Description |
VChooseKO(V, K) creates a matrix, which rows are all permutations of choosing K elements of the vector V with order and without repetitions.
INPUT:
V: Array of class DOUBLE, SINGLE, (U)INT8/16/32/64, LOGICAL, CHAR.
K: Number of elements to choose.
OUTPUT:
Y: [N!/(N-K)!, K] matrix with N is the number of elements of V.
Y has the same class as the input V.
The rows are sorted in lexicographical order: smaller indices at first.
EXAMPLES:
Choose 2 elements from [1, 2, 3]:
VChooseKO(1:3, 2) % ==> [1,2; 1,3; 2,1; 2,3; 3,1; 3,2]
For speed cast the input to integer types or SINGLE whenever possible:
Y = VChooseKO(uint8(1:100), 3); % 5 times faster than:
Y = VChooseKO(1:100, 3);
To get the permutations of cell arrays, permute the index:
C = {'a', 'b', 'c', 'd'};
C2 = C(VChooseKO(uint8(1:4), 2))
==> C2 = {'a','b'; 'a','c'; 'a','d'; 'b','a'; 'b','c'; 'b','d'; ...
'c','a'; 'c','b'; 'c','d'; 'd','a'; 'd','b'; 'd','c'}
Equivalent to PERMS:
isequal(sortrows(perms(1:5)), VChooseKO(1:5, 5)) % TRUE
For an output with sorted values (not indices!), sort the input:
X = [3, 1, 2]; VChooseKO(sort(X), 3)
==> [1,2,3; 1,3,2; 2,1,3; 2,3,1; 3,1,2; 3,2,1]
The output of VCHOOSEKO(V, K) is equivalent to COMBINATOR(NUMEL(V), K, 'p'), but is remarkably faster (see screenshot). The lexicographical output of VCHOOSEKO can be a benefit also, because a time-consuming SORTROWS can be omitted.
Tested: Matlab 6.5, 7.7, 7.8, WinXP, 32 bit, Compilers: BCC5.5, LCC2.4/3.8, Open Watcom 1.8
The unit-test function TestVChooseKO is included to test the validitiy and compare the speed with PICK, COMBINATOR and Matlab's PERMS.
Precompiled mex: http://www.n-simon.de/mex
See also:
VChooseK (no repetitions, no order): FEX #26190
VChooseKRO (repetitions, order): FEX #26242
VChooseKR (repetitions, no order): FEX #26277
I'd appreciate suggestions for improvements and bug reports sent through email - thanks. |