Project Euler | Problem 9 | Special Pythagorean Triplet

Problem Description :

A Pythagorean triplet is a set of three natural numbers, a < b < c, for which, a^2 + b^2 = c^2
For example, 32 + 42 = 9 + 16 = 25 = 52. There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc.

Project Euler Problem 9

Concept :

We have following two equations.

1) a^2+b^2=c^2

2) a+b+c=1000

on solving these equations mathematically.

1<=a<=999

b=(1000^2-(2*a*1000))/(2*(1000-a))

c=1000-b-a

Java Program :

	package com.javamultiplex.projecteuler;
	/**
	*
	* @author Rohit Agarwal
	* @category Project Euler Problems
	* @problem Problem 9
	*
	*/
	public class Problem9 {
	public static void main(String[] args) {
	int limit = 1000, a, b, c, result;
	for (int i = 1; i < limit; i++) {
	a = i;
	/*
	* if a+b+c=n and c^2=a^2+b^2 on solving above equations we can find
	* value of b in terms of a and n b=(n^2-2an)/2(n-a)
	*/
	b = (int) ((Math.pow(limit, 2) - 2 * a * limit) / (2 * (limit - a)));
	c = limit - b - a;
	if (isPythagoreanTriplet(a, b, c)) {
	if (a + b + c == limit) {
	result = a * b * c;
	System.out.println("Pythagorean triplet for which a + b + c = 1000 is : "+ result);
	break;
	}
	}
	}
	}
	// a,b and c are Pythagorean Triplets if c>b>a and c^2=a^2+b^2
	private static boolean isPythagoreanTriplet(int a, int b, int c) {
	boolean result = false;
	if (c > b && b > a) {
	if (c * c == a * a + b * b) {
	result = true;
	}
	}
	return result;
	}
	}

view raw Problem9.java hosted with ❤ by GitHub

Output :

Output - Project Euler Problem 9 Solution in Java

References :

https://projecteuler.net/problem=9

https://en.wikipedia.org/wiki/Pythagorean_triple

https://docs.oracle.com/javase/7/docs/api/java/lang/Math.html

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Tags : Project Euler Problem 9 solution in Java, Mathematics problems, Special Pythagorean Triplet, for loop, if else statement.

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