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KTHCOMBN

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KTHCOMBN

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24 Nov 2011 (Updated )

K-th combination(s) of elements

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KTHCOMBN - the K-th combination of elements

M = KTHCOMBN(V,N,K) returns the K-th combination(s) of N elements of the elements in vector V. N is a positive scalar, and K is a vector of one or more integers between 1 and numel(V)^N.
V can be a vector of numbers, characters, cells strings, or even structures.
 
[M,IDX] = KTHCOMBN(V,N,K) also returns an index matrix, so that M = V(IDX).
 
Examples:
      V = [7 31] , N = 3 , K = [7 4]
      M = kthcombn(V, N, K)
      % returns the 2-by-3 matrix:
      % -> 31 31 7
      % 7 31 31
      % being the 7th and 4th combination (out of 9) of 3 elements of the V.
 
      kthcombn('abcde',10, 5^9)
      % -> aeeeeeeeee
      
      V = cellstr(['a':'z'].') ; N = 5 ; K = [1 10000000 11881376] ;
      M = kthcombn(V,N,K)
      % returns the first, 10 millionth, and the last combination
      % -> 'a' 'a' 'a' 'a' 'a'
      % 'v' 'w' 'y' 'x' 'j'
      % 'z' 'z' 'z' 'z' 'z'
 
All elements in V are regarded as unique, so M = KTHCOMBN([2 2],3, K) returns [2 2] for all values of K.
 
This function does the same as
      M = COMBN(V,N)
      M = M(K,:)
but it does not need to create all combinations first, before selecting, thereby avoiding some obvious memory issues with large values of N.
Beware of round-off errors for large values of N and K (see INTMAX).
For V = [0 1], KTHCOMBN returns a similar results as dec2bin(K-1,N)-'0'
 
See also nchoosek, perms
and combn, allcomb, nchoose on the File Exchange

MATLAB release MATLAB 7.12 (R2011a)
Other requirements should work on most releases
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Comments and Ratings (1)
15 Jan 2012 Manu

love it! I have been using combn a lot but this time I really needed something which can give me the kth combination without storing the whole big matrix. This is perfect.

Updates
17 Jan 2012

check K > 0 instead of K >= 0; fixed some spelling in the help

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