1910072盧富毓插點(diǎn)問(wèn)題

1、云南大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院 實(shí) 驗(yàn) 報(bào) 告課程名稱：算法圖論實(shí)驗(yàn)學(xué)期：20132014學(xué)年上學(xué)期成績(jī)：指導(dǎo)教師：李建平姓名：盧富毓學(xué)號(hào)：20101910072實(shí)驗(yàn)名稱：插值點(diǎn)問(wèn)題實(shí)驗(yàn)要求：必做實(shí)驗(yàn)學(xué)時(shí)：2學(xué)時(shí)實(shí)驗(yàn)編號(hào)：02實(shí)驗(yàn)日期：2013-10-10完成日期：2013-10-21學(xué)院：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院專業(yè) ：信息與計(jì)算科學(xué)年級(jí)：2010級(jí) 一、實(shí)驗(yàn)?zāi)康睦胐ijskra算法實(shí)現(xiàn)路的插點(diǎn)問(wèn)題，掌握如何尋找最短路集合的方法二、實(shí)驗(yàn)環(huán)境vs2010(c+)三、實(shí)驗(yàn)內(nèi)容最短路的插點(diǎn)問(wèn)題：給定一個(gè)連通賦權(quán)圖g=（v,e;w.c;s.t）以及正整數(shù)d,這里w,c:e-r+s和t 是兩個(gè)固定的頂點(diǎn)，找到s 到

2、t 的最短路集合構(gòu)造一個(gè)新的輔助圖，然后修改權(quán)值，再次調(diào)用dijskra算法尋求最短路。4、 實(shí)驗(yàn)過(guò)程a、插值算法具體描述如下：s和t 是兩個(gè)固定的頂點(diǎn)，在圖g中尋找一條從s到t的路ps,t，使得路ps,t的權(quán)重w(ps,t)不超過(guò)常數(shù)b，并向路ps,t的一些特殊邊上插入一些頂點(diǎn)，不妨設(shè)得到的新路為p*s,t,使得新路中任意邊的權(quán)重都不超過(guò)常數(shù)的d,目標(biāo)是在滿足上述條件情況下，求出插入頂點(diǎn)后所產(chǎn)生的費(fèi)用達(dá)到最小.即實(shí)現(xiàn),這里insert(e)表示加入到邊e中新點(diǎn)的個(gè)數(shù)。dijskra算法即標(biāo)號(hào)法，在上學(xué)期學(xué)過(guò)，這里就不作贅述。b、算法運(yùn)行結(jié)果如下：/圖的輸入/圖的創(chuàng)建以及插值點(diǎn)的限制/最后插值

3、點(diǎn)的結(jié)果五、實(shí)驗(yàn)總結(jié)通過(guò)編程，對(duì)尋找最短路徑的dijkstra算法也體會(huì)更深；復(fù)習(xí)了求最短路的算法，思考了反圈算法在其中的一些應(yīng)用。六、源代碼#include#include#include#includeusing namespace std;#define max_vex 100#define m 1000/settextc1是原來(lái)的顏色/settextc2 是設(shè)置的輸出輸入顏色#define settextc1 setconsoletextattribute(getstdhandle(std_output_handle),foreground_intensity | foreground

4、_red | foreground_green |foreground_blue)#define settextc2 setconsoletextattribute(getstdhandle(std_output_handle),foreground_intensity | foreground_green)#define settextc3 setconsoletextattribute(getstdhandle(std_output_handle),foreground_intensity | foreground_green | foreground_blue)#define sette

5、xtc4 setconsoletextattribute(getstdhandle(std_output_handle),foreground_intensity | foreground_red)#define settextc5 setconsoletextattribute(getstdhandle(std_output_handle),foreground_intensity | foreground_red | foreground_blue)#define settextc6 setconsoletextattribute(getstdhandle(std_output_handl

6、e),foreground_red | foreground_green |foreground_blue)#define settextc7 setconsoletextattribute(getstdhandle(std_output_handle),foreground_green)double dmax_vex;/最短路徑p帶權(quán)長(zhǎng)度和dbool pmax_vexmax_vex;/最短路徑pstring vex,vex2;int v0,v1;class arcllpublic:double weight; /權(quán)重;class graphics /創(chuàng)建一個(gè)圖的類private:int ve

7、xnum; /頂點(diǎn)數(shù)int arcnum; /邊數(shù)string vexsmax_vex; /存儲(chǔ)定點(diǎn)名稱arcll arcsmax_vexmax_vex; /邊數(shù)double d;/邊的限制public:void creategraphics(graphics &g);/創(chuàng)建一個(gè)圖int locateindex(graphics g, string v); / 尋找下標(biāo)void dijkstra(graphics &g);void insertpoint(graphics &g);/找到相應(yīng)頂點(diǎn)的下標(biāo)int graphics:locateindex(graphics g, string v)i

8、nt i=0;for(i=0; ig.vexnum; i+)if(g.pare(v) = 0)return i;return -1;/創(chuàng)建一個(gè)圖void graphics:creategraphics(graphics &g)int i,j,k;string vi,vj;double w; /權(quán)值settextc1;cout-創(chuàng)建有向圖的存儲(chǔ)-endl;coutg.vexnum;settextc1;/設(shè)置顏色coutg.arcnum;settextc1;cout請(qǐng)輸入頂點(diǎn)名:;settextc4;for(i=0; ig.vexsi;settextc1;for(i=0; ig.

9、vexnum; i+) /初始化邊f(xié)or(j=0; jg.vexnum; j+)g.arcsij.weight = m;for(k=0; kg.arcnum; k+)cout請(qǐng)輸入第k+1vivjw;settextc1;i = locateindex(g,vi);j = locateindex(g,vj);if(i = -1 | j = -1)cout輸入錯(cuò)誤！請(qǐng)檢查.endl;return;g.arcsij.weight = w;g.arcsji.weight = w;coutendl;cout各頂點(diǎn)的關(guān)系：endl;settextc2;for(i=0; ig.vexnum; i+) if(

10、i=0)coutttg.vexsi ;else couttg.vexsi ;coutendl;settextc3;for(i=0; ig.vexnum; i+) /初始化邊settextc2;couttg.vexsi ;settextc3;for(j=0; jg.vexnum; j+)if(g.arcsij.weight = m)settextc6;couttm ;settextc3; else couttg.arcsij.weight ;coutendl;settextc1;coutendl圖創(chuàng)建完畢！endl;coutvex;coutendlvex2;coutendlg.d;/*-dijk

11、stra算法-*/void graphics:dijkstra(graphics &g)/bool pmax_vexmax_vex;/最短路徑pbool finalmax_vex;/控制變量int i,j,v,w;double min;cout-v0到v1的最短路徑-endl;v0 = locateindex(g,vex);v1 = locateindex(g,vex2);if(v0 = -1 | v1= -1)cout輸入錯(cuò)誤！請(qǐng)檢查.endl;return;for(v = 0; v g.vexnum; v+ ) /初始化finalv = false;dv = g.arcsv0v.weigh

12、t;for(w = 0; w g.vexnum; w+)pvw = false;if(dv m)pvv0 = true;pvv = true;dv0 = 0;finalv0 = true;for(i = 1; i g.vexnum; +i)min = m;for(w = 0; w g.vexnum; +w)if(!finalw)if(dwmin)v = w;min = dw; finalv = true;for(w = 0; w g.vexnum; +w)if(!finalw & (min + g.arcsvw.weight dw)dw = min + g.arcsvw.weight;for(

13、j = 0; jg.vexnum; +j)pwj = pvj;pww = true;if(dv1=m)cout不連通！最短路不存在！endl;elsecout從g.vexsv0到g.vexsv1的最短路長(zhǎng)度：;coutdv1endl;/*-路的插值算法-*/void graphics:insertpoint(graphics &g)int i,j;for(i=0;ig.vexnum;i+)for(j=0;jg.vexnum;j+)if(i=j)continue;elseif(g.arcsij.weight+di=dj)g.arcsij.weight = ceil(g.arcsij.weight

14、/g.d)-1;elseg.arcsij.weight=m;coutendl;settextc2;for(i=0; ig.vexnum; i+) if(i=0)coutttg.vexsi ; else couttg.vexsi ;coutendl;for(i=0; ig.vexnum; i+)settextc2;couttg.vexsi ;settextc3;for(j=0; jg.vexnum; j+)if(g.arcsij.weight = m)if(g.arcsji.weight!= m)g.arcsij.weight = g.arcsji.weight;couttg.arcsij.weight ; else settextc6;couttm ;settextc3; else couttg.arcsij.weight ;coutendl;settextc6;g.dijkstra(g);/構(gòu)造新的權(quán)值后，再尋找最短路cout最短路：;for(j=0;