022 · Time Complexity: O(n) Space Complexity: O(1) Note: Time & Space Complexity is given for this specific example. From basic algorithms to advanced programming concepts, our problems cover a wide range of languages and difficulty levels. Recursive tree of previous example for n = 3. So it was seen that in case of loop the Space Complexity is O(1) so it was better to write code in loop instead of tail recursion in terms of Space Complexity which is more efficient than tail recursion. Write a program in C for binary search using recursion. Apr 22, 2020 · Recursion Recap. This course breaks down what recursion is, why you would and wouldn’t want to use it, and shows a variety of examples for how it can be used. Many problems in computational geometry (and 3D games) can be solved recursively using binary space partitioning (BSP) trees, fat subdivisions , or This visualization can visualize the recursion tree of any recursive algorithm or the recursion tree of a Divide and Conquer (D&C) algorithm recurrence (e. Solutions will be posted to the website on Tuesday; feel free to ask questions about these problems on the staff email list, or at office hours. Dec 20, 2024 · Write a program in C# Sharp to get the reverse of a string using recursion. - aksh0001/Recursion-Problems May 27, 2024 · Recursive case: In the recursive case, the function calls itself with the modified arguments. Since you're recursing, you only need to fill in one cell - the recursion will take care of the rest. When we repeat a similar process many times, it is known as Recursion. Nov 6, 2019 · Recursion is a distinct algorithmic problem-solving technique. Test Data: [1, 2, [3,4], [5,6]] Dec 17, 2024 · Strengthen your **recursion skills** with **GeeksforGeeks practice problems** solved step-by-step in **C++**! 🎯 This video covers popular **recursion-based May 22, 2023 · Recursion: Recursion involves calling the same function again, and hence, has a very small length of code. We continue calling the same problem for smaller input sizes until we reach the base case of recursion. b^c = b * b ^ (c-1) Every recursive method “merges” the result of each recursive call We use recursion and backtracking to break down complex problems into smaller, manageable parts, which results in elegant and concise code while handling recursive data structures efficiently and exploring systematically for solutions. Our recursive Tower of Hanoi algorithm is trivially correct when n = 0. don’t do it. As an easy example, let’s start with a problem closely related to Example 1. Write a Python program to convert an integer to a string in any base using recursion . Recursive trees are useful to help us understand how the function acts. In some cases, using recursion may result in slower execution time. 3 Calculating the Sum of a List of Numbers; 5. ASSUME the recursive call works . unit-testing es2015 recursion recursion-joy recursion-problem Updated Jul 29, 2018; JavaScript; BaseMax Report A Problem; This Chapter. Level up your coding skills and quickly land a job. In other words, recursion is the process of solving a problem by breaking it down into smaller, simpler sub-problems. Problems like printing all permutations, combination or subsets uses explicit use of recursion also known as "Complete Search". For all these problems, be sure to carefully consider your base and recursive cases Iteration + Recursion • It’s completely reasonable to mix iteration and recursion in the same function. Dec 28, 2023 · Examples of recursion . There are s A recursive implementation always has two parts: base case, which is the simplest, smallest instance of the problem, that can’t be decomposed any further. Using a recursive algorithm, certain problems can be solved quite easily. It may vary for another example. May 21, 2021 · Recursion is a programming concept that involves solving a problem by breaking it down into smaller versions of the same problem. In the “Introduction to the Recursive function” blog, you will learn recursive functions with the factorial problem. Using Recursion, certain problems can be solved quite easily. I can write good code for simple recursion problems such as calculating the factorial of a number, but not recursion problems like these: Advantages and Disadvantages of Recursion. Lets understand how recursion really works with the help of an example. Dividing a problem into smaller parts aids in conquering it. Each recursion practice problem has its solution with the examples, detailed explanations of the solution approaches. In this video, we take a look at one of the more challenging computer science concepts: Recursion. A few Java recursion examples are Towers of Hanoi (TOH) This repository contains a collection of programs that demonstrate the concept of recursion. , Master Theorem) that we can legally write in JavaScript. g. 5 Converting an Integer to a String in Any Base; 5. To solve this problem, let’s examine the head-tail technique for implementing recursive functions. We will finish up by looking at a deceptive problem that at first looks like it has an elegant recursive solution but in fact does not. 15. Write a Java recursive method to calculate the nth In this section we will look at some problems that are really difficult to solve using an iterative programming style but are very elegant and easy to solve using recursion. Bit manipulation is Recursion. How to Solve an Algorithms Problem (Review) • Reduce to a problem you already know (use data structure or algorithm) Search Data Structures Sort Algorithms Graph Algorithms Array Insertion Sort Breadth First Search Recursive drawing of a Sierpiński Triangle through turtle graphics. Aug 21, 2022 · In Java, Recursion is a process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. Jul 19, 2021 · Recursion is a powerful technique that helps us bridge the gap between complex problems being solved with elegant code. Mar 28, 2012 · Determine what smaller problem (or problems) to solve. In programming languages, if a program allows you to call a function inside the same function, then it is called a recursive call of the function. Lecture 15: Recursive Algorithms. recursive problems and recursive data; comparing alternative decompositions of a recursive problem; using helper methods to strengthen a recursive step; recursion vs. 74%. 4 (114 reviews) 3 lessons Beginner level. be able to identify the components of a recursive algorithm. Recursive implementations often consume more memory than non-recursive ones. Let’s see how we can implement recursion using Python. That's what this wiki page will explain, so brace yourself for some problem solving that feels a bit loopy Solve practice problems for Recursion and Backtracking to test your programming skills. In the nSum() function, Recursive Case is Platform to practice programming problems. Recursion comes directly from Mathematics, where there are many examples of expressions written in terms of themselves. In computer science, recursion is a method of solving a computational problem where the solution depends on solutions to smaller instances of the same problem. Feb 6, 2024 · The process in which a function calls itself directly or indirectly is called Recursion and the corresponding function is called a Recursive function. List of popular algorithmic recursion questions and solutions for practice dealing with recursive problem structure. That might sound a little intimidating, but it essentially boils down to creating smaller and smaller versions of the same problem until the smallest solution is easily solved and then going in reverse to solve the larger problem piece by piece. Platform to practice programming problems. Hi, I'm currently learning recursion in Java, and I was solving problems on CodingBat to familiarize myself with the concept; however, I'm struggling with directing my thought process for recursive methods. A recursive implementation then has the advantage that it stays close to the specification. function recurse() { // function code recurse(); // function code } recurse(); Here, the recurse() function is a recursive problems and recursive data comparing alternative decompositions of a recursive problem using helper methods to strengthen a recursive step recursion vs. This test contains 11 AP computer science a practice questions with detailed explanations, to be completed in 25 minutes. Approach to solve a problem recursively. Click me to see the sample solution. Dec 7, 2024 · Write a JavaScript program to check whether a given string is a palindrome or not using recursion. (If this is done INCORRECTLY, the solutions of Sep 3, 2021 · Click here to “Read all Medium Articles” Factorial of a Number. 8 Sierpinski Triangle; 5. But, for the sake of this article, let’s consider the recursive solution. When solving a problem through recursion one must think of breaking the current problem into sub-problem. Apr 29, 2015 · One major issue is the line for i in l: in the solve method. So instead of for i in l:, just recurse on the one cell that is the best candidate (curCell):. Test Data: Input the string : w3resource Expected Output: The reverse of the string is : ecruoser3w Click me to see the solution. Dec 20, 2024 · C programming, exercises, solution: Write a program in C to print the first 50 natural numbers using recursion. Disadvantages of using recursion Test your Recursion knowledge with our Sum of N Natural Numbers practice problem. Assume that the recursive call works correctly, and fix up what it returns to make the answer. Basic Structure of a Recursive Function • Parameters to start the function • Appropriate base case(s) to end the recursion • Recursively solve the sub-problems • Process the result and return the value Oct 16, 2024 · Recursion list Bit Manipulation: A Bonus to Problem Solving. Learn how to write recursive code and apply recursion to easily solve problems. Nov 12, 2020 · About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Press Copyright Apr 6, 2017 · I'm trying to return a index for the where the word i am searching for (in the case above it would be **7) the recursive method i have is as follows - i can't seem to get it to return the index properly. Recursive case: Which is a call to the function itself with a smaller version of the problem. This function solves this in C# for positive integers (not tested - there may be a bug). factorial has the following paramter: int n: an integer ; Returns. Factorial is a math problem where factorial of 5, for example, is 5 * 4 * 3 * 2 * 1. Dec 18, 2024 · Simplicity: Recursive code is generally simpler and cleaner, especially for problems inherently recursive in nature (e. The recursive case should move closer to the base case with each iteration. 6k Learners. You can use recursion in basically any type of problem but it maps nicest to tree problems, graphs and backtracking. Nov 6, 2024 · A recursive algorithm is an algorithm that uses recursion to solve a problem. Since you are reading this article, I’m assume that you have a vague idea of recursion, so I won’t go deep into the Recursion is a powerful problem-solving tool with tons of practical applications. Examples of such problems are Towers of Hanoi (TOH), Inorder/Preorder/Postorder Tree Tr Nov 28, 2023 · Learn and practice recursion problems for SDE interviews with this curated list of easy, medium and hard questions. Here are some examples of problems that can be solved using recursion : Calculate the sum of two numbers . Oh i forget something. C++ Recursion. This assignment consists of a "sampler" of different recursion problems each of which is interesting in their own way. There are several different recursion types and Be sure to use recursion. Hence, recursion is a divide-and-conquer approach to solving problems. Mar 22, 2024 · Recursion is a problem-solving technique that works in a similar way. To understand how C recursion works, we will again refer to the example above and trace the flow of the program. java recursion recursive big-o dynamic-programming recursive-algorithm codingbat recursion-problem explanations codingbat-solutions Recursion . Explore various recursion problems with solutions in different domains such as backtracking, string, array, matrix, divide and conquer, and linked list. 189 IAP 2011: Optional Recursion Exercises These exercises are optional, have fun playing around with them. Aug 6, 2018 · But using recursion yields an elegant solution that is more readable. ⌛ A set of recursion problems to be solved. In this article, I have provided a few examples of using recursion in Python. Share your videos with friends, family, and the world May 9, 2024 · What is Recursion? The process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. Recursion makes program elegant. Dec 20, 2024 · Write a program in C to find the first capital letter in a string using recursion. Also go through detailed tutorials to improve your understanding to the topic. Learning to solve problems recursively can be challenging, especially at first. Otherwise, make a recursive a call for a smaller case (that is, a case which is a step towards the base case). Of course you can still use some ingredient like memoization in "regular" loop. 1- Use the iterable-approach first. The great Level up your coding skills and quickly land a job. We can also visualize the Directed Acyclic Graph (DAG) of a Dynamic Programming (DP) algorithm and compare the dramatic search-space difference of a DP problem versus when its This is a must to crack many faang interviews because tree/graph problems typically require recursion. Click me to see the solution. In Recursion, a function calls itself many times till it hits some base case, making a recursive tree where we pass every child's output is to its parent. Recursion problems, levels 8 to 5. Many times, a problem broken down into smaller parts is more efficient. Recursion is a fascinating topic and can produce elegant code solutions. As each function call uses some memory, it may eventually lead to the stack overflow problem. This is the essence of recursion – solving a larger problem by breaking it down into smaller instances of the same problem. Collections are a way for you to organize kata so that you can create your own training routines. Jul 25, 2024 · Recursion involves breaking down a problem into smaller pieces to the point that it cannot be further broken down. Algorithms on trees and sorted lists are a natural fit. [1] [2] Recursion solves such recursive problems by using functions that call themselves from within their own code Recursion formalizes the process of recognizing how solutions to smaller cases of a problem can, layer by layer, be built up to solve any case of a problem, no matter how enormous. Typically, the readability of the code will be the biggest determining factor. Write a C++ program to implement a recursive function to reverse a linked list. Dec 7, 2022 · Recursion is now a fundamental technique employed by software engineers for solving complex problems. The recursive structure is an idea to design a solution to a problem via the solution of its smaller sub-problems, i. Reduced Code Length: Recursion can reduce the length of the code since the repetitive tasks are handled through repeated function calls. 9. With detailed and elaborate explanations. Recursive call stacks take memory which risks stack overflow exceptions. Real Life Analogy of Recursion. A good example of this is a factorial function. Nov 22, 2023 · Recursive strategies shine in problems that can be effectively solved by breaking them down into smaller, solvable sub-problems. Needless to say, it can be tricky to figure out how to solve infinitely many problems simultaneously. Syntax Structure of Recursion ⬜Scenarios that we can solve easily without recursion ⬜0! = 1 . Aug 26, 2023 · Recursion is a way to solve a problem by solving smaller subproblems. , small in the sum() example). This is the implicit use of recursion. It means that there will be one or more function calls within that function definition itself. You solve the small pieces and put them together to solve the overall problem. calling the recursive function: index = index_of(imput. iteration The topics of today’s reading connect to our three key properties of good software as follows: Safe from bugs. Break a problem into smaller subproblems of the same form, and call the same function again on that smaller form. 5. Recursion is the technique of making a function call itself. This technique provides a way to break complicated problems down into simple problems which are easier to solve. For most recursive algorithms, unrolling the recursion is neither necessary nor helpful. Of course, recursion may be a very good way to simplify the algorithm what surely helps you to understand how it works (and why it's correct). 63%. Once my professor told me that any problem solved via recursion could be solved iteratively, I completely blocked out trying recursion. As i mentioned earlier some numbers will fly high and produce a great deal of stacks which will lead into stack overflow. A few Java recursion examples are Towers of Hanoi (TOH) Instructors: Erik Demaine, Jason Ku, and Justin Solomon Lecture 15: Recursive Algorithms . Recursion involves calling the same function within itself, which leads to a call stack. understand the benefits of recursion as a problem-solving strategy. It is used in a lot of important algorithms like DFS, Dynamic Programming and Backtracking. 2. 2 Using Recursion with Conditioning As we have seen so far, conditioning is a powerful method for solving probability problems. understand the features of recursion and recursive processes. A few Java recursion examples are Towers of Hanoi (TOH) Recursion in computer programming is exemplified when a function is defined in terms of simpler, often smaller versions of itself. Still, summing numbers in an array (or some other calculation based on processing data in a linear data structure) is a common enough recursion problem in coding interviews that it deserves our attention. Example 3. They work by trying out different paths and if one doesn't work, they backtrack and try another until they find the right one. Before you say it, I know there are other ways to solve this problem — that arguably are better and easier to recursion. Examples of such problems are Towers of Hanoi (TOH), Inord Oct 13, 2024 · Hi everyone! This is the first episode of the Recursion Problem Set in The Python Series. 4. Recursive Nth Fibonacci Number. Recursion means "defining a problem in terms of itself". Recursion is a powerful algorithm that uses code reusability and repeated usage of the same piece of code. ” • Iteration and recursion can be very powerful in combination! 7 Recursion is a method of solving problems that involves breaking a problem down into smaller and smaller subproblems until you get to a small enough problem that it can be solved trivially. recursive problems and recursive data comparing alternative decompositions of a recursive problem using helper methods to strengthen a recursive step recursion vs. iteration; The topics of today’s reading connect to our three key properties of good software as follows: Safe from bugs. However, if performance is vital, use loops instead as recursion is usually much slower. axgft lwm kfhra eroi zqvtzxz lgdps thueu kmnzqk yafc utikl ihng zuagri tasny szxdyf ykxhno