﻿ Java programming exercises: Prove that Euclid’s algorithm computes the greatest common divisor of two positive given integers - w3resource # Java Exercises: Prove that Euclid’s algorithm computes the greatest common divisor of two positive given integers

## Java Basic: Exercise-157 with Solution

Write a Java program to prove that Euclid’s algorithm computes the greatest common divisor of two positive given integers.

According to Wikipedia "The Euclidean algorithm is based on the principle that the greatest common divisor of two numbers does not change if the larger number is replaced by its difference with the smaller number. For example, 21 is the GCD of 252 and 105 (as 252 = 21 × 12 and 105 = 21 × 5), and the same number 21 is also the GCD of 105 and 252 − 105 = 147. Since this replacement reduces the larger of the two numbers, repeating this process gives successively smaller pairs of numbers until the two numbers become equal. When that occurs, they are the GCD of the original two numbers. 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:

``````import java.util.Scanner;
public class Solution {
public static int euclid(int x, int y) {
if (x == 0 || y == 0) {
return 1;
}
if (x < y) {
int t = x;
x = y;
y = t;
}
if (x % y == 0) {
return y;
} else {
return euclid(y, x % y);
}
}

public static void main(String[] args) {
System.out.println("result: " + euclid(48, 24));
System.out.println("result: " + euclid(125463, 9658));
}
}
```
```

Sample Output:

```result: 24
result: 1
```

Flowchart: Java Code Editor:

What is the difficulty level of this exercise?

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## Java: Tips of the Day

Array vs ArrayLists:

The main difference between these two is that an Array is of fixed size so once you have created an Array you cannot change it but the ArrayList is not of fixed size. You can create instances of ArrayLists without specifying its size. So if you create such instances of an ArrayList without specifying its size Java will create an instance of an ArrayList of default size.

Once an ArrayList is full it re-sizes itself. In fact, an ArrayList is internally supported by an array. So when an ArrayList is resized it will slow down its performance a bit as the contents of the old Array must be copied to a new Array.

At the same time, it's compulsory to specify the size of an Array directly or indirectly while creating it. And also Arrays can store both primitives and objects while ArrayLists only can store objects.

Ref: https://bit.ly/3o8L2KH