All Questions
5
questions with no upvoted or accepted answers
4
votes
0
answers
93
views
Counting the number of partitions that are a distance d away from a fixed partition.
Given a positive integer $N \in \mathbb{Z}^{\geq 0}$ let $Partitions(N)$ denote the set of all partitions of $N$, where a tuple $\left(f_1,\ldots,f_N \right)$ is a partition of $N$ if $\sum_{i=1}^N ...
- 41
3
votes
0
answers
86
views
Given $n\in\mathbb{N}_{\geqslant 2}$, find the partition $(a_1,...,a_k)\in\mathbb{N}^k:\sum_{i=1}^k a_i=n$ of $n$ that maximizes $\prod_{i=1}^k a_i$
I am a solving programming question in Leetcode in which, given a number $n \in \mathbb{N}_{\geqslant 2}$, I have to find $(a_1, ..., a_k) \in \mathbb{N}^k$ such that $k \in \mathbb{N}$, $2 \leqslant ...
3
votes
0
answers
1k
views
How to make a canonical coin system so that greedy solution is the only optimal solution for change-making problem
Related to the paper: http://arxiv.org/PS_cache/arxiv/pdf/0809/0809.0400v1.pdf and coin-change problem in general.
We say that a coin system of coins canonical if the greedy algorithm to the coin ...
- 31
2
votes
0
answers
127
views
Integer partitions without rotated solutions?
I'm searching for an algorithm to determine a list of all integer partitions of a number $n$ into a fixed number $m$ of summands (say $n=6$ and $m=4$), for instance to be stored into a list of (...
- 35k
1
vote
0
answers
298
views
An algorithm to generate all unique combinations of addends for a sum, from a range of small addends which are greater than 1?
I'm looking for an algorithm to generate all unique combinations of addends for a given sum, within a certain given range of addends. The size of the sum could range from two digits to five digits, ...
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