partitionsGeneral.RdThe algorithms in RcppAlgos go beyond the traditional integer partition algorithms and can tackle a wide variety of cases.
Efficient algorithms for partitioning numbers under various constraints:
Standard (with repetition)
Distinct
Restricted
Where each part has a specific multiplicity (i.e. when using freqs for multisets).
Arbitrary target and source vector (e.g. partitionsGeneral(sample(1000, 20), 10, TRUE, target = 5000))
Produce results in parallel using the nThreads arguments.
Alternatively, the arguments lower and upper make it possible to generate partitions/compositions in chunks allowing for parallelization via the parallel package.
GMP support allows for exploration of cases where the number of partitions/compositions is large.
The output is in lexicographical order.
partitionsGeneral(v, m = NULL, ...)
compositionsGeneral(v, m = NULL, ...)
# S3 method for default
partitionsGeneral(
v, m = NULL, repetition = FALSE, freqs = NULL, target = NULL,
lower = NULL, upper = NULL, nThreads = NULL, tolerance = NULL, ...
)
# S3 method for default
compositionsGeneral(
v, m = NULL, repetition = FALSE, freqs = NULL, target = NULL, weak = FALSE,
lower = NULL, upper = NULL, nThreads = NULL, tolerance = NULL, ...
)
# S3 method for table
partitionsGeneral(
v, m = NULL, target = NULL, lower = NULL,
upper = NULL, nThreads = NULL, tolerance = NULL, ...
)
# S3 method for table
compositionsGeneral(
v, m = NULL, target = NULL, weak = FALSE, lower = NULL,
upper = NULL, nThreads = NULL, tolerance = NULL, ...
)Source vector. If v is a positive integer, it will be converted to the sequence 1:v. If v is a negative integer, it will be converted to the sequence v:-1. Only integer and numeric vectors are accepted.
Width of the partition. If m = NULL, the length will be determined by the partitioning case (e.g. When we are generating distinct partitions of \(n\), the width will be equal to the smallest \(m\) such that sum(1:m) >= n).
Further arguments passed to methods.
Logical value indicating whether partitions/compositions should be with or without repetition. The default is FALSE.
A vector of frequencies used for producing all partitions of a multiset of v. Each element of freqs represents how many times each element of the source vector, v, is repeated. It is analogous to the times argument in rep. The default value is NULL.
The lower bound. Partitions/compositions are generated lexicographically, thus utilizing this argument will determine which specific partition to start generating from (e.g. partitionsGeneral(15, 3, lower = 6) is equivalent to partitionsGeneral(15, 3)[6:partitionsCount(15, 3), ]). This argument along with upper is very useful for generating partitions/compositions in chunks allowing for easy parallelization.
The upper bound. Similar to lower, however this parameter allows the user to stop generation at a specific partition (e.g. partitionsGeneral(15, 3, upper = 5) is equivalent to partitionsGeneral(15, 3)[1:5, ])
Number to be partitioned. If NULL, max(v) will be used.
(Compositions only) Logical flag indicating whether to allow terms of the sequence to be zero.
Specific number of threads to be used. The default is NULL.
A numeric value greater than or equal to zero. This parameter is utilized when a constraint is applied on a numeric vector. The default value is 0 when it can be determined that whole values are being utilized, otherwise it is sqrt(.Machine$double.eps) which is approximately \(1.5e-8\). N.B. If the input vector is of type integer, this parameter will be ignored and strict equality will be enforced.
A matrix is returned with each row containing a vector of length \(m\).
nThreads will be ignored in the following cases (i.e. Generating the \(n^{th}\) partition in these cases are currently unavailable):
With standard multisets. If zero is the only element with a non-trivial multiplicity, multithreading is possible (e.g. partitionsGeneral(0:100, freqs = c(100, rep(1, 100)), nThreads = 4)).
If the source vector is not isomorphic to 1:length(v) (e.g. v = c(1, 4, 6, 7, 8)).
The maximum number of partitions/compositions that can be generated at one time is \(2^{31} - 1\). Utilizing lower and upper makes it possible to generate additional partitions/compositions.
partitionsGeneral(1)
#> [,1]
#> [1,] 1
partitionsGeneral(-1:0, 1)
#> [,1]
#> [1,] 0
partitionsGeneral(-1:0, 1, target = -1)
#> [,1]
#> [1,] -1
partitionsGeneral(20, 5)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 1 2 3 4 10
#> [2,] 1 2 3 5 9
#> [3,] 1 2 3 6 8
#> [4,] 1 2 4 5 8
#> [5,] 1 2 4 6 7
#> [6,] 1 3 4 5 7
#> [7,] 2 3 4 5 6
partitionsGeneral(20, 5, repetition = TRUE)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 1 1 1 1 16
#> [2,] 1 1 1 2 15
#> [3,] 1 1 1 3 14
#> [4,] 1 1 1 4 13
#> [5,] 1 1 1 5 12
#> [6,] 1 1 1 6 11
#> [7,] 1 1 1 7 10
#> [8,] 1 1 1 8 9
#> [9,] 1 1 2 2 14
#> [10,] 1 1 2 3 13
#> [11,] 1 1 2 4 12
#> [12,] 1 1 2 5 11
#> [13,] 1 1 2 6 10
#> [14,] 1 1 2 7 9
#> [15,] 1 1 2 8 8
#> [16,] 1 1 3 3 12
#> [17,] 1 1 3 4 11
#> [18,] 1 1 3 5 10
#> [19,] 1 1 3 6 9
#> [20,] 1 1 3 7 8
#> [21,] 1 1 4 4 10
#> [22,] 1 1 4 5 9
#> [23,] 1 1 4 6 8
#> [24,] 1 1 4 7 7
#> [25,] 1 1 5 5 8
#> [26,] 1 1 5 6 7
#> [27,] 1 1 6 6 6
#> [28,] 1 2 2 2 13
#> [29,] 1 2 2 3 12
#> [30,] 1 2 2 4 11
#> [31,] 1 2 2 5 10
#> [32,] 1 2 2 6 9
#> [33,] 1 2 2 7 8
#> [34,] 1 2 3 3 11
#> [35,] 1 2 3 4 10
#> [36,] 1 2 3 5 9
#> [37,] 1 2 3 6 8
#> [38,] 1 2 3 7 7
#> [39,] 1 2 4 4 9
#> [40,] 1 2 4 5 8
#> [41,] 1 2 4 6 7
#> [42,] 1 2 5 5 7
#> [43,] 1 2 5 6 6
#> [44,] 1 3 3 3 10
#> [45,] 1 3 3 4 9
#> [46,] 1 3 3 5 8
#> [47,] 1 3 3 6 7
#> [48,] 1 3 4 4 8
#> [49,] 1 3 4 5 7
#> [50,] 1 3 4 6 6
#> [51,] 1 3 5 5 6
#> [52,] 1 4 4 4 7
#> [53,] 1 4 4 5 6
#> [54,] 1 4 5 5 5
#> [55,] 2 2 2 2 12
#> [56,] 2 2 2 3 11
#> [57,] 2 2 2 4 10
#> [58,] 2 2 2 5 9
#> [59,] 2 2 2 6 8
#> [60,] 2 2 2 7 7
#> [61,] 2 2 3 3 10
#> [62,] 2 2 3 4 9
#> [63,] 2 2 3 5 8
#> [64,] 2 2 3 6 7
#> [65,] 2 2 4 4 8
#> [66,] 2 2 4 5 7
#> [67,] 2 2 4 6 6
#> [68,] 2 2 5 5 6
#> [69,] 2 3 3 3 9
#> [70,] 2 3 3 4 8
#> [71,] 2 3 3 5 7
#> [72,] 2 3 3 6 6
#> [73,] 2 3 4 4 7
#> [74,] 2 3 4 5 6
#> [75,] 2 3 5 5 5
#> [76,] 2 4 4 4 6
#> [77,] 2 4 4 5 5
#> [78,] 3 3 3 3 8
#> [79,] 3 3 3 4 7
#> [80,] 3 3 3 5 6
#> [81,] 3 3 4 4 6
#> [82,] 3 3 4 5 5
#> [83,] 3 4 4 4 5
#> [84,] 4 4 4 4 4
partitionsGeneral(20, 5, freqs = rep(1:4, 5))
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 1 2 2 3 12
#> [2,] 1 2 2 4 11
#> [3,] 1 2 2 5 10
#> [4,] 1 2 2 6 9
#> [5,] 1 2 2 7 8
#> [6,] 1 2 3 3 11
#> [7,] 1 2 3 4 10
#> [8,] 1 2 3 5 9
#> [9,] 1 2 3 6 8
#> [10,] 1 2 3 7 7
#> [11,] 1 2 4 4 9
#> [12,] 1 2 4 5 8
#> [13,] 1 2 4 6 7
#> [14,] 1 2 5 6 6
#> [15,] 1 3 3 3 10
#> [16,] 1 3 3 4 9
#> [17,] 1 3 3 5 8
#> [18,] 1 3 3 6 7
#> [19,] 1 3 4 4 8
#> [20,] 1 3 4 5 7
#> [21,] 1 3 4 6 6
#> [22,] 1 4 4 4 7
#> [23,] 1 4 4 5 6
#> [24,] 2 2 3 3 10
#> [25,] 2 2 3 4 9
#> [26,] 2 2 3 5 8
#> [27,] 2 2 3 6 7
#> [28,] 2 2 4 4 8
#> [29,] 2 2 4 5 7
#> [30,] 2 2 4 6 6
#> [31,] 2 3 3 3 9
#> [32,] 2 3 3 4 8
#> [33,] 2 3 3 5 7
#> [34,] 2 3 3 6 6
#> [35,] 2 3 4 4 7
#> [36,] 2 3 4 5 6
#> [37,] 2 4 4 4 6
#> [38,] 3 3 3 4 7
#> [39,] 3 3 3 5 6
#> [40,] 3 3 4 4 6
#> [41,] 3 4 4 4 5
partitionsGeneral(20, 5, TRUE, target = 80)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 1 19 20 20 20
#> [2,] 2 18 20 20 20
#> [3,] 2 19 19 20 20
#> [4,] 3 17 20 20 20
#> [5,] 3 18 19 20 20
#> [6,] 3 19 19 19 20
#> [7,] 4 16 20 20 20
#> [8,] 4 17 19 20 20
#> [9,] 4 18 18 20 20
#> [10,] 4 18 19 19 20
#> [11,] 4 19 19 19 19
#> [12,] 5 15 20 20 20
#> [13,] 5 16 19 20 20
#> [14,] 5 17 18 20 20
#> [15,] 5 17 19 19 20
#> [16,] 5 18 18 19 20
#> [17,] 5 18 19 19 19
#> [18,] 6 14 20 20 20
#> [19,] 6 15 19 20 20
#> [20,] 6 16 18 20 20
#> [21,] 6 16 19 19 20
#> [22,] 6 17 17 20 20
#> [23,] 6 17 18 19 20
#> [24,] 6 17 19 19 19
#> [25,] 6 18 18 18 20
#> [26,] 6 18 18 19 19
#> [27,] 7 13 20 20 20
#> [28,] 7 14 19 20 20
#> [29,] 7 15 18 20 20
#> [30,] 7 15 19 19 20
#> [31,] 7 16 17 20 20
#> [32,] 7 16 18 19 20
#> [33,] 7 16 19 19 19
#> [34,] 7 17 17 19 20
#> [35,] 7 17 18 18 20
#> [36,] 7 17 18 19 19
#> [37,] 7 18 18 18 19
#> [38,] 8 12 20 20 20
#> [39,] 8 13 19 20 20
#> [40,] 8 14 18 20 20
#> [41,] 8 14 19 19 20
#> [42,] 8 15 17 20 20
#> [43,] 8 15 18 19 20
#> [44,] 8 15 19 19 19
#> [45,] 8 16 16 20 20
#> [46,] 8 16 17 19 20
#> [47,] 8 16 18 18 20
#> [48,] 8 16 18 19 19
#> [49,] 8 17 17 18 20
#> [50,] 8 17 17 19 19
#> [51,] 8 17 18 18 19
#> [52,] 8 18 18 18 18
#> [53,] 9 11 20 20 20
#> [54,] 9 12 19 20 20
#> [55,] 9 13 18 20 20
#> [56,] 9 13 19 19 20
#> [57,] 9 14 17 20 20
#> [58,] 9 14 18 19 20
#> [59,] 9 14 19 19 19
#> [60,] 9 15 16 20 20
#> [61,] 9 15 17 19 20
#> [62,] 9 15 18 18 20
#> [63,] 9 15 18 19 19
#> [64,] 9 16 16 19 20
#> [65,] 9 16 17 18 20
#> [66,] 9 16 17 19 19
#> [67,] 9 16 18 18 19
#> [68,] 9 17 17 17 20
#> [69,] 9 17 17 18 19
#> [70,] 9 17 18 18 18
#> [71,] 10 10 20 20 20
#> [72,] 10 11 19 20 20
#> [73,] 10 12 18 20 20
#> [74,] 10 12 19 19 20
#> [75,] 10 13 17 20 20
#> [76,] 10 13 18 19 20
#> [77,] 10 13 19 19 19
#> [78,] 10 14 16 20 20
#> [79,] 10 14 17 19 20
#> [80,] 10 14 18 18 20
#> [81,] 10 14 18 19 19
#> [82,] 10 15 15 20 20
#> [83,] 10 15 16 19 20
#> [84,] 10 15 17 18 20
#> [85,] 10 15 17 19 19
#> [86,] 10 15 18 18 19
#> [87,] 10 16 16 18 20
#> [88,] 10 16 16 19 19
#> [89,] 10 16 17 17 20
#> [90,] 10 16 17 18 19
#> [91,] 10 16 18 18 18
#> [92,] 10 17 17 17 19
#> [93,] 10 17 17 18 18
#> [94,] 11 11 18 20 20
#> [95,] 11 11 19 19 20
#> [96,] 11 12 17 20 20
#> [97,] 11 12 18 19 20
#> [98,] 11 12 19 19 19
#> [99,] 11 13 16 20 20
#> [100,] 11 13 17 19 20
#> [101,] 11 13 18 18 20
#> [102,] 11 13 18 19 19
#> [103,] 11 14 15 20 20
#> [104,] 11 14 16 19 20
#> [105,] 11 14 17 18 20
#> [106,] 11 14 17 19 19
#> [107,] 11 14 18 18 19
#> [108,] 11 15 15 19 20
#> [109,] 11 15 16 18 20
#> [110,] 11 15 16 19 19
#> [111,] 11 15 17 17 20
#> [112,] 11 15 17 18 19
#> [113,] 11 15 18 18 18
#> [114,] 11 16 16 17 20
#> [115,] 11 16 16 18 19
#> [116,] 11 16 17 17 19
#> [117,] 11 16 17 18 18
#> [118,] 11 17 17 17 18
#> [119,] 12 12 16 20 20
#> [120,] 12 12 17 19 20
#> [121,] 12 12 18 18 20
#> [122,] 12 12 18 19 19
#> [123,] 12 13 15 20 20
#> [124,] 12 13 16 19 20
#> [125,] 12 13 17 18 20
#> [126,] 12 13 17 19 19
#> [127,] 12 13 18 18 19
#> [128,] 12 14 14 20 20
#> [129,] 12 14 15 19 20
#> [130,] 12 14 16 18 20
#> [131,] 12 14 16 19 19
#> [132,] 12 14 17 17 20
#> [133,] 12 14 17 18 19
#> [134,] 12 14 18 18 18
#> [135,] 12 15 15 18 20
#> [136,] 12 15 15 19 19
#> [137,] 12 15 16 17 20
#> [138,] 12 15 16 18 19
#> [139,] 12 15 17 17 19
#> [140,] 12 15 17 18 18
#> [141,] 12 16 16 16 20
#> [142,] 12 16 16 17 19
#> [143,] 12 16 16 18 18
#> [144,] 12 16 17 17 18
#> [145,] 12 17 17 17 17
#> [146,] 13 13 14 20 20
#> [147,] 13 13 15 19 20
#> [148,] 13 13 16 18 20
#> [149,] 13 13 16 19 19
#> [150,] 13 13 17 17 20
#> [151,] 13 13 17 18 19
#> [152,] 13 13 18 18 18
#> [153,] 13 14 14 19 20
#> [154,] 13 14 15 18 20
#> [155,] 13 14 15 19 19
#> [156,] 13 14 16 17 20
#> [157,] 13 14 16 18 19
#> [158,] 13 14 17 17 19
#> [159,] 13 14 17 18 18
#> [160,] 13 15 15 17 20
#> [161,] 13 15 15 18 19
#> [162,] 13 15 16 16 20
#> [163,] 13 15 16 17 19
#> [164,] 13 15 16 18 18
#> [165,] 13 15 17 17 18
#> [166,] 13 16 16 16 19
#> [167,] 13 16 16 17 18
#> [168,] 13 16 17 17 17
#> [169,] 14 14 14 18 20
#> [170,] 14 14 14 19 19
#> [171,] 14 14 15 17 20
#> [172,] 14 14 15 18 19
#> [173,] 14 14 16 16 20
#> [174,] 14 14 16 17 19
#> [175,] 14 14 16 18 18
#> [176,] 14 14 17 17 18
#> [177,] 14 15 15 16 20
#> [178,] 14 15 15 17 19
#> [179,] 14 15 15 18 18
#> [180,] 14 15 16 16 19
#> [181,] 14 15 16 17 18
#> [182,] 14 15 17 17 17
#> [183,] 14 16 16 16 18
#> [184,] 14 16 16 17 17
#> [185,] 15 15 15 15 20
#> [186,] 15 15 15 16 19
#> [187,] 15 15 15 17 18
#> [188,] 15 15 16 16 18
#> [189,] 15 15 16 17 17
#> [190,] 15 16 16 16 17
#> [191,] 16 16 16 16 16
partitionsGeneral(0:10, repetition = TRUE)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
#> [1,] 0 0 0 0 0 0 0 0 0 10
#> [2,] 0 0 0 0 0 0 0 0 1 9
#> [3,] 0 0 0 0 0 0 0 0 2 8
#> [4,] 0 0 0 0 0 0 0 0 3 7
#> [5,] 0 0 0 0 0 0 0 0 4 6
#> [6,] 0 0 0 0 0 0 0 0 5 5
#> [7,] 0 0 0 0 0 0 0 1 1 8
#> [8,] 0 0 0 0 0 0 0 1 2 7
#> [9,] 0 0 0 0 0 0 0 1 3 6
#> [10,] 0 0 0 0 0 0 0 1 4 5
#> [11,] 0 0 0 0 0 0 0 2 2 6
#> [12,] 0 0 0 0 0 0 0 2 3 5
#> [13,] 0 0 0 0 0 0 0 2 4 4
#> [14,] 0 0 0 0 0 0 0 3 3 4
#> [15,] 0 0 0 0 0 0 1 1 1 7
#> [16,] 0 0 0 0 0 0 1 1 2 6
#> [17,] 0 0 0 0 0 0 1 1 3 5
#> [18,] 0 0 0 0 0 0 1 1 4 4
#> [19,] 0 0 0 0 0 0 1 2 2 5
#> [20,] 0 0 0 0 0 0 1 2 3 4
#> [21,] 0 0 0 0 0 0 1 3 3 3
#> [22,] 0 0 0 0 0 0 2 2 2 4
#> [23,] 0 0 0 0 0 0 2 2 3 3
#> [24,] 0 0 0 0 0 1 1 1 1 6
#> [25,] 0 0 0 0 0 1 1 1 2 5
#> [26,] 0 0 0 0 0 1 1 1 3 4
#> [27,] 0 0 0 0 0 1 1 2 2 4
#> [28,] 0 0 0 0 0 1 1 2 3 3
#> [29,] 0 0 0 0 0 1 2 2 2 3
#> [30,] 0 0 0 0 0 2 2 2 2 2
#> [31,] 0 0 0 0 1 1 1 1 1 5
#> [32,] 0 0 0 0 1 1 1 1 2 4
#> [33,] 0 0 0 0 1 1 1 1 3 3
#> [34,] 0 0 0 0 1 1 1 2 2 3
#> [35,] 0 0 0 0 1 1 2 2 2 2
#> [36,] 0 0 0 1 1 1 1 1 1 4
#> [37,] 0 0 0 1 1 1 1 1 2 3
#> [38,] 0 0 0 1 1 1 1 2 2 2
#> [39,] 0 0 1 1 1 1 1 1 1 3
#> [40,] 0 0 1 1 1 1 1 1 2 2
#> [41,] 0 1 1 1 1 1 1 1 1 2
#> [42,] 1 1 1 1 1 1 1 1 1 1
partitionsGeneral(seq(2L, 500L, 23L), 5, target = 1804)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 2 416 439 462 485
#> [2,] 25 393 439 462 485
#> [3,] 48 370 439 462 485
#> [4,] 48 393 416 462 485
#> [5,] 71 347 439 462 485
#> [6,] 71 370 416 462 485
#> [7,] 71 393 416 439 485
#> [8,] 94 324 439 462 485
#> [9,] 94 347 416 462 485
#> [10,] 94 370 393 462 485
#> [11,] 94 370 416 439 485
#> [12,] 94 393 416 439 462
#> [13,] 117 301 439 462 485
#> [14,] 117 324 416 462 485
#> [15,] 117 347 393 462 485
#> [16,] 117 347 416 439 485
#> [17,] 117 370 393 439 485
#> [18,] 117 370 416 439 462
#> [19,] 140 278 439 462 485
#> [20,] 140 301 416 462 485
#> [21,] 140 324 393 462 485
#> [22,] 140 324 416 439 485
#> [23,] 140 347 370 462 485
#> [24,] 140 347 393 439 485
#> [25,] 140 347 416 439 462
#> [26,] 140 370 393 416 485
#> [27,] 140 370 393 439 462
#> [28,] 163 255 439 462 485
#> [29,] 163 278 416 462 485
#> [30,] 163 301 393 462 485
#> [31,] 163 301 416 439 485
#> [32,] 163 324 370 462 485
#> [33,] 163 324 393 439 485
#> [34,] 163 324 416 439 462
#> [35,] 163 347 370 439 485
#> [36,] 163 347 393 416 485
#> [37,] 163 347 393 439 462
#> [38,] 163 370 393 416 462
#> [39,] 186 232 439 462 485
#> [40,] 186 255 416 462 485
#> [41,] 186 278 393 462 485
#> [42,] 186 278 416 439 485
#> [43,] 186 301 370 462 485
#> [44,] 186 301 393 439 485
#> [45,] 186 301 416 439 462
#> [46,] 186 324 347 462 485
#> [47,] 186 324 370 439 485
#> [48,] 186 324 393 416 485
#> [49,] 186 324 393 439 462
#> [50,] 186 347 370 416 485
#> [51,] 186 347 370 439 462
#> [52,] 186 347 393 416 462
#> [53,] 186 370 393 416 439
#> [54,] 209 232 416 462 485
#> [55,] 209 255 393 462 485
#> [56,] 209 255 416 439 485
#> [57,] 209 278 370 462 485
#> [58,] 209 278 393 439 485
#> [59,] 209 278 416 439 462
#> [60,] 209 301 347 462 485
#> [61,] 209 301 370 439 485
#> [62,] 209 301 393 416 485
#> [63,] 209 301 393 439 462
#> [64,] 209 324 347 439 485
#> [65,] 209 324 370 416 485
#> [66,] 209 324 370 439 462
#> [67,] 209 324 393 416 462
#> [68,] 209 347 370 393 485
#> [69,] 209 347 370 416 462
#> [70,] 209 347 393 416 439
#> [71,] 232 255 370 462 485
#> [72,] 232 255 393 439 485
#> [73,] 232 255 416 439 462
#> [74,] 232 278 347 462 485
#> [75,] 232 278 370 439 485
#> [76,] 232 278 393 416 485
#> [77,] 232 278 393 439 462
#> [78,] 232 301 324 462 485
#> [79,] 232 301 347 439 485
#> [80,] 232 301 370 416 485
#> [81,] 232 301 370 439 462
#> [82,] 232 301 393 416 462
#> [83,] 232 324 347 416 485
#> [84,] 232 324 347 439 462
#> [85,] 232 324 370 393 485
#> [86,] 232 324 370 416 462
#> [87,] 232 324 393 416 439
#> [88,] 232 347 370 393 462
#> [89,] 232 347 370 416 439
#> [90,] 255 278 324 462 485
#> [91,] 255 278 347 439 485
#> [92,] 255 278 370 416 485
#> [93,] 255 278 370 439 462
#> [94,] 255 278 393 416 462
#> [95,] 255 301 324 439 485
#> [96,] 255 301 347 416 485
#> [97,] 255 301 347 439 462
#> [98,] 255 301 370 393 485
#> [99,] 255 301 370 416 462
#> [100,] 255 301 393 416 439
#> [101,] 255 324 347 393 485
#> [102,] 255 324 347 416 462
#> [103,] 255 324 370 393 462
#> [104,] 255 324 370 416 439
#> [105,] 255 347 370 393 439
#> [106,] 278 301 324 416 485
#> [107,] 278 301 324 439 462
#> [108,] 278 301 347 393 485
#> [109,] 278 301 347 416 462
#> [110,] 278 301 370 393 462
#> [111,] 278 301 370 416 439
#> [112,] 278 324 347 370 485
#> [113,] 278 324 347 393 462
#> [114,] 278 324 347 416 439
#> [115,] 278 324 370 393 439
#> [116,] 278 347 370 393 416
#> [117,] 301 324 347 370 462
#> [118,] 301 324 347 393 439
#> [119,] 301 324 370 393 416
compositionsGeneral(0:10, 5, repetition = TRUE)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0 0 0 0 10
#> [2,] 0 0 0 1 9
#> [3,] 0 0 0 2 8
#> [4,] 0 0 0 3 7
#> [5,] 0 0 0 4 6
#> [6,] 0 0 0 5 5
#> [7,] 0 0 0 6 4
#> [8,] 0 0 0 7 3
#> [9,] 0 0 0 8 2
#> [10,] 0 0 0 9 1
#> [11,] 0 0 1 1 8
#> [12,] 0 0 1 2 7
#> [13,] 0 0 1 3 6
#> [14,] 0 0 1 4 5
#> [15,] 0 0 1 5 4
#> [16,] 0 0 1 6 3
#> [17,] 0 0 1 7 2
#> [18,] 0 0 1 8 1
#> [19,] 0 0 2 1 7
#> [20,] 0 0 2 2 6
#> [21,] 0 0 2 3 5
#> [22,] 0 0 2 4 4
#> [23,] 0 0 2 5 3
#> [24,] 0 0 2 6 2
#> [25,] 0 0 2 7 1
#> [26,] 0 0 3 1 6
#> [27,] 0 0 3 2 5
#> [28,] 0 0 3 3 4
#> [29,] 0 0 3 4 3
#> [30,] 0 0 3 5 2
#> [31,] 0 0 3 6 1
#> [32,] 0 0 4 1 5
#> [33,] 0 0 4 2 4
#> [34,] 0 0 4 3 3
#> [35,] 0 0 4 4 2
#> [36,] 0 0 4 5 1
#> [37,] 0 0 5 1 4
#> [38,] 0 0 5 2 3
#> [39,] 0 0 5 3 2
#> [40,] 0 0 5 4 1
#> [41,] 0 0 6 1 3
#> [42,] 0 0 6 2 2
#> [43,] 0 0 6 3 1
#> [44,] 0 0 7 1 2
#> [45,] 0 0 7 2 1
#> [46,] 0 0 8 1 1
#> [47,] 0 1 1 1 7
#> [48,] 0 1 1 2 6
#> [49,] 0 1 1 3 5
#> [50,] 0 1 1 4 4
#> [51,] 0 1 1 5 3
#> [52,] 0 1 1 6 2
#> [53,] 0 1 1 7 1
#> [54,] 0 1 2 1 6
#> [55,] 0 1 2 2 5
#> [56,] 0 1 2 3 4
#> [57,] 0 1 2 4 3
#> [58,] 0 1 2 5 2
#> [59,] 0 1 2 6 1
#> [60,] 0 1 3 1 5
#> [61,] 0 1 3 2 4
#> [62,] 0 1 3 3 3
#> [63,] 0 1 3 4 2
#> [64,] 0 1 3 5 1
#> [65,] 0 1 4 1 4
#> [66,] 0 1 4 2 3
#> [67,] 0 1 4 3 2
#> [68,] 0 1 4 4 1
#> [69,] 0 1 5 1 3
#> [70,] 0 1 5 2 2
#> [71,] 0 1 5 3 1
#> [72,] 0 1 6 1 2
#> [73,] 0 1 6 2 1
#> [74,] 0 1 7 1 1
#> [75,] 0 2 1 1 6
#> [76,] 0 2 1 2 5
#> [77,] 0 2 1 3 4
#> [78,] 0 2 1 4 3
#> [79,] 0 2 1 5 2
#> [80,] 0 2 1 6 1
#> [81,] 0 2 2 1 5
#> [82,] 0 2 2 2 4
#> [83,] 0 2 2 3 3
#> [84,] 0 2 2 4 2
#> [85,] 0 2 2 5 1
#> [86,] 0 2 3 1 4
#> [87,] 0 2 3 2 3
#> [88,] 0 2 3 3 2
#> [89,] 0 2 3 4 1
#> [90,] 0 2 4 1 3
#> [91,] 0 2 4 2 2
#> [92,] 0 2 4 3 1
#> [93,] 0 2 5 1 2
#> [94,] 0 2 5 2 1
#> [95,] 0 2 6 1 1
#> [96,] 0 3 1 1 5
#> [97,] 0 3 1 2 4
#> [98,] 0 3 1 3 3
#> [99,] 0 3 1 4 2
#> [100,] 0 3 1 5 1
#> [101,] 0 3 2 1 4
#> [102,] 0 3 2 2 3
#> [103,] 0 3 2 3 2
#> [104,] 0 3 2 4 1
#> [105,] 0 3 3 1 3
#> [106,] 0 3 3 2 2
#> [107,] 0 3 3 3 1
#> [108,] 0 3 4 1 2
#> [109,] 0 3 4 2 1
#> [110,] 0 3 5 1 1
#> [111,] 0 4 1 1 4
#> [112,] 0 4 1 2 3
#> [113,] 0 4 1 3 2
#> [114,] 0 4 1 4 1
#> [115,] 0 4 2 1 3
#> [116,] 0 4 2 2 2
#> [117,] 0 4 2 3 1
#> [118,] 0 4 3 1 2
#> [119,] 0 4 3 2 1
#> [120,] 0 4 4 1 1
#> [121,] 0 5 1 1 3
#> [122,] 0 5 1 2 2
#> [123,] 0 5 1 3 1
#> [124,] 0 5 2 1 2
#> [125,] 0 5 2 2 1
#> [126,] 0 5 3 1 1
#> [127,] 0 6 1 1 2
#> [128,] 0 6 1 2 1
#> [129,] 0 6 2 1 1
#> [130,] 0 7 1 1 1
#> [131,] 1 1 1 1 6
#> [132,] 1 1 1 2 5
#> [133,] 1 1 1 3 4
#> [134,] 1 1 1 4 3
#> [135,] 1 1 1 5 2
#> [136,] 1 1 1 6 1
#> [137,] 1 1 2 1 5
#> [138,] 1 1 2 2 4
#> [139,] 1 1 2 3 3
#> [140,] 1 1 2 4 2
#> [141,] 1 1 2 5 1
#> [142,] 1 1 3 1 4
#> [143,] 1 1 3 2 3
#> [144,] 1 1 3 3 2
#> [145,] 1 1 3 4 1
#> [146,] 1 1 4 1 3
#> [147,] 1 1 4 2 2
#> [148,] 1 1 4 3 1
#> [149,] 1 1 5 1 2
#> [150,] 1 1 5 2 1
#> [151,] 1 1 6 1 1
#> [152,] 1 2 1 1 5
#> [153,] 1 2 1 2 4
#> [154,] 1 2 1 3 3
#> [155,] 1 2 1 4 2
#> [156,] 1 2 1 5 1
#> [157,] 1 2 2 1 4
#> [158,] 1 2 2 2 3
#> [159,] 1 2 2 3 2
#> [160,] 1 2 2 4 1
#> [161,] 1 2 3 1 3
#> [162,] 1 2 3 2 2
#> [163,] 1 2 3 3 1
#> [164,] 1 2 4 1 2
#> [165,] 1 2 4 2 1
#> [166,] 1 2 5 1 1
#> [167,] 1 3 1 1 4
#> [168,] 1 3 1 2 3
#> [169,] 1 3 1 3 2
#> [170,] 1 3 1 4 1
#> [171,] 1 3 2 1 3
#> [172,] 1 3 2 2 2
#> [173,] 1 3 2 3 1
#> [174,] 1 3 3 1 2
#> [175,] 1 3 3 2 1
#> [176,] 1 3 4 1 1
#> [177,] 1 4 1 1 3
#> [178,] 1 4 1 2 2
#> [179,] 1 4 1 3 1
#> [180,] 1 4 2 1 2
#> [181,] 1 4 2 2 1
#> [182,] 1 4 3 1 1
#> [183,] 1 5 1 1 2
#> [184,] 1 5 1 2 1
#> [185,] 1 5 2 1 1
#> [186,] 1 6 1 1 1
#> [187,] 2 1 1 1 5
#> [188,] 2 1 1 2 4
#> [189,] 2 1 1 3 3
#> [190,] 2 1 1 4 2
#> [191,] 2 1 1 5 1
#> [192,] 2 1 2 1 4
#> [193,] 2 1 2 2 3
#> [194,] 2 1 2 3 2
#> [195,] 2 1 2 4 1
#> [196,] 2 1 3 1 3
#> [197,] 2 1 3 2 2
#> [198,] 2 1 3 3 1
#> [199,] 2 1 4 1 2
#> [200,] 2 1 4 2 1
#> [201,] 2 1 5 1 1
#> [202,] 2 2 1 1 4
#> [203,] 2 2 1 2 3
#> [204,] 2 2 1 3 2
#> [205,] 2 2 1 4 1
#> [206,] 2 2 2 1 3
#> [207,] 2 2 2 2 2
#> [208,] 2 2 2 3 1
#> [209,] 2 2 3 1 2
#> [210,] 2 2 3 2 1
#> [211,] 2 2 4 1 1
#> [212,] 2 3 1 1 3
#> [213,] 2 3 1 2 2
#> [214,] 2 3 1 3 1
#> [215,] 2 3 2 1 2
#> [216,] 2 3 2 2 1
#> [217,] 2 3 3 1 1
#> [218,] 2 4 1 1 2
#> [219,] 2 4 1 2 1
#> [220,] 2 4 2 1 1
#> [221,] 2 5 1 1 1
#> [222,] 3 1 1 1 4
#> [223,] 3 1 1 2 3
#> [224,] 3 1 1 3 2
#> [225,] 3 1 1 4 1
#> [226,] 3 1 2 1 3
#> [227,] 3 1 2 2 2
#> [228,] 3 1 2 3 1
#> [229,] 3 1 3 1 2
#> [230,] 3 1 3 2 1
#> [231,] 3 1 4 1 1
#> [232,] 3 2 1 1 3
#> [233,] 3 2 1 2 2
#> [234,] 3 2 1 3 1
#> [235,] 3 2 2 1 2
#> [236,] 3 2 2 2 1
#> [237,] 3 2 3 1 1
#> [238,] 3 3 1 1 2
#> [239,] 3 3 1 2 1
#> [240,] 3 3 2 1 1
#> [241,] 3 4 1 1 1
#> [242,] 4 1 1 1 3
#> [243,] 4 1 1 2 2
#> [244,] 4 1 1 3 1
#> [245,] 4 1 2 1 2
#> [246,] 4 1 2 2 1
#> [247,] 4 1 3 1 1
#> [248,] 4 2 1 1 2
#> [249,] 4 2 1 2 1
#> [250,] 4 2 2 1 1
#> [251,] 4 3 1 1 1
#> [252,] 5 1 1 1 2
#> [253,] 5 1 1 2 1
#> [254,] 5 1 2 1 1
#> [255,] 5 2 1 1 1
#> [256,] 6 1 1 1 1
set.seed(111)
partitionsGeneral(sample(1000, 20), 5, TRUE, target = 2500)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 45 45 586 904 920
#> [2,] 45 45 602 904 904
#> [3,] 45 175 507 794 979
#> [4,] 45 175 602 699 979
#> [5,] 45 281 334 920 920
#> [6,] 45 281 586 794 794
#> [7,] 45 584 586 586 699
#> [8,] 69 175 584 793 879
#> [9,] 69 175 602 675 979
#> [10,] 69 305 507 699 920
#> [11,] 69 334 699 699 699
#> [12,] 69 584 586 586 675
#> [13,] 281 334 507 584 794
#> [14,] 281 334 584 602 699
#> [15,] 305 334 584 602 675
system.time(one_thread <- partitionsGeneral(80, 10, TRUE))
#> user system elapsed
#> 0.004 0.001 0.005
system.time(two_threads <- partitionsGeneral(80, 10, TRUE, nThreads = 2))
#> user system elapsed
#> 0.004 0.002 0.003
identical(one_thread, two_threads)
#> [1] TRUE