CODEWITHSUNDEEP
javacollectionspolynomial-math
Andulos
Andulos

Reputation: 475

Solve a polynomial equation in Java

I have an equation.

a4 + b4 = c4 + d4

The variables a, b, c and d can take any value from 0 to 1000. Write a program that would print all possible pairs of a, b and c, d that satisfy the above equation.

I tried to do it using Java.

One of the approaches I attempted was to build a map containing the key value pairs : <0,04>, <1,14>, <2,24>....<1000,10004>. After the map is built, I am looking to iterate through the values list and see if the sum of two elements in the list match the sum of two other elements in the list. I am stuck at this point. 

public static void getMatchingPairs()
    {
        long a;
        long b;
        long c;
        long d;
        Map<Integer,Long> map = new HashMap<Integer, Long>();
        for(int i = 0; i < 1001; i++)
        {
            long res = Double.valueOf(Math.pow(i, 4)).longValue();
            map.put(i,res);
        }

        List<Long> lst = (List<Long>) map.values();
    }

Upvotes: 0

Views: 951

Answers (2)

Peter Lawrey
Peter Lawrey

Reputation: 533660

In addition to Andres' comments, using an LongStream is a much more natural solution.

Lets assume that a^4 + b^4 = b^4 + a^4 is not an interesting solution so instead what you want to find is when a <= b and c and d != a or b

    Map<Long, List<long[]>> sums = LongStream.range(0, 1001)
            .boxed()
            .flatMap(a -> LongStream.range(a, 1001)
                    .boxed()
                    .map(b -> new long[]{a, b, a * a * a * a + b * b * b * b}))
            .collect(Collectors.groupingBy(triple -> triple[2]));
    sums.entrySet().stream()
            .filter(e -> e.getValue().size() > 1)
            .forEach(e -> System.out.println(
                    e.getValue().stream()
                            .map(t -> "(" + t[0] + "," + t[1] + ")")
                            .collect(Collectors.joining(", "))));

I have included the code here for you interest as you wouldn't be expect to write this for your homework yet.

Upvotes: 1

Andreas
Andreas

Reputation: 159135

Don't use double math to calculate power of 4. Just multiply 3 times, i.e. calculate a*a*a*a + b*b*b*b.

Then create a Map of the result to a List of the pairs used to calculate the result: Map<Long, List<int[]>> where the int[] is an array of two values, i.e. a "pair".

As an example, the pair (1,2) results in value 17, so does reverse pair (2,1). Since those are the only pairs with that result, your maps would include 17 = [(1,2), (2,1)].

Not sure what "print all possible pairs of a, b and c, d" means. Simple answer is just those 2 pairs (for result 17).

More complex answer is that you need to print each combination of pairs, since each pair can be an (a,b) pair or a (c,d) pair, so you create all combination of pairs: (1,2),(1,2), (1,2),(2,1), (2,1),(1,2), and (2,1),(2,1).

That all seems very redundant, because for each (a,b) pair where a != b, there will be 4 combinations, so perhaps you only need to print results of a pair (not combination of pairs), and only when a <= b, since a > b is redundant.

Anyway, you need to print from all the value lists in the map for the full answer.

Upvotes: 2

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