Write following code in Java following example: JAVA! Background A Pythagorean t

Question

Write following code in Java following example:

JAVA!

Background A Pythagorean triplet is three positive whole numbers a, b, and c,such that 2+2-2. For example, (3, 4, 5) is a Pythagorean triplet, since 3 +4 5 In this project, we will refer to the sum of a Pythagorean triplet to mean the sum of those three numbers. So if a b -c,then its sum is a+b+c. So for the Pythagorean triplet (3, 4, 5), its sum is 3+4+5 12. Description You will write a Java program that will repeatedly find all Pythagorean triplets for a given sum, or find the sum that has the most Pythagorean triplets. Here is a sample run of the program (user input is in red)

Explanation / Answer

A Pythagorean triplet is an arrangement of three whole numbers a, b and c with the end goal that a2 + b2 = c2. Given a farthest point, create every Pythagorean Triple with values littler than given breaking point.

Info : restrain = 20

Yield : 3 4 5

8 6 10

5 12 13

15 8 17

12 16 20

A Simple Solution is to produce these triplets littler than given farthest point utilizing three settled circle. For each triplet, check if Pythagorean condition is valid, assuming genuine, at that point print the triplet. Time many-sided quality of this arrangement is O(limit3) where 'restrict' is given point of confinement.

An Efficient Solution can print all triplets in O(k) time where k is number of triplets printed. The thought is to utilize square whole connection of Pythagorean triplet, i.e., expansion of squares of an and b is equivalent to square of c, we can compose these number as far as m and n with the end goal that,

a = m2 - n2

b = 2 * m * n

c = m2 + n2

since,

a2 = m4 + n4 – 2 * m2 * n2

b2 = 4 * m2 * n2

c2 = m4 + n4 + 2* m2 * n2

We can see that a2 + b2 = c2, so as opposed to repeating for a, b and c we can emphasize for m and n and can produce these triplets.

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