From octave-sources-request at bevo dot che dot wisc dot edu Fri Nov 28 15:47:33 2003
Subject: n_choose_r function
From: Henry Gomersall <whg21 at cam dot ac dot uk>
To: octave-sources at bevo dot che dot wisc dot edu
Date: Fri, 28 Nov 2003 08:29:47 -0600


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I have written a function that returns a matrix containing all the
values of n choose r, with the different combinations in the rows.

Its probably not the fastest way of doing it, but its short and does the
job.

its called by n_choose_r(n,r)

Apologies if it already exists.

Henry Gomersall

-- 
Henry Gomersall
Trinity College, Cambridge
Mobile: 07764 756059
whg21 at cam dot ac dot uk
http://www.heng.pwp.blueyonder.co.uk/

Please avoid sending me any WORD or POWERPOINT attachments.
See http://www.fsf.org/philosophy/no-word-attachments.html

"If your only contribution is to quote another, that is no contibution
at all."


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	1;

function [comb_matrix, row] = calc_comb(comb_matrix, row, column, start, n, r)
	
	%while still room in columns above to hold values up to n...
	while(start <= n-(r-column));

		comb_matrix(row, column) = start;

		if(column < r);
			[comb_matrix, row] = calc_comb(comb_matrix, row, column+1, start+1, n, r);
		endif;
			
		++start;
		if(start <= n-(r-column))
			++row;
			idx = column-1;

			%copy previous row if working above first column
			while(idx>0);
				comb_matrix(row, idx) = comb_matrix(row-1, idx);
				--idx;
			endwhile;
		endif;

	endwhile;
endfunction;

function comb_matrix = n_choose_r(n, r);
	number_rows = factorial(n)/(factorial(r)*factorial(n-r));
	number_columns = r;

	comb_matrix = zeros(number_rows, number_columns);
	
	comb_matrix = calc_comb(comb_matrix, 1, 1, 1, n, r);

endfunction;

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