TobePDFcreatedwithpdfFactoryProtrialversion 三、最短路算PDFcreatedwithpdfFactoryProtrialversion

例已知如例已知如下圖所示的單行線交通網(wǎng)，每弧1要從v1出發(fā)，通過(guò)這個(gè)交通網(wǎng)到去。求使總費(fèi)用最小的旅行路 22 PDFcreatedwithpdfFactoryProtrialversion 一、最短路問(wèn)P0，

w(0PPDFcreatedwithpdfFactoryProtrialversion 用P，T分別表示某個(gè)頂點(diǎn)的P標(biāo)號(hào)和T標(biāo)號(hào)Si表示第i步時(shí),具有P*λ(v)=m表示在從vs到v的最短 λ(v)=M表示D中不含從vs到v的路λ(v)0表示PDFcreatedwithpdfFactoryProtrialversion 2、最短路算法(Dijkstra算法每一個(gè)v≠vs,令T(v)=+∞,λ(v)=M;k=s(當(dāng)前點(diǎn)（１）判斷：如果Si=V,算法終止。此時(shí),對(duì)每v∈Si，d(vs,v)=P(v)；否則轉(zhuǎn)入 (vkvjA且vjSi的點(diǎn)vj如果T(vj)>P(vk)+wkjT(vj)P(vk)wkj,(vj)否則轉(zhuǎn)入PDFcreatedwithpdfFactoryProtrialversion TTji)min{T(vvjj如果T(vji)<+∞,則把vji的T標(biāo)號(hào)變?yōu)镻iiSi1轉(zhuǎn)入

},kj,iivSi,d(vs,v)T注意、Dijkstra算法同樣適用于無(wú)向、DijkstraPDFcreatedwithpdfFactoryProtrialversion 最短路算法(Dijkstra算法PDFcreatedwithpdfFactoryProtrialversion ．現(xiàn) 要從v1出發(fā)，通過(guò)這個(gè)交通網(wǎng)

2 3 21

4v2v 例例已知如下圖所示的單每弧旁的數(shù)字表示通PDFcreatedwithpdfFactoryProtrialversion i0

S0v1},P(v1)0,(v1)0;T(vi)(vi)M(i2,3,...,9),kT(v)p(v)w

(2)(v1,(2)(v1,v2)v2 2

442)

v6 PDFcreatedwithpdfFactoryProtrialversion T4)vjj)}14)T4)632632262643421113 PDFcreatedwithpdfFactoryProtrialversion (v4,v6(v4,v6v6T(v6)Mp(v4)w46110T(v)P(v) 11,(v)(3)T(v3)(3)T(v3)min{T(vjvjmin{T(v2)6,T(v3)3,T(v6)11}v63v632624vv61v v 1TobePDFcreatedwithpdfFactoryProtrialversion i2(v3,v2v2T(v2)6p(v3)w3232miT(vjminT(vmiT(vjminT(v26S3S26363262612434 v6

vvTobePDFcreatedwithpdfFactoryProtrialversion i3(v2v5A且v5S T5minTT5minTvj5)6,T61}6363262612434 3

TobePDFcreatedwithpdfFactoryProtrialversion i4T

)11p(v

)

6410,(2)(v5,v6)v66T(v6)P(v5)w56(2)(v5,v6)v66同理T(v7p(v5w57639,(v7)T(v7)miT(vj)}minT(v6)10,T()T(v7)miT(vj)}minT(v6)10,T(v7)9,T(v8)12}5v16v16262vv9vTobePDFcreatedwithpdfFactoryProtrialversion i5(2(v7,v8)v8T(v8)12p(v7)w7894Tv8))6)miT(vj)}minT(6)10,T(v8))6)miT(vj)}minT(6)10,T(v8)162616262v9vPDFcreatedwithpdfFactoryProtrialversion

Tobei6(2(v6,v7)Av7

(T(v8)12p(v7)7894 8jT(v) 8jv

)}T(v)P(v8)T(v8)S7S6{v8}{v1,v2,v3,v4,v5,v6,v7,v8},kvv2

v8最短路262664 PDFcreatedwithpdfFactoryProtrialversion clearallV=[00;11;10;1-1;21;20;21;330;3-1;4E=[125;135;145;232;32;25262;365;372;473;567585;682;693;792;73;899102;8115;9114;1011PDFcreatedwithpdfFactoryProtrialversion [dSP,sp]=grShortPath(E,s,t);%thematrixofshortestgrPlot(V(:,1:2),[sp(1:end-PDFcreatedwithpdfFactoryProtrialversion 中國(guó)郵遞員問(wèn)圖論描述給定一個(gè)賦權(quán)的連通圖,求最 回路 （Euler）行跡＊ 行跡稱(chēng) 回路＊ 回路的圖稱(chēng) 圖PDFcreatedwithpdfFactoryProtrialversion 連通圖G上郵遞員問(wèn)題的算法(Fleury算法、求出G’的Euler閉跡C,則C就是G的最優(yōu)郵路.結(jié)束PDFcreatedwit