Matlab的学习历程：统计棋盘连通分量（空值区域）的大小和个数
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1.问题引入
在20x20的棋盘矩阵中，设定黑子为1，空值为0，如下所示：
现需要统计空值（连通分量）的大小和个数并标记，如下所示：
以此类推……
其中，最大的连通分量如下所示：
2.matlab程序
以连通分量大小为6举例，对其进行红色标记，并且统计其数量，matlab程序如下所示：
clear,clc,close all
m = 20;
n = 20;
markersize = floor(80-(max([m n])));
rng('default');
A = randn(m,n);
A(abs(A)<=1) = 1;
A(abs(A)>1) = 0;
Ar = 1-A;
cc4 = bwconncomp(Ar,4);
L4 = labelmatrix(cc4);
counts = [];
for i = 1:numel(cc4.PixelIdxList)
idx = cc4.PixelIdxList{1,i};
Ar(idx) = numel(cc4.PixelIdxList{1,i});
counts(i) = numel(cc4.PixelIdxList{1,i});
end
size=flip(unique(counts));
fprintf('编号\t\t连通分量大小\t\t个数\n');
for i = 1:numel(size)
fprintf('%d\t\t\t%d\t\t\t%d\n',i,size(i),sum(counts==size(i)));
end
fprintf('连通分量总个数：%d\n',cc4.NumObjects);
mark = 6; % 需要标记的连通分量大小
Ar(Ar~=mark)=0;
fprintf('原始棋盘矩阵：\n');
disp(A); % 黑子为1，空值为0
fprintf('红色标记的棋盘矩阵：\n');
disp(Ar); % 红子为1，其余为0
go(A,markersize,m,n,[],[],[])
go(A,markersize,m,n,Ar,mark,sum(counts==mark))
function go(A,markersize,m,n,Ar,mark,count)
figure('color',[1 1 1],'position',[600,100,400*1.5,400*1.5]);
hold on
spy(A,'k',markersize);
spy(Ar,'r',markersize);
axis([1 n 1 m]);
xticks([1:n]);
yticks([1:m]);
xlabel("红色标记的连通分量大小为："+mark+"，个数为："+count);
ax = gca;
ax.GridColor = [0 .5 .5];
ax.GridLineStyle = '-';
ax.GridAlpha = 0.5;
ax.Layer = 'top';
ax.XRuler.TickLabelGapOffset = 20;
ax.YRuler.TickLabelGapOffset = 20;
ax.YAxis.Label.Visible = 'off';
grid on
end
3.效果展示
编号 连通分量大小 个数
1 10 1
2 8 1
3 7 2
4 6 4
5 5 2
6 4 2
7 3 3
8 2 12
9 1 22
连通分量总个数：49
原始棋盘矩阵：
1 1 1 0 0 1 0 1 1 0 1 0 0 0 1 1 0 0 1 0
0 0 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1
0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 1 1 1 0 1
1 0 1 0 0 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1
1 1 1 0 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 0
0 0 1 1 1 1 1 1 1 0 1 1 0 0 1 1 1 0 1 0
1 1 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 1 1 0 1
0 1 0 0 1 0 1 0 1 1 1 1 1 1 0 1 0 1 1 1
0 1 0 0 0 1 0 1 1 1 1 1 1 1 0 1 0 1 1 1
0 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1
0 0 1 1 1 1 1 1 0 1 0 0 1 0 0 1 0 1 1 1
1 0 0 1 1 0 0 1 0 1 1 1 1 0 0 1 1 1 1 1
1 1 0 1 0 0 1 1 1 1 1 1 1 1 1 0 0 0 1 0
1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1
1 0 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1
1 1 1 0 1 0 0 1 1 0 1 1 0 0 0 0 0 1 1 0
0 1 1 1 0 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1
0 0 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 1 0 1
0 0 0 1 0 0 1 1 1 1 1 0 1 1 0 1 1 1 0 1
红色标记的棋盘矩阵：
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 6 6 6 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 6 0 6 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 6 6 6 6 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 6 6 0 0 0 0 0 0 0 0 0 0 0 0 0
6 0 0 0 6 6 6 6 0 0 0 0 0 0 0 0 0 0 0 0
6 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 6 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Last updated on 2025-05-13