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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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-----------------------------------------------------------------------------
Statistic identifier: St000835
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The minimal difference in size when partitioning the integer partition into two subpartitions.
This is the optimal value of the optimisation version of the partition problem [1].
-----------------------------------------------------------------------------
References: [1] [[wikipedia:Partition_problem]]
-----------------------------------------------------------------------------
Code:
def statistic(la):
size = sum(la)
mn = size
for s in Subsets(la, submultiset=True):
sum_s = sum(s)
if 2*sum_s >= size:
mn = min(2*sum_s-size, mn)
return mn
-----------------------------------------------------------------------------
Statistic values:
[] => 0
[1] => 1
[2] => 2
[1,1] => 0
[3] => 3
[2,1] => 1
[1,1,1] => 1
[4] => 4
[3,1] => 2
[2,2] => 0
[2,1,1] => 0
[1,1,1,1] => 0
[5] => 5
[4,1] => 3
[3,2] => 1
[3,1,1] => 1
[2,2,1] => 1
[2,1,1,1] => 1
[1,1,1,1,1] => 1
[6] => 6
[5,1] => 4
[4,2] => 2
[4,1,1] => 2
[3,3] => 0
[3,2,1] => 0
[3,1,1,1] => 0
[2,2,2] => 2
[2,2,1,1] => 0
[2,1,1,1,1] => 0
[1,1,1,1,1,1] => 0
[7] => 7
[6,1] => 5
[5,2] => 3
[5,1,1] => 3
[4,3] => 1
[4,2,1] => 1
[4,1,1,1] => 1
[3,3,1] => 1
[3,2,2] => 1
[3,2,1,1] => 1
[3,1,1,1,1] => 1
[2,2,2,1] => 1
[2,2,1,1,1] => 1
[2,1,1,1,1,1] => 1
[1,1,1,1,1,1,1] => 1
[8] => 8
[7,1] => 6
[6,2] => 4
[6,1,1] => 4
[5,3] => 2
[5,2,1] => 2
[5,1,1,1] => 2
[4,4] => 0
[4,3,1] => 0
[4,2,2] => 0
[4,2,1,1] => 0
[4,1,1,1,1] => 0
[3,3,2] => 2
[3,3,1,1] => 0
[3,2,2,1] => 0
[3,2,1,1,1] => 0
[3,1,1,1,1,1] => 0
[2,2,2,2] => 0
[2,2,2,1,1] => 0
[2,2,1,1,1,1] => 0
[2,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1] => 0
[9] => 9
[8,1] => 7
[7,2] => 5
[7,1,1] => 5
[6,3] => 3
[6,2,1] => 3
[6,1,1,1] => 3
[5,4] => 1
[5,3,1] => 1
[5,2,2] => 1
[5,2,1,1] => 1
[5,1,1,1,1] => 1
[4,4,1] => 1
[4,3,2] => 1
[4,3,1,1] => 1
[4,2,2,1] => 1
[4,2,1,1,1] => 1
[4,1,1,1,1,1] => 1
[3,3,3] => 3
[3,3,2,1] => 1
[3,3,1,1,1] => 1
[3,2,2,2] => 1
[3,2,2,1,1] => 1
[3,2,1,1,1,1] => 1
[3,1,1,1,1,1,1] => 1
[2,2,2,2,1] => 1
[2,2,2,1,1,1] => 1
[2,2,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1] => 1
[10] => 10
[9,1] => 8
[8,2] => 6
[8,1,1] => 6
[7,3] => 4
[7,2,1] => 4
[7,1,1,1] => 4
[6,4] => 2
[6,3,1] => 2
[6,2,2] => 2
[6,2,1,1] => 2
[6,1,1,1,1] => 2
[5,5] => 0
[5,4,1] => 0
[5,3,2] => 0
[5,3,1,1] => 0
[5,2,2,1] => 0
[5,2,1,1,1] => 0
[5,1,1,1,1,1] => 0
[4,4,2] => 2
[4,4,1,1] => 0
[4,3,3] => 2
[4,3,2,1] => 0
[4,3,1,1,1] => 0
[4,2,2,2] => 2
[4,2,2,1,1] => 0
[4,2,1,1,1,1] => 0
[4,1,1,1,1,1,1] => 0
[3,3,3,1] => 2
[3,3,2,2] => 0
[3,3,2,1,1] => 0
[3,3,1,1,1,1] => 0
[3,2,2,2,1] => 0
[3,2,2,1,1,1] => 0
[3,2,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1] => 0
[2,2,2,2,2] => 2
[2,2,2,2,1,1] => 0
[2,2,2,1,1,1,1] => 0
[2,2,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1] => 0
[11] => 11
[10,1] => 9
[9,2] => 7
[9,1,1] => 7
[8,3] => 5
[8,2,1] => 5
[8,1,1,1] => 5
[7,4] => 3
[7,3,1] => 3
[7,2,2] => 3
[7,2,1,1] => 3
[7,1,1,1,1] => 3
[6,5] => 1
[6,4,1] => 1
[6,3,2] => 1
[6,3,1,1] => 1
[6,2,2,1] => 1
[6,2,1,1,1] => 1
[6,1,1,1,1,1] => 1
[5,5,1] => 1
[5,4,2] => 1
[5,4,1,1] => 1
[5,3,3] => 1
[5,3,2,1] => 1
[5,3,1,1,1] => 1
[5,2,2,2] => 1
[5,2,2,1,1] => 1
[5,2,1,1,1,1] => 1
[5,1,1,1,1,1,1] => 1
[4,4,3] => 3
[4,4,2,1] => 1
[4,4,1,1,1] => 1
[4,3,3,1] => 1
[4,3,2,2] => 1
[4,3,2,1,1] => 1
[4,3,1,1,1,1] => 1
[4,2,2,2,1] => 1
[4,2,2,1,1,1] => 1
[4,2,1,1,1,1,1] => 1
[4,1,1,1,1,1,1,1] => 1
[3,3,3,2] => 1
[3,3,3,1,1] => 1
[3,3,2,2,1] => 1
[3,3,2,1,1,1] => 1
[3,3,1,1,1,1,1] => 1
[3,2,2,2,2] => 1
[3,2,2,2,1,1] => 1
[3,2,2,1,1,1,1] => 1
[3,2,1,1,1,1,1,1] => 1
[3,1,1,1,1,1,1,1,1] => 1
[2,2,2,2,2,1] => 1
[2,2,2,2,1,1,1] => 1
[2,2,2,1,1,1,1,1] => 1
[2,2,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,1] => 1
[12] => 12
[11,1] => 10
[10,2] => 8
[10,1,1] => 8
[9,3] => 6
[9,2,1] => 6
[9,1,1,1] => 6
[8,4] => 4
[8,3,1] => 4
[8,2,2] => 4
[8,2,1,1] => 4
[8,1,1,1,1] => 4
[7,5] => 2
[7,4,1] => 2
[7,3,2] => 2
[7,3,1,1] => 2
[7,2,2,1] => 2
[7,2,1,1,1] => 2
[7,1,1,1,1,1] => 2
[6,6] => 0
[6,5,1] => 0
[6,4,2] => 0
[6,4,1,1] => 0
[6,3,3] => 0
[6,3,2,1] => 0
[6,3,1,1,1] => 0
[6,2,2,2] => 0
[6,2,2,1,1] => 0
[6,2,1,1,1,1] => 0
[6,1,1,1,1,1,1] => 0
[5,5,2] => 2
[5,5,1,1] => 0
[5,4,3] => 2
[5,4,2,1] => 0
[5,4,1,1,1] => 0
[5,3,3,1] => 0
[5,3,2,2] => 2
[5,3,2,1,1] => 0
[5,3,1,1,1,1] => 0
[5,2,2,2,1] => 0
[5,2,2,1,1,1] => 0
[5,2,1,1,1,1,1] => 0
[5,1,1,1,1,1,1,1] => 0
[4,4,4] => 4
[4,4,3,1] => 2
[4,4,2,2] => 0
[4,4,2,1,1] => 0
[4,4,1,1,1,1] => 0
[4,3,3,2] => 0
[4,3,3,1,1] => 0
[4,3,2,2,1] => 0
[4,3,2,1,1,1] => 0
[4,3,1,1,1,1,1] => 0
[4,2,2,2,2] => 0
[4,2,2,2,1,1] => 0
[4,2,2,1,1,1,1] => 0
[4,2,1,1,1,1,1,1] => 0
[4,1,1,1,1,1,1,1,1] => 0
[3,3,3,3] => 0
[3,3,3,2,1] => 0
[3,3,3,1,1,1] => 0
[3,3,2,2,2] => 0
[3,3,2,2,1,1] => 0
[3,3,2,1,1,1,1] => 0
[3,3,1,1,1,1,1,1] => 0
[3,2,2,2,2,1] => 0
[3,2,2,2,1,1,1] => 0
[3,2,2,1,1,1,1,1] => 0
[3,2,1,1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1,1] => 0
[2,2,2,2,2,2] => 0
[2,2,2,2,2,1,1] => 0
[2,2,2,2,1,1,1,1] => 0
[2,2,2,1,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1] => 0
[5,4,3,1] => 1
[5,4,2,2] => 1
[5,4,2,1,1] => 1
[5,3,3,2] => 1
[5,3,3,1,1] => 1
[5,3,2,2,1] => 1
[4,4,3,2] => 1
[4,4,3,1,1] => 1
[4,4,2,2,1] => 1
[4,3,3,2,1] => 1
[5,4,3,2] => 0
[5,4,3,1,1] => 0
[5,4,2,2,1] => 0
[5,3,3,2,1] => 0
[4,4,3,2,1] => 0
[5,4,3,2,1] => 1
-----------------------------------------------------------------------------
Created: Jun 05, 2017 at 21:40 by Martin Rubey
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Last Updated: Oct 10, 2019 at 18:33 by Martin Rubey