- The gcd () method of Java BigInteger class is used to get the greatest common divisor of absolute values of two BigInteger. This method returns a BigInteger whose value is the greatest common divisor of abs (this) and abs (val)
- Java Program to Compute GCD Last Updated : 26 Nov, 2020 GCD (Greatest Common Divisor) of two given numbers A and B is the highest number that can divide both A and B completely, i.e., leaving remainder 0 in each case. GCD is also called HCF (Highest Common Factor)
- Overview. In mathematics, the GCD of two integers, which are non-zero, is the largest positive integer that divides each of the integers evenly. In this tutorial, we'll look at three approaches to find the Greatest Common Divisor (GCD) of two integers. Further, we'll look at their implementation in Java. 2
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- Euclid's algorithm is an efficient way to find GCD of two numbers and it's pretty easy to implement using recursion in Java program. According to Euclid's method GCD of two numbers, a, b is equal to GCD (b, a mod b) and GCD (a, 0) = a. The latter case is the base case of our Java program to find GCD of two numbers using recursion
- The % going to give us the gcd Between two numbers, it means:- % or mod of big_number/small_number are =gcd, and we write it on java like this big_number % small_number. EX1: for two integer
- es GCD of numbers 2 at a time using the recursive GCD method we defined earlier

Write a Java program to find the GCD of N numbers or more than two numbers. GCD of three or more numbers can be calculated by repeatedly taking the GCD of pairs of numbers. gcd (a, b, c) = gcd (a, gcd (b, c)) = gcd (gcd (a, b), c) = gcd (gcd (a, c), b * The GCD (Greatest Common Divisor) of two numbers is the largest positive integer number that divides both the numbers without leaving any remainder*. For example. GCD of 30 and 45 is 15. GCD also known as HCF (Highest Common Factor). In this tutorial we will write couple of different Java programs to find out the GCD of two numbers The java.math.BigInteger.gcd (BigInteger val) returns a BigInteger whose value is the greatest common divisor of abs (this) and abs (val). It returns 0 if this == 0 && val == 0

- OnlineGDB is online IDE with java compiler. Quick and easy way to run java program online
- GCD stands for Greatest Common Divisor. As its name suggests, a GCD of two or more numbers is the highest number that completely divides all those numbers. In other words, a number which divides two or more numbers with remainder as zero is called the GCD of those numbers. How to calculate ? GCD can be calculated in many ways using a java program
- Java program to find the GCD or HCF of two numbers. Equal partition of an array of numbers - JavaScript. Find GCD of factorial of elements of given array in C++. Finding LCM of more than two (or array) numbers without using GCD in C++. Program to find GCD of floating point numbers in C++
- GCD (Greatest Common Divisor) also known as HCF (Highest Common Factor) of two or more integers is the largest positive number which exactly divides each and every input integers. In Java GCD or HCF can be computed using the following methods
- GCD in Java - YouTube
- Java Program to find GCD (Greatest Common Divisor) | GCD of two numbers In This Tutorial, We will learn about the Java Program to find GCD (Greatest Common D..
- According to Mathematics, GCD of two or more integers is the largest positive integer that divides the given integer without any remainder. For example, Java GCD of 8 and 12 is 4 because both 8 and 12 are divisible by 1, 2, and 4. The largest positive integer among the factors 1, 2, and 4 is 4

The GCD program in Java outputs the GCD of the given numbers. In mathematics, Greatest Common Divisor (GCD), Greatest Common Factor or Highest Common Factor (HCF) of two numbers, x and y, is represented by GCD (x, y) or HCF (x, y).To find the GCD of number, first we need to find factors of that numbers. Let's understand what is factors So GCD(12,54) is 6. The following code illustrates how to find Greatest Common Divisior (GCD) of two numbers which are passed through command line. We can find GCD in several ways. In our code, we have written two functions to find GCD. One is using loop and another is using recursion. Now let us calculate GCD using loop for the input (12 & 54

GCD (Greatest Common Divisor) or HCF (Highest Common Factor) of two numbers is the largest number that divides both of them. For example GCD of 20 and 28 is 4 and GCD of 98 and 56 is 14. Recommended: Please solve it on PRACTICE first, before moving on to the solution **Java** program to find out the **GCD** between two numbers. Here, we will discuss the various methods to find out the **GCD** between two numbers. Also, we'll learn how to calculate the **GCD** of n numbers. Soon Compiler has added to it so that you can execute the set of programs yourself. The methods as. Now in this post, we will develop the HCF or GCD program in Java to find the HCF or GCD of two numbers. The highest common factor (HCF) of two or more numbers is the greatest number which divides each of them exactly. Greatest Common Measure (GCM) and Greatest Common Divisor (GCD) are the other terms used to refer to HCF

gcd in java Write a JavaFx program that accepts two numbers as shown in the picture below. When you click on a button you compute and find the gcd of two numbers ** Problem: Write a Java program to find GCD of n numbers or array of n numbers**. Example: Input: [16, 8, 24] Output: 8 Input: [16, 8, 24, 4] Output: 4. Greatest Common Divisor (GCD) of two or more positive numbers is the largest possible integer which divides each of them.. For example, GCD of 16, 8, and 24 is 8

GCD of Two Numbers in Java. Let's discuss how to find GCD of two numbers in Java. A GCD is a positive and largest integer among all the common divisors of two numbers. It is also called as Greatest Common Factor (GCF). Greatest Divisor of 16 is 16 and the greatest divisor of 28 is 28 In this post, we will see how to find Greatest common divisor(GCD) and Least Common Multiple(LCM) in java. GCD is calculated using Euclidean algorithm and LCM is calculated using reduction by GCD. Eucid algo for calculating GCD is: Lets say , there are two numbers , a and b so GCD of two numbers = GCD (b,a%b) and GCD(a,0)= BigInteger类gcd()方法 (BigInteger Class gcd() method) gcd() method is available in java.math package. gcd()方法在java.math包中可用。 gcd() method is used to return the greatest common divisor of the absolute of.. Java Program to Find G.C.D Using Recursion. In this program, you'll learn to find the GCD (Greatest Common Divisor) or HCF using a recursive function in Java Exception in thread main java.lang.ArithmeticException: / by zero at com.java.w3schools.blog.java.program.to.GCDForLoop.main(GCDForLoop.java:30) 5. Conclusion In this article, We have seen how to find the GCD of two numbers in java using two methods

BigInteger Class gcd() method: Here, we are going to learn about the gcd() method of BigInteger Class with its syntax and example. Submitted by Preeti Jain, on May 10, 2020 BigInteger Class gcd() method. gcd() method is available in java.math package This program demonstrates the logic and code for finding GCD ( Greatest Common Divisor ) or GCF ( Greatest Common Factor ) for the given two numbers.Example:.. GCD is a primitive in J (and anyone that has studied the right kind of mathematics should instantly recognize why the same operation is used for both GCD and OR -- among other things, GCD and boolean OR both have the same identity element: 0, and of course they produce the same numeric results on the same arguments (when we are allowed to use the usual 1 bit implementation of 0 and 1 for false. For this topic you must know about Greatest Common Divisor (GCD) and the MOD operation first. Greatest Common Divisor (GCD)The GCD of two or more integers is the largest integer that divides each of the integers such that their remainder is zero. Example- GCD of 20, 30 = 10 (1 GCD.java package math; /** * This is a utility class that provides the functionality of calculating the * GCD or Greatest Common Divisor (also known as HCF or Highest Common * Factor) of two or more integers

jasonbai2014 Create gcd.java. Latest commit 69f5b3d Nov 25, 2014 History. 1 contributor Users who have contributed to this file 15 lines (12 sloc) 287 Bytes Raw Blame /* * Write a method named gcd that accepts two integers as parameters * and. I know that Euclid's algorithm is the best algorithm for getting the GCD (great common divisor) of a list of positive integers. But in practice you can code this algorithm in various ways. (In my case, I decided to use Java, but C/C++ may be another option). I need to use the most efficient code possible in my program

To compute the gcd, I created a for loop that assigns min to i. I decrement this variable until the modulo operation for count % numbers.length - 1 equals 0. This indicates that a gcd has been found for all integers and will break out of the main for loop Let's learn to find GCD of three numbers in java. Find GCD of three numbers in java. GCD is largest positive integer that can exactly divide each one of the number. Here's an example on to find GCD of three numbers Write a JavaScript function to get the greatest common divisor (gcd) of two integers. Note: According to Wikipedia - In mathematics, the greatest common divisor (gcd) of two or more integers, when at least one of them is not zero, is the largest positive integer that divides the numbers without a remainder. For example, the GCD of 8 and 12 is 4 GCD is the largest number from the common multiples of numerator and denominator. Both the numerator and denominator are divided by GCD to get the reduced form of fraction. In above case GCD of 56 and 12 is 4, dividing numerator and denominator by 4 gives 14/3 which is the simplest form of fraction. Operations of Fraction

/***** * Compilation: javac ExtendedEuclid.java * Execution: java ExtendedEuclid p q * * Reads two positive command-line arguments p and q and compute the greatest * common divisor of p and q using the extended Euclid's algorithm Write a Program in Java to input 2 numbers and find their Greatest Common Divisor (GCD). Note: If the 2 numbers are 54 and 24, then the divisors (factors) of 54 are: 1, 2, 3, 6, 9, 18, 27, 54 Write a Java program to find GCD of two numbers using Recursion. Given two input integers, we have to write a code to find GCD of two numbers using recursion. For this program, I assume you are familiar with the concept of recursion. If you don't know about recursion then check my previous post on recursion vs iteration By reversing the steps, the GCD can be expressed as a sum of the two original numbers each multiplied by a positive or negative integer, e.g., 21 = 5 × 105 + (−2) × 252. The fact that the GCD can always be expressed in this way is known as Bézout's identity. Pictorial Presentation: Sample Solution: Java Code

Java program to find the GCD (Greatest Common Divisor) of any two given numbers. GCD is a largest number that exactly divides two or more integers. In general, Greatest Common Divisor (GCD) is otherwise called as Greatest Common Factor (GCF) or Highest Common Factor (HCF) Java / Maths / GCD.java / Jump to. Code definitions. GCD Class gcd Method gcd Method main Method. Code navigation index up-to-date Go to file Go to file T; Go to line L; Go to definition R; Copy path Cannot retrieve contributors at this time. 57 lines (49 sloc) 1.23 KB Raw. GCD and Rational Number Java Program Java Queue Program using exception Java Stack Program using exception Addition of three integers java progra ** Let GCD(x,y) be the GCD of positive integers x and y**. If x = y, then obviously GCD(x,y) = GCD(x,x) = x Euclid's insight was to observe that, if x > y, then GCD(x,y) = GCD(x-y,y). Actually, this is easy to prove. Suppose that d is a divisor of both x and y. Then there exist integers q 1 and q 2 such that x = q 1 d and y = q 2 d

The greatest common divisor (gcd) of two positive integers is the largest integer that divides both without remainder. Euclid's algorithm is based on the following property: if p>q then the gcd of p and q is the same as the gcd of p%q and q. p%q is the remainder of p which cannot be divided by q, e.g. 33 % 5 is 3 * The Euclid's algorithm (or Euclidean Algorithm) is a method for efficiently finding the greatest common divisor (GCD) of two numbers*. Implementation available in 10 languages along wth questions, applications, sample calculation, complexity, pseudocode Java Program to calculate lcm and hcf. In this program, we first take two numbers as input from user and store them in variable a and b. Then using a while loop, we calculate the gcd of a and b and store it in variable gcd

** As it turns out, if the greatest common divisor (gcd) of 2 numbers a and b is 1 (i**.e. gcd(a, b) = 1) then a and b are relatively prime. As a result, determining whether two numbers are relatively prime consists simply of finding if the gcd is 1. 3. Euclidean Algorithm Implementatio Java program find GCD and LCM of two numbers using euclid's algorithm. In the below java program user enters two numbers using nextLong() method of Scanner class. These two numbers are divided and remainder will become divisor and previous divisor become dividend pepcoding, online java course, learn java for free, best place to learn coding in delhi, sumeet malik, basics of java, java programming home online-java-foundation getting-started gcd-and-lcm-officia JAVA program to find lcm and gcd/hcf of two numbers This JAVA program is to find LCM and GCD/HCF of two numbers. LCM(Least Common Multiple) is the smallest positive number which is divisble by both the numbers. For example, lcm of 8 and 12 is 24 as 24 is divisble by both 8(8*3) and 12(12*2). HCF(Highest [

In some languages that not support tail recursion, the space needed for computing gcd as in our example will never be constant, in fact, this will cost us O(n) space.. Tail-recursive function in Scala. In Scala, direct calls to the current function are optimized, however, an indirect call to the current recursive function is not optimized by default GCD of two numbers is the largest number that divides both of them. A simple way to find GCD is to factorize both numbers and multiply common factors. Basic Euclidean Algorithm for GCD The algorithm is based on below facts. If we subtract smaller number from larger (we reduce larger number), GCD doesn't change For example, the gcd(102, 68) = 34. We can efficiently compute the gcd using the following property, which holds for positive integers p and q: If p > q, the gcd of p and q is the same as the gcd of q and p % q. The static method gcd() in Euclid.java is a compact recursive function whose reduction step is based on this property GCD of two numbers Euclidean algorithm in java (iterative/ recursive) The greatest common divisor (GCD) is the largest natural number that divides two numbers without leaving a remainder. e.g gcd ( 10,15) = 5 or gcd ( 12, 18) = 1

Java Program to find LCM of Two Numbers using Recursive Method This program for lcm of two numbers in java calculates the Greatest Common Divisor by calling HCFofTwo function recursively. Next, this Java program finds the Least Common Multiple from GCD Brute Force Approach for GCD The basic idea is to try all integers from n (where n is the given second number, i.e., the smaller one) down until finding one that divides both the numbers. Let's take an example of 24 and 12 This JAVA program is to find gcd/hcf using Euclidean algorithm using recursion. HCF(Highest Common Factor)/GCD(Greatest Common Divisor) is the largest positive integer which divides each of the two numbers.For example gcd of 42 and 18 is 6 as divisors of 42 are 1,2,3,4,6,7,14,21 and divisors of 18 are 1,2,3,6,9,18 , so the greatest common divisor is In mathematics, the greatest common divisor (GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted (,).For example, the GCD of 8 and 12 is 4, that is, (,) =. In the name greatest common divisor, the adjective greatest may be replaced by highest, and. gcd of two numbers in java (self.flowerbrackets) submitted 1 minute ago by flowerbrackets GCD of two numbers is the largest positive number that divides both numbers without remainder

A Java method that implements Euclid's algorithm is as follows: int gcd(int K, int M) { int k = K; // In order to state a simple, elegant loop invariant, int m = M; // we keep the formal arguments constant and use // local variables to do the calculations Here, we are going to learn how to find the greatest common divisor (GCD) in C#? Submitted by Nidhi, on September 21, 2020 . Here, we will find the Greatest Common Divisor of two numbers.The GCD is the highest positive number that can divide both numbers without any remainder GCD.java - public class GCD public static void main(String args int n1 = 366 n2 = 60 int hcf = hcf(n1 n2 System.out.printf\G.C.D of%d and%d is%d n1 n The greatest common divisor (gcd) of two or more integers, when at least one of them is not zero, is the largest positive integer that is a divisor of both numbers.. For example, the GCD of 8 and 12 is 4.. This is java program to find the gcd of given two numbers. GCD is calculated using Euclidean Algorithm. Here is the source code of the Java Program to Find the GCD of 2 Numbers

Finally, we get the **GCD** of 10 and 20 i.e. 10 as a result. Finding **GCD** of two numbers using a recursive function in Python. Firstly, we take input from the user. We define a function 'calc_gcd' which recursively calculates the **GCD** and returns the final result. Finally, we store the **GCD** in the variable 'result'. The Python program is. GCD Algorithm: Greatest Common Divisor in Java Posted on October 7, 2013 January 9, 2014 by Code Puppet Here are three different implementations of the classic GCD (Greatest Common Divisor) problem To compute gcd (48, 18) first divide 48 by 18 to get quotient as 2 and remainder as 12. Then divide 18 by 12 to get quotient as 1 and remainder as 6. Then divide 12 by 6 to get remainder as 0, which means that 6 is the gcd. Java Program to Find GCD of Two Numbers. Now lets implement this algorithm recursively to find gcd in Java Java Program to Implement Euclid GCD Algorithm using Recursion. May 7, 2017 Data Structure, Java, Pratice Problem gcd, gcf, gcm, hcd, hcf, Java, recursion sanikamal. The Euclidean algorithm calculates the greatest common divisor (GCD) of two number a and b

If your going to post code examples, at least you could check if it works. CD_Finder.java:18: cannot find symbol symbol : method GCD(int,int) location: class GCD_Finder.GCD System.out.println(GCD of +num1+ and +num2+ is +obj.GCD(num1,num2)); home > topics > java > questions > gcd common divisor Post your question to a community of 468,075 developers. It's quick & easy. gcd common divisor. judge82. 24 I'm new to Java and I was looking for some help on this particular problem. I.

In this tutorial we will learn to find GCD or Greatest Common Divisor using recursion. What is GCD or Greatest Common Divisor. In mathematics GCD or Greatest Common Divisor of two or more integers is the largest positive integer that divides both the number without leaving any remainder cnau / Java 8 GCD and LCM Lambda. Created Dec 20, 2017. Star 1 Fork 0; Star Code Revisions 1 Stars 1. Embed. What would you like to do? Embed Embed this gist in your website. Share Copy sharable link for this gist. Clone via HTTPS. BigInteger provides analogues to all of Java's primitive integer operators, and all relevant methods from java.lang.Math. Additionally, BigInteger provides operations for modular arithmetic, GCD calculation, primality testing, prime generation, bit manipulation, and a few other miscellaneous operations

Java求最大公约数和最小公倍数 最大公约数(Greatest Common Divisor(GCD)) 最大公因数，也称最大公约数、最大公因子，指两个或多个整数共有约数中最大的一个 GCD Example Java Program Definition The greatest common divisor (gcd) of two or more integers, when at least one of them is not zero, is the largest positive integer that divides the numbers without a remainder Data Type Parameter Description; BigInteger: val: value with which the GCD is to be computed

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- GCD or HCF of two numbers using Java : GCD(Greatest Common Divisor) or HCF(Highest Common Factor) of two numbers is the number which is the largest common factor of both numbers.It is also referred as Greatest Common Factor(GCF), Greatest Common Measure(GCM), Highest Common Divisor(HCD) Or, we can say that GCD or HCF of two [
- For this topic you must know about the Greatest Common Divisor (GCD) and the MOD operation first. Greatest Common Divisor (GCD)The GCD of two or more integers is the largest integer that divides each of the integers such that their remainder is zero. Here's an example: GCD of 20
- Example Input: 60 15 36 60 Output: 15 12 Iterative approach. Implementation. We will loop until both the given numbers are not eqaul. Then in each iteration we will check if num1 is greater than num2 or not.; If it is greater then we will subtract num2 from num1 else we will subtract num1 from num2.; This approach is based on Euclidean Algorithm.; let gcd = (num1, num2) => { //Loop till both.

- GCD (наибольший общий делитель) или HCF (наибольший общий фактор) из двух чисел — это наибольшее число, которое разделяет их оба.Метод java.math.BigInteger.gcd (BigInteger val) используется для вычисления gcd двух BigInteger
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- Java Code Examples for java.math.BigInteger # gcd() The following examples show how to use java.math.BigInteger#gcd() . These examples are extracted from open source projects. You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example

In mathematics, the Euclidean algorithm, or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers (numbers), the largest number that divides them both without a remainder.It is named after the ancient Greek mathematician Euclid, who first described it in his Elements (c. 300 BC). It is an example of an algorithm, a step-by-step procedure for. java gcd javagcd java中求gcd java中的gcd js前端截图保存 js将图片排成字 js取客户端信息 js中判断必填项 js正则表达+或 js写mac递增 js li 列表 js 长字符换行 js家庭地址正则 用js移除css js原生代码动效 js遍历所有结点 js局部重新加载 js 布尔 取反 js弹窗固定代 First, we will see how to find GCD of two numbers. It is also known as Highest Common Factor - HCF. Then we will move on to find the GCD of a list of numbers and code it in both C++ as well as Pytho

GCD Calculator Instructions. The GCD calculator allows you to quickly find the greatest common divisor of a set of numbers. You may enter between two and ten non-zero integers between -2147483648 and 2147483647. The numbers must be separated by commas, spaces or tabs or may be entered on separate lines Binary GCD algorithm or Stein's algorithm is an algorithm that calculates two non-negative integer's largest common divisor by using simpler arithmetic operations than the standard euclidean algorithm and it reinstates division by numerical shifts, comparisons, and subtraction operations Compute the gcd of two integer It is good for finding the GCD when one or both of the numbers is large. If you're interested, Wikipedia has a great article on Euclid's algorithm. Well, that's it for finding the GCD! Pick a method you like, and keep practicing. Pretty soon you will be able to find the GCD of some numbers in your head

gcd Euclid, the ancient Greek mathematician, discovered how to find the GCD ( G reatest C ommon D ivisor ) of two integers, the biggest integer that divides evenly into both LC Python has an inbuilt method to find out the GCD. We even doesn't need to think how to code to find GCD. All we have to do is just use math.gcd() method and it will return the GCD. Method 4: Using Euclidean Algorithm. Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two numbers The recursive function above returns the GCD and the values of coefficients to x and y (which are passed by reference to the function). This implementation of extended Euclidean algorithm produces correct results for negative integers as well The last non-zero remainder is 3 and therefore gcd(93, 219) = 3. Bezout's identity. Given any integers a and b, not both zero, there exist integers x and y such that gcd(a, b) = xa + yb In other words, you can always write gcd(a, b) as an integer combination of a and b. Part (b) of most exam questions involve this

Java Program to Find GCD and LCM of Two Numbers Using Euclid's Algorithm. 02, Dec 20. Java Program to Find GCD or HCF of Two Numbers. 23, Mar 21. Make all the elements of array odd by incrementing odd-indexed elements of odd-length subarrays. 16, Dec 20 Greatest Common Divisor (GCD) of positive integer numbers : Math « Development Class « Java Hello, in this tutorial, we will understand how to find GCD of two numbers in C++ in various ways.. Greatest Common Divisor (GCD) or Highest Common Factor (HCF) of two number a and b is the largest number that divides a and b. It is denoted by GCD(a, b).. let's understand GCD with a simple example. Example : Finding GCD of 24 and 36 24 = 2 × 2 × 2 × 3 × 1 and, 36 = 2 × 2 × 3 × 3 × 1. Brute force Approach to find GCD of Two numbers: In this approach we first check if both a and b have the value 0.If yes, the GCD(a,b) is not defined. If not we check if either of a and b is 0.In this case the non-zero number among a and b is the GCD(a,b). If the values of both a and b is not 0, we check for all numbers from 1 to min(a,b) and find the largest number which divides both a and b

В качестве аргументов методу **gcd** передаются 2 числа, в качестве результата он возвращает их НОД. Вычисления производятся с типом данных int (при необходимости, разумеется, можно заменить его на любой другой целочисленный) The GCD or HCF of a integer is the highest positive integer that divides the given integer without remainder. A C program to find GCD of two numbers Program to find the GCD or HCF of two numbers Here we will discuss how to find the GCD or HCF of two numbers entered by the user using C++ programming language. GCD i.e. Greatest Common Divisible or HCF i.e. Highest Common Factor of two numbers is the largest positive integer that can divide both the number GCD Using Math GCD Function. Before we can make use of the math.gcd() function to compute the GCD of numbers in Python, let's take a look at its various parameters. Syntax: math.gcd( x,y) Parameters. X: is the non negative integer whose gcd needs to be computed. Y: is the second non negative integer whose gcd needs to be computed

Java based on mathmatic GCD. brucezu created at: March 16, 2021 11:31 PM | No replies yet. 0. 77. Test Case Answer Seems to be Confusing. xiao_vanessa created at: March 15, 2021 1:37 AM | Last Reply: jopethemetalmessiah March 20, 2021 5:48 AM. 1. 18. 0 ms, faster than 100.00% of Java | recursion Java: public boolean hasGroupsSizeX When I use reduce() and fractions.gcd in leetcode, I still need to. from functools import reduce import fractions 4. Show 3 replies. Reply. Share. Report. baojiawei 242. Last Edit: September 30, 2018 6:47 PM. Read More. We can return false as soon as the divisor turns to 1. 4 Algorithms and data structures source codes on Java and C++. Euclidean algorithm. GCD, LCM, modular inverse, Chinese remainder theorem - Algorithms and Data Structure