Efficient Data Structures for Storing the Partitions of Integers
نویسنده
چکیده
Algorithms for enumerating the partitions of a positive integer n have long been invented. However, data structure for storing the partitions is not received due attention. In this paper, several data structures, ranging from the most intuitive one to the most efficient one, are proposed. The space and time complexity for creating the most efficient data structure is O(n). The space complexity is low enough to make possible for storing all the partitions of an integer up to several ten thousands. This data structure can be used to enumerate the partitions of any integer smaller than or equal to n.
منابع مشابه
Fast Algorithm for Generating Ascending Compositions
In this paper we give a fast algorithm to generate all partitions of a positive integer n. Integer partitions may be encoded as either ascending or descending compositions for the purposes of systematic generation. It is known the fact that the ascending composition generation algorithm is substantially more efficient than its descending composition counterpart. Using tree structures for storin...
متن کاملk-Efficient partitions of graphs
A set $S = {u_1,u_2, ldots, u_t}$ of vertices of $G$ is an efficientdominating set if every vertex of $G$ is dominated exactly once by thevertices of $S$. Letting $U_i$ denote the set of vertices dominated by $u_i$%, we note that ${U_1, U_2, ldots U_t}$ is a partition of the vertex setof $G$ and that each $U_i$ contains the vertex $u_i$ and all the vertices atdistance~1 from it in $G$. In this ...
متن کاملBinary Diagrams for Storing Ascending Compositions
It is known that the integer partitions may be encoded as either ascending or descending compositions for the purposes of systematic generation. In this paper we give an efficient data structure for storing all ascending compositions of a positive integer. Using this structure, we improved the fastest known algorithm for generating integer partitions.
متن کاملPeriodic Temporal Notions as ‘Tree Partitionings’
The key notion for modelling calendar systems and many other periodic temporal notion is the mathematical concept of a partitioning of the real numbers. A partitioning of R splits the time axis into a sequence of intervals. Basic time units like seconds, minutes, hours, days, weeks, months, years etc. can all be represented as partitionings of R with finite partitions. Besides the basic time un...
متن کاملEmbedded Crack Identification in Beam-Column Structures Under Axial Load Using an Efficient Static Data Based Indicator
A triangular model base on an investigation which has done by Sinha et al. has been developed for evaluating embedded crack localization in beam-column structures. In the assessment of this member’s behavior, the effects of displacement slope are necessary. In order to propose a crack localization method for embedded crack, an efficient static data based indicator is proposed for this crack in ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005