Canadian Computing Competition: 2018 Stage 1, Senior #4
Trees have many fascinating properties. While this is primarily true for trees in nature, the concept of trees in math and computer science is also interesting. A particular kind of tree, a perfectly balanced tree, is defined as follows.
Every perfectly balanced tree has a positive integer weight. A perfectly balanced tree of weight always consists of a single node. Otherwise, if the weight of a perfectly balanced tree is
and
, then the tree consists of a root node with branches to
subtrees, such that
. In this case, all
subtrees must be completely identical, and be perfectly balanced themselves.
In particular, all subtrees must have the same weight. This common weight must be the maximum integer value such that the sum of the weights of all
subtrees does not exceed
, the weight of the overall tree. For example, if a perfectly balanced tree of weight
has
subtrees, then each subtree would have weight
, since
.
Given , find the number of perfectly balanced trees with weight
.
Input Specification
The input will be a single line containing the integer
.
For of the
marks available,
.
For an additional of the
marks available,
.
For an additional of the
marks available,
.
Output Specification
Output a single integer, the number of perfectly balanced trees with weight .
Sample Input 1
4
Sample Output 1
3
Explanation for Sample Output 1
One tree has a root with four subtrees of weight ; a second tree has a root with two subtrees of weight
; the third tree has a root with three subtrees of weight
.
Sample Input 2
10
Sample Output 2
13
Comments
lmAO you cant even use int in this question cus it will integer overflow. I found out whilst debugging. r/todayilearned
I still have questions about the second sample input. I tried and got the same result as that guy got--17. Can anyone specify what the situation is when input is 10? ty
I don't know why I get seg fault on the last batch... I doubled checked my indexing, and nothing seems to be wrong..
You're running out of memory
Slow judge? Or is my code just too slow
Edit: Nvm passed
Please give an explanation to Sample Output 2. I tried it on a whiteboard and got 17.
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If you would like a detailed explanation, please go to https://slack.dmoj.ca/ and reach me in direct messages. (This could end up being a long conversation so I would prefer it not be in comments)