二分图最大匹配算法的应用及Matlab实现+++

一共有RecuCal.m LockMap.m BuildMatrix.m Edmonds.m GUI1.m 这几个文件，我把它们合到一块粘上去了,你再把他们分开保存就可以了.其中前三个文件都是为建立邻接矩阵服务的，Edmonds.m是匈牙利算法的主文件，GUI1.m只是调用Edmonds.m做个界面而已。

调用关系是GUI1.m调用Edmonds.m；Edmonds.m调用BuildMatrix.m和LockMap.m ；LockMap.m调用RecuCal.m最后运行GUI1.m就ok了#LockMap.mfunction [LMA, LMB] = LockMap(n, m)% LOCKMAP - 求解满足条件锁并设置相应的映射% 输入参数:n 表槽数,m 表高度数。

% 输出参数:LMA,LMB 分别为二维矩阵表示自然数到满足条件锁之间的映射。

global jiA ouB ary A B mm NN = n; mm = m;jiA=0; ouB=0;A=[]; B=[];ary = zeros(1, n);RecuCal(n);LMA=A; LMB=B;[lena, n] = size(LMA);[lenb, n] =size(LMB);if lena>lenbtemp = LMA; LMA=LMB;LMB=temp;temp = lena;lena=lenb;lenb=temp;end#RecuCal.mfunction RecuCal(n)% RECUCAL - 递归函数global jiA ouB ary A B mm Nif n ==1for k=1:mm% 调用递归函数时要用到的变量所以% 设为全局ary(1) = k;Max = max(ary); Min = min(ary);num = 0; neighbor = 0;for i=1:Nnum = num + (Max-ary(i))*(ary(i)-Min);if (i~=N)neighbor = max(neighbor, abs(ary(i)-ary(i+1)));endendif (neighbor > mm-1.5)&&(num > 0.5)if mod(sum(ary), 2)% 奇数,属于 A 类jiA = jiA+1;A(jiA,:) = ary;else% 偶数,属于 B 类ouB = ouB+1;B(ouB,:) = ary;endendendelsefor k=1:mmary(n) = k;RecuCal(n-1);endend#BuildMatrix.mfunction AB = BuildMatrix(LMA, LMB)% BUILDMATRIX - 建立邻接矩阵,若 i 与 j 之间可以互开则 AB(i,j)=1,否则为0。

AB = [];[lena, n] = size(LMA);[lenb, n] =size(LMB);for i = 1:lenafor j=1:lenbtmp = 0;for k=1:ntmp = tmp + abs(LMA(i,k)-LMB(j,k));endif tmp == 1AB(i, j)=1;endendend#Edmonds.mfunction str = Edmonds(n, m)% EDMONDS - Edmonds 算法寻找完美匹配str = [];[LMA, LMB] = LockMap(n, m);AB = BuildMatrix(LMA, LMB);lena = length(LMA);lenb = length(LMB);if lena==0disp('其中一个分组为空,无法匹配'); %当 n=m=3 时只有偶数组无奇数组,不能完成匹配return;endMatA = zeros(1, lena);MatB = zeros(1, lenb);X = MatA; Y=MatB; Z=Y;NumNoMat = 0;% 无法匹配的点的个数% 最初匹配,只有一个匹配j = find(AB(1,:), 1);MatA(1)=j; MatB(j)=1;while length(find(MatA==0)) ~= 0% 存在不匹配的元素J = find(MatA==0); i = J(1);% 第 i 个元素未被匹配init = i; X(i)=0;J = find(AB(i,:));% J 为所有与 i 相邻结点Y(J) = i; j=J(1);while ~isempty(find(Y~=Z))if MatB(j) ~= 0% j 是匹配点Z(j) = Y(j);i = MatB(j);X(i)=j;J = find(AB(i,:));Y(J)=i;J = find(Y);JJ = find(Z);J = setxor(intersect(J, JJ), J);j=J(1);else% j 不是匹配点i = Y(j);MatA(i) = j;MatB(j) = i;while X(i)j = X(i);i = Z(j);MatA(i) = j;MatB(j) = i;endbreak;endend% 如果 Y==Z 则表明该点没有与之相应的匹配,即不存在完美匹配,在 MatA 中标 % 记为-1。

if isempty(find(Y~=Z, 1))NumNoMat = NumNoMat + 1;MatA(init) = -1;endX(1:lena)=0; Y(1:lenb)=0; Z=Y;endtotal = 0;for i=1:lenak = MatA(i);if k<=0continue; end% k<=0时表明匹配不存在stra = ''; strb = '';for j=1:nstra = [stra, num2str(LMA(i, j)), ''];strb = [strb, num2str(LMB(k, j)), ''];endstr = [str, stra, '------ ', strb, 10];total = total + 1;endstr = [str, '匹配个数有:', num2str(total)];#GUI1.mfunction varargout = GUI1(varargin)gui_Singleton = 1;gui_State = struct('gui_Name',mfilename, ...'gui_Singleton', gui_Singleton, ...'gui_OpeningFcn', @GUI1_OpeningFcn, ...'gui_OutputFcn', @GUI1_OutputFcn, ...'gui_LayoutFcn', [] , ...'gui_Callback', []);if nargin && ischar(varargin{1})gui_State.gui_Callback = str2func(varargin{1});endif nargout[varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:}); elsegui_mainfcn(gui_State, varargin{:});end% End initialization code - DO NOT EDIT% --- Executes just before GUI1 is made visible.function GUI1_OpeningFcn(hObject, eventdata, handles, varargin) handles.output = hObject;guidata(hObject, handles);function varargout = GUI1_OutputFcn(hObject, eventdata, handles) varargout{1} = handles.output;function pushbutton1_Callback(hObject, eventdata, handles)a = get(handles.edit1, 'String');b = get(handles.edit2, 'String');str = Edmonds(str2num(a), str2num(b));set(handles.edit4, 'String', str);guidata(hObject, handles);function edit1_Callback(hObject, eventdata, handles)input = str2num(get(hObject, 'String'));guidata(hObject, handles);function edit1_CreateFcn(hObject, eventdata, handles)if ispc && isequal(get(hObject,'BackgroundColor'),get(0,'defaultUicontrolBackgroundColor'))set(hObject,'BackgroundColor','white');endfunction edit2_Callback(hObject, eventdata, handles)input = str2num(get(hObject, 'String'));guidata(hObject, handles);function edit2_CreateFcn(hObject, eventdata, handles)if ispc && isequal(get(hObject,'BackgroundColor'),get(0,'defaultUicontrolBackgroundColor'))set(hObject,'BackgroundColor','white');endfunction slider1_Callback(hObject, eventdata, handles) function slider1_CreateFcn(hObject, eventdata, handles)if isequal(get(hObject,'BackgroundColor'),get(0,'defaultUicontrolBackgroundColor'))set(hObject,'BackgroundColor',[.9 .9 .9]);endfunction text_result_Callback(hObject, eventdata, handles) function text_result_CreateFcn(hObject, eventdata, handles) if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))set(hObject,'BackgroundColor','white');endfunction edit4_Callback(hObject, eventdata, handles) function edit4_CreateFcn(hObject, eventdata, handles)if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))set(hObject,'BackgroundColor','white');endfunction pushbutton2_Callback(hObject, eventdata, handles) set(handles.edit4, 'String', '');set(handles.edit1, 'String', '');set(handles.edit2, 'String', '');。