MATLAB: How to find all the possible permutations in a given array

MATLABpermutation

The following vector is x = [1 ; 2 ; 3 ; 4 ; 8 ];

I want to find all possible permutations of the given vector by taking 5 elements, 4 elements & 3 elements at a time. The 'perms' function only provides the permutations by taking all the elements of the array at a time.

Kindly suggest any predefined function or process to get this.

Best Answer

x = [1 ; 2 ; 3 ; 4 ; 8 ]
p=arrayfun(@(k) num2cell(nchoosek(x,k),2), 3:length(x), 'unif', 0);
p=cat(1,p{:});
p=cellfun(@(x) num2cell(perms(x),2),p,'unif',0);
p=cat(1,p{:});
p{:}

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MATLAB: How to sort data in cells

This solution can be reduced two lines but I added a third so it's easier to understand. Fake data are created at the top.

% Create fake data
data = { 
    {6 5 rand(3,4)}, {0 2 rand(3,4)}, {1 1 rand(3,4)}, ...
    {9 4 rand(3,4)}, {3 3 rand(3,4)}, {1 6 rand(3,4)}
    };
% Pull out the 2nd numbers and put them into a vector
secondNumber = cell2mat(cellfun(@(x)x(2),data)); 
% determine the sorted index of the vector
[~, sortIdx] = sort(secondNumber); 
%Resort the data
dataSorted = data(sortIdx);

MATLAB: How to find area of all possible polygons

n = 5; % No. of control points
array = 1:1:n;
p=arrayfun(@(k) num2cell(nchoosek(array,k),2), 3:length(array), 'unif', 0);
p=cat(1,p{:});
p=cellfun(@(array) num2cell(perms(array),2),p,'unif',0);
p=cat(1,p{:});
x = [1 ; 2 ; 3 ; 4 ; 2 ];   % coordinate of control points

y = [8 ; 5 ; 8 ; 7 ; 6 ];   % coordinate of control points
% Vectorize the computing of areas (in S(:))
% by group of polygonals having the same length
np = cellfun('length',p);
[npu,~,J] = unique(np); % npu is logically [3,4,5]
s = zeros(size(p)); % allocate array of area result
for i = 1:length(npu) % == 3
    b = J==i;
    Pi = cat(1,p{b});
    s(b) = polyarea(x(Pi),y(Pi),2);
end
% Many of them represents the same geometrical polygon
% The entire procedure seems redundant thus wasteful
allimax = find(s==max(s));
for j=1:length(allimax)
    imax = allimax(j);
    pmax = p{imax};
    xpmax = x(pmax);
    ypmax = y(pmax);
    figure;
    plot(xpmax([1:end 1]),ypmax([1:end 1]));
end

Best Answer

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MATLAB: How to find area of all possible polygons

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