64 lines
1.8 KiB
Markdown
64 lines
1.8 KiB
Markdown
---
|
|
id: 5900f3d61000cf542c50fee7
|
|
challengeType: 5
|
|
title: 'Problem 103: Special subset sums: optimum'
|
|
---
|
|
|
|
## Description
|
|
<section id='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:
|
|
S(B) ≠ S(C); that is, sums of subsets cannot be equal.
|
|
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.
|
|
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}
|
|
It seems that for a given optimum set, A = {a1, a2, ... , an}, the next optimum set is of the form B = {b, a1+b, a2+b, ... ,an+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.
|
|
</section>
|
|
|
|
## Instructions
|
|
<section id='instructions'>
|
|
|
|
</section>
|
|
|
|
## Tests
|
|
<section id='tests'>
|
|
|
|
```yml
|
|
tests:
|
|
- text: <code>euler103()</code> should return 20313839404245.
|
|
testString: assert.strictEqual(euler103(), 20313839404245, '<code>euler103()</code> should return 20313839404245.');
|
|
|
|
```
|
|
|
|
</section>
|
|
|
|
## Challenge Seed
|
|
<section id='challengeSeed'>
|
|
|
|
<div id='js-seed'>
|
|
|
|
```js
|
|
function euler103() {
|
|
// Good luck!
|
|
return true;
|
|
}
|
|
|
|
euler103();
|
|
```
|
|
|
|
</div>
|
|
|
|
|
|
|
|
</section>
|
|
|
|
## Solution
|
|
<section id='solution'>
|
|
|
|
```js
|
|
// solution required
|
|
```
|
|
</section>
|