论文标题
总和问题
The Sum Composition Problem
论文作者
论文摘要
在本文中，我们研究了两个列表$ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $的“总成分问题”。首先，当存在一个订购的$ m $ - 分区$ [a_1，\ ldots，a_m] $ a $ a $ a $ a $ $ m $的$ b $的长度，每个零件$ a_k $的总和等于$ b $的相应零件等于，$ b $是$ a $的“总和”。然后，我们考虑以下两个问题：$ i）$“详尽的问题”，包括生成$ b $的所有分区的生成$ b $是$ a $ $ a $的sum组成，$ ii）$ $ $ $ b $ a $ a $ a $ a $ a $ sum a $ a $ a $ a $ a $ a $ a $的分区的存在。从总和组成的某些一般属性开始，我们提出了第一个算法解决详尽的问题，然后提出了第二种算法解决存在问题。我们还提供了正确性和实验分析的证明，以评估所提出的解决方案的质量以及与相关工作的比较。
In this paper, we study the "sum composition problem" between two lists $A$ and $B$ of positive integers. We start by saying that $B$ is "sum composition" of $A$ when there exists an ordered $m$-partition $[A_1,\ldots,A_m]$ of $A$ where $m$ is the length of $B$ and the sum of each part $A_k$ is equal to the corresponding part of $B$. Then, we consider the following two problems: $i)$ the "exhaustive problem", consisting in the generation of all partitions of $A$ for which $B$ is sum composition of $A$, and $ii)$ the "existential problem", consisting in the verification of the existence of a partition of $A$ for which $B$ is sum composition of $A$. Starting from some general properties of the sum compositions, we present a first algorithm solving the exhaustive problem and then a second algorithm solving the existential problem. We also provide proofs of correctness and experimental analysis for assessing the quality of the proposed solutions along with a comparison with related works.
