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SELECT * FROM (SELECT ROW_NUMBER OVER (ORDER BY sort_key ASC) AS row_number, columns FROM tablename) AS foo WHERE row_number <= 10 ROW_NUMBER can be non-deterministic : if sort_key is not unique, each time you run the query it is possible to get different row numbers assigned to any rows where sort_key is the same.
Such a partition is called a partition with distinct parts. If we count the partitions of 8 with distinct parts, we also obtain 6: 8; 7 + 1; 6 + 2; 5 + 3; 5 + 2 + 1; 4 + 3 + 1; This is a general property. For each positive number, the number of partitions with odd parts equals the number of partitions with distinct parts, denoted by q(n).
These two types of partition are in bijection with each other, by a diagonal reflection of their Young diagrams. Their numbers can be arranged into a triangle, the triangle of partition numbers , in which the n {\displaystyle n} th row gives the partition numbers p 1 ( n ) , p 2 ( n ) , … , p n ( n ) {\displaystyle p_{1}(n),p_{2}(n),\dots ,p ...
For example, all rows where the column Country is either Iceland, Norway, Sweden, Finland or Denmark could build a partition for the Nordic countries. Composite partitioning : allows for certain combinations of the above partitioning schemes, by for example first applying a range partitioning and then a hash partitioning.
[6] [7] The partition lattice of a 4-element set has 15 elements and is depicted in the Hasse diagram on the left. The meet and join of partitions α and ρ are defined as follows. The meet is the partition whose blocks are the intersections of a block of α and a block of ρ, except for
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).
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 ...
Greedy number partitioning – loops over the numbers, and puts each number in the set whose current sum is smallest. If the numbers are not sorted, then the runtime is O( n ) and the approximation ratio is at most 3/2 ("approximation ratio" means the larger sum in the algorithm output, divided by the larger sum in an optimal partition).