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xadro's solution

to Pythagorean Triplet in the Java Track

Published at Jul 13 2020 · 1 comment
Instructions
Test suite
Solution

A Pythagorean triplet is a set of three natural numbers, {a, b, c}, for which,

a**2 + b**2 = c**2

and such that,

a < b < c

For example,

3**2 + 4**2 = 9 + 16 = 25 = 5**2.

Given an input integer N, find all Pythagorean triplets for which a + b + c = N.

For example, with N = 1000, there is exactly one Pythagorean triplet for which a + b + c = 1000: {200, 375, 425}.

Setup

Go through the setup instructions for Java to install the necessary dependencies:

https://exercism.io/tracks/java/installation

Running the tests

You can run all the tests for an exercise by entering the following in your terminal:

$ gradle test

In the test suites all tests but the first have been skipped.

Once you get a test passing, you can enable the next one by removing the @Ignore("Remove to run test") annotation.

Source

Problem 9 at Project Euler http://projecteuler.net/problem=9

Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

PythagoreanTripletTest.java

import java.util.Arrays;
import java.util.List;
import java.util.Collections;
import static org.junit.Assert.assertEquals;
import org.junit.Test;
import org.junit.Ignore;

public class PythagoreanTripletTest {

    @Test
    public void tripletsWhoseSumIs12() {
        List<PythagoreanTriplet> actual
                = PythagoreanTriplet
                        .makeTripletsList()
                        .withFactorsLessThanOrEqualTo(12)
                        .thatSumTo(12)
                        .build();
        List<PythagoreanTriplet> expected
                = Collections.singletonList(new PythagoreanTriplet(3, 4, 5));
        assertEquals(expected, actual);
    }

    @Ignore("Remove to run test")
    @Test
    public void tripletsWhoseSumIs108() {
        List<PythagoreanTriplet> actual
                = PythagoreanTriplet
                        .makeTripletsList()
                        .withFactorsLessThanOrEqualTo(108)
                        .thatSumTo(108)
                        .build();
        List<PythagoreanTriplet> expected
                = Collections.singletonList(new PythagoreanTriplet(27, 36, 45));
        assertEquals(expected, actual);
    }

    @Ignore("Remove to run test")
    @Test
    public void tripletsWhoseSumIs1000() {
        List<PythagoreanTriplet> actual
                = PythagoreanTriplet
                        .makeTripletsList()
                        .withFactorsLessThanOrEqualTo(1000)
                        .thatSumTo(1000)
                        .build();
        List<PythagoreanTriplet> expected
                = Collections.singletonList(new PythagoreanTriplet(200, 375, 425));
        assertEquals(expected, actual);
    }

    @Ignore("Remove to run test")
    @Test
    public void tripletsWhoseSumIs1001() {
        List<PythagoreanTriplet> actual
                = PythagoreanTriplet
                        .makeTripletsList()
                        .withFactorsLessThanOrEqualTo(1001)
                        .thatSumTo(1001)
                        .build();
        List<PythagoreanTriplet> expected = Collections.emptyList();
        assertEquals(expected, actual);
    }

    @Ignore("Remove to run test")
    @Test
    public void tripletsWhoseSumIs90() {
        List<PythagoreanTriplet> actual
                = PythagoreanTriplet
                        .makeTripletsList()
                        .withFactorsLessThanOrEqualTo(90)
                        .thatSumTo(90)
                        .build();
        List<PythagoreanTriplet> expected
                = Arrays.asList(
                        new PythagoreanTriplet(9, 40, 41),
                        new PythagoreanTriplet(15, 36, 39));
        assertEquals(expected, actual);
    }

    @Ignore("Remove to run test")
    @Test
    public void tripletsWhoseSumIs840() {
        List<PythagoreanTriplet> actual
                = PythagoreanTriplet
                        .makeTripletsList()
                        .withFactorsLessThanOrEqualTo(840)
                        .thatSumTo(840)
                        .build();
        List<PythagoreanTriplet> expected
                = Arrays.asList(
                        new PythagoreanTriplet(40, 399, 401),
                        new PythagoreanTriplet(56, 390, 394),
                        new PythagoreanTriplet(105, 360, 375),
                        new PythagoreanTriplet(120, 350, 370),
                        new PythagoreanTriplet(140, 336, 364),
                        new PythagoreanTriplet(168, 315, 357),
                        new PythagoreanTriplet(210, 280, 350),
                        new PythagoreanTriplet(240, 252, 348));
        assertEquals(expected, actual);
    }

    @Ignore("Remove to run test")
    @Test
    public void tripletsWhoseSumIs30000() {
        List<PythagoreanTriplet> actual
                = PythagoreanTriplet
                        .makeTripletsList()
                        .withFactorsLessThanOrEqualTo(30000)
                        .thatSumTo(30000)
                        .build();
        List<PythagoreanTriplet> expected
                = Arrays.asList(
                        new PythagoreanTriplet(1200, 14375, 14425),
                        new PythagoreanTriplet(1875, 14000, 14125),
                        new PythagoreanTriplet(5000, 12000, 13000),
                        new PythagoreanTriplet(6000, 11250, 12750),
                        new PythagoreanTriplet(7500, 10000, 12500));
        assertEquals(expected, actual);
    }

}
import java.util.List;
import java.util.Objects;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

class PythagoreanTriplet {

	final int a;
	final int b;
	final int c;

	PythagoreanTriplet(final int a, final int b, final int c) {
		this.a = a;
		this.b = b;
		this.c = c;
	}

	static PythagoreanTripletBuilder makeTripletsList() {
		return new PythagoreanTripletBuilder();
	}

	static class PythagoreanTripletBuilder {

		private int max;
		private int sum;

		PythagoreanTripletBuilder withFactorsLessThanOrEqualTo(final int max) {
			this.max = max;
			return this;
		}

		PythagoreanTripletBuilder thatSumTo(final int sum) {
			this.sum = sum;
			return this;
		}

		List<PythagoreanTriplet> build() {
			return IntStream.rangeClosed(1, this.max - 2)
				.mapToObj(i -> new double[] {i, this.sum *(2.0 * i - this.sum) / (2.0 * (i - this.sum))})
				.filter(pair -> pair[1] == (int) pair[1] && pair[0] < pair[1])
				.map(pair -> new PythagoreanTriplet((int) pair[0], (int) pair[1], (int) (this.sum - pair[0] - pair[1])))
				.collect(Collectors.toList());
		}
	}

	@Override
	public boolean equals(final Object o) {
		if (this == o) {
			return true;
		}
		if (o == null || getClass() != o.getClass()) {
			return false;
		}
		final PythagoreanTriplet that = (PythagoreanTriplet) o;
		return a == that.a && b == that.b && c == that.c;
	}

	@Override
	public int hashCode() {
		return Objects.hash(a, b, c);
	}
}

Community comments

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Avatar of xadro
Solution Author
commented 280 days ago

Knowing that a^2 + b^2 = c^2 and a + b + c = N you can deduce:

b = N(2a - N) / 2(a - N)

So iterating a from 1 to N - 2 you get all pairs (a,b) where b is integer and greater than a. For each pair c = N - a - b.

(edited 280 days ago)

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