File size: 4,838 Bytes
d4035c1
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
function [matching] = Hungarian(map)
% Hungarian
% Algorithm is from:
% http://www.public.iastate.edu/~ddoty/HungarianAlgorithm.html

    matching = zeros(size(map));

    x_con = find(sum(~isinf(map), 2) ~= 0);
    y_con = find(sum(~isinf(map), 1) ~= 0);
    
    C_size = max(length(x_con),length(y_con));
    C_mat = zeros(C_size);
    C_mat(1:length(x_con), 1:length(y_con)) = map(x_con, y_con);
    if isempty(C_mat)
        return
    end

    stepnum = 1;
    while true
        switch stepnum
          case 1
            C_mat = step1(C_mat);
            stepnum = 2;
          case 2
            [covered_row, covered_col, M] = step2(C_mat);
            stepnum = 3;
          case 3
            [covered_col, stepnum] = step3(M, C_size);
          case 4
            [M, covered_row, covered_col, Z_row, Z_col, stepnum] = step4(C_mat,covered_row,covered_col,M);
          case 5
            [M, covered_row, covered_col] = step5(M,Z_row,Z_col,covered_row,covered_col);
            stepnum = 3;
          case 6
            C_mat = step6(C_mat, covered_row, covered_col);
            stepnum = 4;
          case 7
            break;
        end
    end

    matching(x_con, y_con) = M(1:length(x_con), 1:length(y_con));
end

function C_mat = step1(C_mat)
    for i = 1:length(C_mat)
        min_val = min(C_mat(i, :));
        C_mat(i,:) = C_mat(i,:) - min_val;
    end
end
  
function [covered_row, covered_col, M] = step2(C_mat)
    n = length(C_mat);
    covered_row = zeros(n, 1);
    covered_col = zeros(n, 1);
    M = zeros(n, n);
    
    for i = 1:n
        for j = 1:n
            if C_mat(i,j) == 0 && covered_row(i) == 0 && covered_col(j) == 0
                M(i,j) = 1;
                covered_row(i) = 1;
                covered_col(j) = 1;
            end
        end
    end
    
    covered_row(:) = 0;
    covered_col(:) = 0;
end
    
function [covered_col,stepnum] = step3(M, C_size)
    covered_col = sum(M, 1);
    if sum(covered_col) == C_size
        stepnum = 7;
    else
        stepnum = 4;
    end
end
  
function [M, covered_row, covered_col, Z_row, Z_col, stepnum] = step4(C_mat, covered_row, covered_col, M)
    function [row, col] = find_a_zero() 
        row = 0;
        col = 0;
        i = 1;
        done2 = false;
        while ~done2
            j = 1;
            while true
                if C_mat(i,j) == 0 && covered_row(i) == 0 && covered_col(j) == 0
                    row = i;
                    col = j;
                    done2 = true;
                end
                j = j + 1;
                if j > n
                    break;
                end
            end
            i = i + 1;
            if i > n
                done2 = true;
            end
        end
    end

    n = length(C_mat);
    done = false;
    while ~done
        [row, col] = find_a_zero();
        if row == 0
            stepnum = 6;
            done = true;
            Z_row = 0;
            Z_col = 0;
        else
            M(row,col) = 2;
            if sum(find(M(row,:)==1)) ~= 0
                covered_row(row) = 1;
                zcol = find(M(row,:)==1);
                covered_col(zcol) = 0;
            else
                stepnum = 5;
                done = true;
                Z_row = row;
                Z_col = col;
            end            
        end
    end
end
    
function [M,covered_row,covered_col] = step5(M, Z_row, Z_col, covered_row, covered_col)
    done = false;
    count = 1;
    while ~done
        rindex = find(M(:,Z_col(count))==1);
        if rindex > 0
            count = count + 1;
            Z_row(count,1) = rindex;
            Z_col(count,1) = Z_col(count - 1);
        else
            done = true;
        end
        
        if ~done
            cindex = find(M(Z_row(count),:)==2);
            count = count + 1;
            Z_row(count, 1) = Z_row(count - 1);
            Z_col(count, 1) = cindex;    
        end    
    end
    
    for i = 1:count
        if M(Z_row(i), Z_col(i)) == 1
            M(Z_row(i), Z_col(i)) = 0;
        else
            M(Z_row(i), Z_col(i)) = 1;
        end
    end
    
    covered_row(:) = 0;
    covered_col(:) = 0;
    
    M(M == 2) = 0;
end
    
function C_mat = step6(C_mat, covered_row, covered_col)
    from_row = find(covered_row == 0);
    from_col = find(covered_col == 0);
    minval = min(min(C_mat(from_row, from_col)));
    
    C_mat(find(covered_row == 1), :) = C_mat(find(covered_row == 1), :) + minval;
    C_mat(:, find(covered_col == 0)) = C_mat(:,find(covered_col == 0)) - minval;
end
    
function cnum = min_line_cover(Edge)
    [covered_row, covered_col, M] = step2(Edge);
    covered_col = step3(M, length(Edge));
    [M, covered_row, covered_col, Z_row, Z_col] = step4(Edge,covered_row,covered_col,M);
    cnum = length(Edge) - sum(covered_row) - sum(covered_col);
end