Obtain all integer partitions for a given integer
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Is there a way to compute all integer partitions for a given integer?
For example n=4
we have
4+ 0 + 0 +0
3+ 1 + 0 +0
2+ 2 + 0 +0
2+ 1 + 1 +0
1+ 1 + 1 +1
I would like to obtain a matrix
[4, 0, 0, 0;
3, 1, 0, 0;
2, 2, 0, 0;
2, 1, 1, 0;
1, 1, 1, 1]
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Answers (2)
Matt J
on 1 Jul 2015
[~,x] = nsumk(4,4);
result=flipud(unique(sort(x,2,'descend'),'rows'))
leads to,
result =
4 0 0 0
3 1 0 0
2 2 0 0
2 1 1 0
1 1 1 1
5 Comments
Michael Vaughan
on 19 Sep 2020
I'm copying and pasting what the original poster typed into the command prompt, that is:
[~,x] = nsumk(4,4);
result=flipud(unique(sort(x,2,'descend'),'rows'))
and i'm not getting any good output. It's getting an error
Error: File: nsumk.m Line: 11 Column: 53
Invalid expression. Check for missing multiplication operator, missing or unbalanced delimiters, or other syntax error. To
construct matrices, use brackets instead of parentheses.
Walter Roberson
on 19 Sep 2020
Line 11 of nsumk.m is a comment, so that does not make any sense
% is a natural way to list coefficients of polynomials in N variables of degree K.
unless you also provided your own nsumk.m ?
Also, which MATLAB version are you using?
Bruno Luong
on 19 Sep 2020
Edited: Bruno Luong
on 19 Sep 2020
I wrote a short function that doesn't need to post-proceesed with UNIQUE (wast of time and memory) when using with NSUMK or allvL1 (order matter)
function v = Partition(n, lgt)
% v = Partition(n)
% INPUT
% n: non negative integer
% lgt: optional non negative integer
% OUTPUT:
% v: (m x lgt) non-negative integer array such as sum(v,2)==n
% each row of v is descending sorted
% v contains all possible combinations
% m = P(n) in case lgt == n, where P is the partition function
% v is (dictionnary) sorted
% Algorithm:
% Recursive
% Example:
% >> Partition(5)
%
% ans =
%
% 5 0 0 0 0
% 4 1 0 0 0
% 3 2 0 0 0
% 3 1 1 0 0
% 2 2 1 0 0
% 2 1 1 1 0
% 1 1 1 1 1
if nargin < 2
lgt = n;
end
v = PartR(lgt+1, n, Inf);
end % Partition
%% Recursive engine of integer partition
function v = PartR(n, L1, head)
rcall = isfinite(head);
if rcall
L1 = L1-head;
end
if n <= 2
if ~rcall
v = L1;
elseif head >= L1
v = [head, L1];
else
v = zeros(0, n, class(L1));
end
else % recursive call
j = min(L1,head):-1:0;
v = arrayfun(@(j) PartR(n-1, L1, j), j(:), 'UniformOutput', false);
v = cat(1,v{:});
if rcall
v = [head+zeros([size(v,1),1], class(head)), v];
end
end
end % PartR
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