2020年APMCM（亞太地區大學生數學建模競賽）A題

題目（英文）

題目（中文）

Matlab中的代碼實現：

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13.50270176 10.44410038 13.50325012 10.37114811 13.50273323 10.22592545 13.49861813 10.0818119 13.49044323 9.939048767 13.47826576 9.797875404 13.46214199 9.658535004 13.44212914 9.521265984 13.41828346 9.386311531 13.39066315 9.253910065 13.35932541 9.124303818 13.32432556 8.997733116 13.28572178 8.87443924 13.24357128 8.754663467 13.19793034 8.638644218 13.14885712 8.526625633 13.09640694 8.418845177 13.04063797 8.366621017 13.01152611 8.315675735 12.98168373 8.218079567 12.92009544 8.126291275 12.85608482 8.040411949 12.78978825 7.960540295 12.72134495 7.886776447 12.65089226 7.819220066 12.5785656 7.75797081 12.50450611 7.703128338 12.42884827 7.654792786 12.3517313 7.613063335 12.27329254 7.5780406 12.19366932 7.549823284 12.11299992 7.528512001 12.03142071 7.514205933 11.94907093 7.507005215 11.86608696 7.506100178 11.82439995 7.507004738 11.78271294 7.514205933 11.69972897 7.528511524 11.61737919 7.549823284 11.53579998 7.578040123 11.45513058 7.613063335 11.37550735 7.654792786 11.2970686 7.703128338 11.21995163 7.75797081 11.14429379 7.819220066 11.0702343 7.886776447 10.99790764 7.960540295 10.92745495 8.040411949 10.85901165 8.126291275 10.79271507 8.218079567 10.72870445 8.315675735 10.66711617 8.366621017 10.63727379 8.418845177 10.60816193 8.526625633 10.55239296 8.638644218 10.49994278 8.754663467 10.45086956 8.87443924 10.40522861 8.997733116 10.36307812 9.124303818 10.32447433 9.253910065 10.28947449 9.386311531 10.25813675 9.521266937 10.23051643 9.658535004 10.20667076 9.797876358 10.18665791 9.939048767 10.17053413 10.0818119 10.15835667 10.22592545 10.15018177 10.37114811 10.14606667 10.44410038 10.14554977 10.51993084 10.14609814 10.67015076 10.15044498 10.81829357 10.15903854 10.96417522 10.171772 11.10760975 10.18854046 11.24841404 10.20923805 11.38640213 10.23375988 11.52139091 10.26200008 11.65319443 10.29385376 11.78162956 10.32921505 11.90651035 10.3679781 12.02765274 10.41003799 12.14487171 10.45528889 12.25798321 10.50362492 12.36680317 10.55494213 12.47114563 10.60913277 12.57082653 10.66609383 12.66566181 10.72571754 12.75546551 10.78789997 12.84005451 10.85253429 12.91924381 10.91951656 12.99284935 10.98874092 13.06068516 11.06010056 13.12256718 11.13349152 13.17831039 11.20880795 13.2277317 11.28594398 13.27064514 11.36479378 13.30686665 11.44525337 13.33621216 11.52721596 13.35849571 11.61057568 13.37353325 11.69522858 13.38114071 11.78106785 13.38210011 11.82439995];data{1}=data3(1:157,:); data{2}=data3(158:237,:); data{3}=data3(238:321,:); data{4}=data3(322:375,:); data{5}=data3(376:425,:); data{6}=data3(426:478,:); data{7}=data3(479:520,:); data{8}=data3(521:767,:); data{9}=data3(768:783,:); data{10}=data3(784:902,:); data{11}=data3(903:989,:); data{12}=data3(990:1084,:); data{13}=data3(1085:1195,:); data{14}=[]; data{15}=data1(1:35,:); data{16}=data1(36:103,:); data{17}=data1(104:136,:); data{18}=[]; data{19}=data2(1:54,:); data{20}=data2(55:162,:); data{21}=data2(163:215,:); data{22}=[]; data{23}=data4(1:34,:); data{24}=data4(35:102,:); data{25}=data4(103:135,:);zd=[]; for i=1:25if mod(i,2)==0dy=-0.1; %此處dy不要改為1 elsedy=0.1; %此處dy不要改為1endif 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 %linearzd=[zd;[x',y']]; end%還有部分數據為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); %繪圖 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));%以下找水平線與圖形出的交點，1,2連線，3,4連線..... dy=1; %此處dy可為0.1 dty=miny+dy; while dty<maxydty=dty+dy;lk=find(abs(zd(:,2)-dty)<0.0000001);lka=sortrows(zd(lk,:),1);if length(lk)==2plot([lka(1,1)+dy,lka(2,1)-dy],[lka(1,2),lka(2,2)],'g-');endif length(lk)==4plot([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-');endif length(lk)==6plot([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-'); endif length(lk)==8plot([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

運行結果：

總結

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