问题：（1） 有一个集合R = [a, b, c, d, e, f, g, h, i, j, k, l, m, n, ],
（2） 由一组R的真子集构成的集合Rn = [R1, R2, R3, R4, R5],其中
R1 = [ a, c, e, g, i, k, l, m]
R2 = [ b, c, d, h, k]
R3 = [ d, f, g, n]
R4 = [ b, f, g, i, j]
R5 = [ b, k, n]
（3） 给定一个目标集 C = [b, d, f, l, n]， C为R的子集
[问题]求在Rn中找出个数最少的一个子集，这个子集的所有元素的并集为U，要求U ∩ C = C，且U ∪ C = U，请写出求解这样的一个子集的通用算法。
matlab实现code
%%%author: qkk%date: 0917%%R = 'abcdefghijklmn'; % full SetS = {'acegiklm', 'bcdhk', 'dfgn', 'bfgij', 'bkn'}; % set composed of subset of RT = 'bdfln'; % target set% convert data to binary Matrix and binary VectorCR = zeros(1,length(R)) + 1;numR = size(S,2);CS = zeros(numR,length(R));for i=1:numRSItem = S{i};for j=1:length(SItem)CS(i,strfind(R, SItem(j))) = 1;endendCT = zeros(1, length(R));for i=1:length(T)CT(strfind(R,T(i))) = 1;end% call functionrIndex = SetDist(CR,CS,CT);% outputdisp('required subset:')rIndex = sort(rIndex);for i=1:length(rIndex)disp(S{rIndex(i)});end%%% input demo：% U = [1 1 1 1 1 1 1 1 1 1 1 1 1 1];% S = [1 0 1 0 1 0 1 0 1 0 1 1 1 0;%0 1 1 1 0 0 0 1 0 0 1 0 0 0;%0 0 0 1 0 1 1 0 0 0 0 0 0 1;%0 1 0 0 0 1 1 0 1 1 0 0 0 0;%0 1 0 0 0 0 0 0 0 0 1 0 0 1];% T = [0 1 0 1 0 1 0 0 0 0 0 1 0 1];function index = SetDist(U, S, T)% INPUT:% -U: Full set，all elements equal 1, size: [1,|R|]% -S: Multiple subset of U，each row represent a subset of U，value 1 denote% the Subset contains the corresponding element, 0 otherwise, size:[|Rn|, |R|]% -T: Target set，within value denote same means with S% OUTPUT:% -index: Index of required subset if nargin ~= 3disp('Warning: Improper number of input parameter');return;endindex = []; [numR, numElm] = size(S);% check inputif length(U) ~= size(S,2) || length(U) ~= length(T) ...|| ~isempty(find(U ~= 1))disp('Warning: Improper input');return;endrowCount = zeros(numR,1); %each element denotes the length of intersetion between each row(R) of S and TcolCount = zeros(1,numElm); % each element denotes the number of subset that contains the element in T%query if solution existbitQ = sum(S)-T;if length(find(bitQ <0)) > 0disp('Warning: no solution！');return;end% solve: cycle until each element in T is contained by a subsetwhile sum(T) ~= 0 satIndex = find(T == 1);colCount = sum(S(:,satIndex));for i=1:numRrowCount(i) = sum(S(i,:) & T);endsortColCount = sort(colCount);firstValIndex = find(colCount == sortColCount(1));if (sortColCount(1) == 1)adjustCols = satIndex(firstValIndex);for i=1:length(adjustCols)whichOne = find(S(:,adjustCols(i)) == 1);index = [index whichOne];% update S and TadjustColsOfi = find(S(whichOne,:) == 1);%S(:,adjustColsOfi) = 0;T(adjustColsOfi) = 0;endelsemaxRowCount = max(rowCount);mRCIndex = find(rowCount == maxRowCount);index = [index mRCIndex(1)];% update TresetIndex = find(S(mRCIndex(1),:)==1);T(resetIndex) = 0;%for i=1:length(resetIndex)% S(:,resetIndex(i)) = 0;%endendendend
算法题：（1） 有一个集合R = [a b c d e f g h i j k l m n ] ....请写出求解这样的一个子集的通用算法。
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