1.3 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f3d71000cf542c50fee9 | Problem 106: Special subset sums: meta-testing | 5 | 301730 | problem-106-special-subset-sums-meta-testing |
--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)
.
For this problem we shall assume that a given set contains n strictly increasing elements and it already satisfies the second rule.
Surprisingly, out of the 25 possible subset pairs that can be obtained from a set for which n = 4, only 1 of these pairs need to be tested for equality (first rule). Similarly, when n = 7, only 70 out of the 966 subset pairs need to be tested.
For n = 12, how many of the 261625 subset pairs that can be obtained need to be tested for equality?
Note: This problem is related to Problem 103 and Problem 105.
--hints--
subsetSumsMetaTesting()
should return 21384
.
assert.strictEqual(subsetSumsMetaTesting(), 21384);
--seed--
--seed-contents--
function subsetSumsMetaTesting() {
return true;
}
subsetSumsMetaTesting();
--solutions--
// solution required