2020年APMCM(亚太地区大学生数学建模竞赛)A题
题目(英文)
![2020年APMCM(亚太地区大学生数学建模竞赛)A题_第1张图片](http://img.e-com-net.com/image/info8/c7425085635d4aa4b90cea08bce2455e.jpg)
![2020年APMCM(亚太地区大学生数学建模竞赛)A题_第2张图片](http://img.e-com-net.com/image/info8/88a4cb229de3496c986c1df72fb86e12.jpg)
![2020年APMCM(亚太地区大学生数学建模竞赛)A题_第3张图片](http://img.e-com-net.com/image/info8/31f1a1d7bdae431a8e1ecf05567cf867.jpg)
题目(中文)
![2020年APMCM(亚太地区大学生数学建模竞赛)A题_第4张图片](http://img.e-com-net.com/image/info8/d5bc3b81690449e88bcbff3d19511f90.jpg)
![2020年APMCM(亚太地区大学生数学建模竞赛)A题_第5张图片](http://img.e-com-net.com/image/info8/20dbd7ffd2334b86abb08448d3b0e37c.jpg)
Matlab中的代码实现:
clear;
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for i=1:25
if mod(i,2)==0
dy=-0.1; %此处dy不要改为1
else
dy=0.1; %此处dy不要改为1
end
if length(data{
i})==0
continue;
end;
by=round(data{
i}(1,2),1);
ey=round(data{
i}(end,2),1);
x=[];
y=[];
y=by:dy:ey;
x=interp1(data{
i}(:,2),data{
i}(:,1),y,'linear');%Spline %linear
zd=[zd;[x',y']];
end
%还有部分数据为NaN
snan=find(isnan(zd(:,1))==1);
for i=1:length(snan)-1
zd(snan(i),1)=(zd(snan(i)-2,1)+zd(snan(i)+2,1))/2;
end
zd(snan(end),1)=zd(snan(end)-1,1);
zd(1829,1)=zd(1828,1);
zd(1934,1)=zd(1933,1);
zd(1935,1)=zd(1933,1);
zd(2076,1)=zd(2077,1);
%绘图
plot(data1(:,1),data1(:,2),'y-');
hold on
plot(data2(:,1),data2(:,2),'y-');
plot(data3(:,1),data3(:,2),'y-');
plot(data4(:,1),data4(:,2),'y-');
plot(zd(:,1),zd(:,2),'b.');
maxy=max(zd(:,2));
miny=min(zd(:,2));
%以下找水平线与图形出的交点,1,2连线,3,4连线.....
dy=1; %此处dy可为0.1
dty=miny+dy;
while dty<maxy
dty=dty+dy;
lk=find(abs(zd(:,2)-dty)<0.0000001);
lka=sortrows(zd(lk,:),1);
if length(lk)==2
plot([lka(1,1)+dy,lka(2,1)-dy],[lka(1,2),lka(2,2)],'g-');
end
if length(lk)==4
plot([lka(1,1)+dy,lka(2,1)-dy],[lka(1,2),lka(2,2)],'g-');
plot([lka(3,1)+dy,lka(4,1)-dy],[lka(3,2),lka(4,2)],'g-');
end
if length(lk)==6
plot([lka(1,1)+dy,lka(2,1)-dy],[lka(1,2),lka(2,2)],'g-');
plot([lka(3,1)+dy,lka(4,1)-dy],[lka(3,2),lka(4,2)],'g-');
plot([lka(5,1)+dy,lka(6,1)-dy],[lka(5,2),lka(6,2)],'g-');
end
if length(lk)==8
plot([lka(1,1)+dy,lka(2,1)-dy],[lka(1,2),lka(2,2)],'g-');
plot([lka(3,1)+dy,lka(4,1)-dy],[lka(3,2),lka(4,2)],'g-');
plot([lka(5,1)+dy,lka(6,1)-dy],[lka(5,2),lka(6,2)],'g-');
plot([lka(7,1)+dy,lka(8,1)-dy],[lka(7,2),lka(8,2)],'g-');
end
end
运行结果:
![2020年APMCM(亚太地区大学生数学建模竞赛)A题_第6张图片](http://img.e-com-net.com/image/info8/4de0369c283443b49d33e79db96a4ae9.jpg)