freeCodeCamp/curriculum/challenges/espanol/10-coding-interview-prep/project-euler/problem-103-special-subset-sums-optimum.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5900f3d61000cf542c50fee7	Problem 103: Special subset sums: optimum	5	301727	problem-103-special-subset-sums-optimum

--description--

Let S(A) represent the sum of elements in set A of size n. We shall call it a special sum set if for any two non-empty disjoint subsets, B and C, the following properties are true:

1. S(B) ≠ S(C); that is, sums of subsets cannot be equal.
2. If B contains more elements than C then S(B) > S(C).

If S(A) is minimised for a given n, we shall call it an optimum special sum set. The first five optimum special sum sets are given below.

\begin{align} & n = 1: \\{1\\} \\\\ & n = 2: \\{1, 2\\} \\\\ & n = 3: \\{2, 3, 4\\} \\\\ & n = 4: \\{3, 5, 6, 7\\} \\\\ & n = 5: \\{6, 9, 11, 12, 13\\} \\\\ \end{align}

It seems that for a given optimum set, A = \\{a_1, a_2, \ldots, a_n\\}, the next optimum set is of the form B = \\{b, a_1 + b, a_2 + b, \ldots, a_n + b\\}, where b is the "middle" element on the previous row.

By applying this "rule" we would expect the optimum set for n = 6 to be A = \\{11, 17, 20, 22, 23, 24\\}, with S(A) = 117. However, this is not the optimum set, as we have merely applied an algorithm to provide a near optimum set. The optimum set for n = 6 is A = \\{11, 18, 19, 20, 22, 25\\}, with S(A) = 115 and corresponding set string: 111819202225.

Given that A is an optimum special sum set for n = 7, find its set string.

Note: This problem is related to Problem 105 and Problem 106.

--hints--

optimumSpecialSumSet() should return the string 20313839404245.

assert.strictEqual(optimumSpecialSumSet(), '20313839404245');

--seed--

--seed-contents--

function optimumSpecialSumSet() {

  return true;
}

optimumSpecialSumSet();

--solutions--

// solution required