Search results
Results from the WOW.Com Content Network
The partition problem - a special case of multiway number partitioning in which the number of subsets is 2. The 3-partition problem - a different and harder problem, in which the number of subsets is not considered a fixed parameter, but is determined by the input (the number of sets is the number of integers divided by 3).
Note that this partition is not optimal: in the partition {8,7}, {6,5,4} the sum-difference is 0. However, there is evidence that it provides a "good" partition: If the numbers are uniformly distributed in [0,1], then the expected difference between the two sums is ( ())).
In computer science, greedy number partitioning is a class of greedy algorithms for multiway number partitioning. The input to the algorithm is a set S of numbers, and a parameter k. The required output is a partition of S into k subsets, such that the sums in the subsets are as nearly equal as possible. Greedy algorithms process the numbers ...
Equal-cardinality partition is a variant in which both parts should have an equal number of items, in addition to having an equal sum. This variant is NP-hard too. [5]: SP12 Proof. Given a standard Partition instance with some n numbers, construct an Equal-Cardinality-Partition instance by adding n zeros. Clearly, the new instance has an equal ...
The following is a dynamic programming implementation (with Python 3) which uses a matrix to keep track of the optimal solutions to sub-problems, and returns the minimum number of coins, or "Infinity" if there is no way to make change with the coins given. A second matrix may be used to obtain the set of coins for the optimal solution.
Balanced number partitioning is a variant of multiway number partitioning in which there are constraints on the number of items allocated to each set. The input to the problem is a set of n items of different sizes, and two integers m, k. The output is a partition of the items into m subsets, such that the number of items in each subset is at ...
Recursive partitioning is a statistical method for multivariable analysis. [1] Recursive partitioning creates a decision tree that strives to correctly classify members of the population by splitting it into sub-populations based on several dichotomous independent variables .
SmartXML, a free programming language with integrated development environment (IDE) for mathematical calculations. Variables of BigNumber type can be used, or regular numbers can be converted to big numbers using conversion operator # (e.g., #2.3^2000.1). SmartXML big numbers can have up to 100,000,000 decimal digits and up to 100,000,000 whole ...