数学建模matlab代码_matlab_matlab例程_数值算法/人工智能下载-pudn.com

<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/622bdb083d2fbb000796acd0/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/622bdb083d2fbb000796acd0/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">图论算法及其 MATLAB 程序代码 </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls0 ws0">求赋权图 G = (V, E , F )中任意两点间的最短路的 Warshall-Floyd 算法： </div><div class="t m0 x2 h2 y3 ff1 fs0 fc0 sc0 ls0 ws0">设 A = (a</div><div class="t m0 x3 h3 y4 ff3 fs1 fc0 sc0 lse ws6">ij </div><div class="t m0 x4 h2 y3 ff2 fs0 fc0 sc0 ls7 ws0">)</div><div class="t m0 x5 h3 y4 ff3 fs1 fc0 sc0 ls6 ws0">n</div><div class="t m0 x6 h4 y5 ff1 fs2 fc0 sc0 ls0 ws0">×</div><div class="t m0 x7 h3 y4 ff3 fs1 fc0 sc0 ls6 ws0">n</div><div class="t m0 x8 h2 y3 ff1 fs0 fc0 sc0 ls0 ws0">为赋权图 G = (V, E , F )的矩阵, 当 v</div><div class="t m0 x9 h3 y4 ff3 fs1 fc0 sc0 ls11 ws0">i</div><div class="t m0 xa h5 y3 ff3 fs0 fc0 sc0 ls10 ws0">v</div><div class="t m0 xb h3 y4 ff3 fs1 fc0 sc0 ls11 ws0">j</div><div class="t m0 xc h5 y3 ff1 fs0 fc0 sc0 ls0 ws0">∈E 时 a</div><div class="t m0 xd h6 y4 ff3 fs1 fc0 sc0 ls11 ws0">ij </div><div class="t m0 xe h2 y3 ff2 fs0 fc0 sc0 ls3 ws0">= F (v</div><div class="t m0 xf h3 y4 ff3 fs1 fc0 sc0 ls11 ws0">i</div><div class="t m0 x10 h5 y3 ff3 fs0 fc0 sc0 ls10 ws0">v</div><div class="t m0 x11 h3 y4 ff3 fs1 fc0 sc0 ls11 ws0">j</div><div class="t m0 x12 h2 y3 ff2 fs0 fc0 sc0 ls12 ws8">), 否则取 a</div><div class="t m0 x13 h6 y4 ff3 fs1 fc0 sc0 ls13 ws0">ii </div><div class="t m0 x14 h2 y3 ff2 fs0 fc0 sc0 ls14 ws9">=0, a</div><div class="t m0 x15 h6 y4 ff3 fs1 fc0 sc0 ls11 ws0">ij </div><div class="t m0 x16 h2 y6 ff2 fs0 fc0 sc0 ls3 wsa">= +∞(i≠j ), d</div><div class="t m0 x17 h3 y7 ff3 fs1 fc0 sc0 ls13 ws0">ij</div><div class="t m0 x18 h5 y6 ff1 fs0 fc0 sc0 ls0 ws0">表示从 v</div><div class="t m0 x19 h3 y7 ff3 fs1 fc0 sc0 ls11 ws0">i</div><div class="t m0 x1a h5 y6 ff1 fs0 fc0 sc0 ls0 ws0">到 v</div><div class="t m0 x1b h3 y7 ff3 fs1 fc0 sc0 ls11 ws0">j</div><div class="t m0 x1c h2 y6 ff1 fs0 fc0 sc0 ls0 ws0">点的距离, r</div><div class="t m0 x1d h3 y7 ff3 fs1 fc0 sc0 ls11 ws0">ij</div><div class="t m0 x1e h5 y6 ff1 fs0 fc0 sc0 ls19 ws0">表示从 v</div><div class="t m0 x1f h3 y7 ff3 fs1 fc0 sc0 ls11 ws0">i</div><div class="t m0 x20 h5 y6 ff1 fs0 fc0 sc0 ls0 ws0">到 v</div><div class="t m0 x21 h3 y7 ff3 fs1 fc0 sc0 ls11 ws0">j</div><div class="t m0 x22 h2 y6 ff1 fs0 fc0 sc0 ls0 ws0">点的最短路中一个点的编号. </div><div class="t m0 x2 h2 y8 ff1 fs0 fc0 sc0 ls0 ws0">① 赋初值. 对所有 i, j, d</div><div class="t m0 x1c h3 y9 ff3 fs1 fc0 sc0 ls11 wsd">ij </div><div class="t m0 x23 h2 y8 ff2 fs0 fc0 sc0 ls3 wsa">= a</div><div class="t m0 x24 h3 y9 ff3 fs1 fc0 sc0 ls11 ws0">ij</div><div class="t m0 x25 h2 y8 ff2 fs0 fc0 sc0 ls6 ws0">, r</div><div class="t m0 x26 h3 y9 ff3 fs1 fc0 sc0 ls11 wsd">ij </div><div class="t m0 x27 h2 y8 ff2 fs0 fc0 sc0 ls1a wsa">= j. k = 1. 转向② </div><div class="t m0 x2 h2 ya ff1 fs0 fc0 sc0 ls0 ws0">② 更新 d</div><div class="t m0 x4 h3 yb ff3 fs1 fc0 sc0 ls11 ws0">ij</div><div class="t m0 x5 h2 ya ff2 fs0 fc0 sc0 ls6 ws0">, r</div><div class="t m0 x28 h3 yb ff3 fs1 fc0 sc0 lse ws6">ij </div><div class="t m0 x29 h2 ya ff2 fs0 fc0 sc0 lsf ws0">. 对所有 i, j, 若 d</div><div class="t m0 x2a h3 yb ff3 fs1 fc0 sc0 ls1d ws10">ik </div><div class="t m0 x27 h2 ya ff2 fs0 fc0 sc0 ls3 ws0">+ d</div><div class="t m0 x2b h3 yb ff3 fs1 fc0 sc0 ls1f ws0">k j</div><div class="t m0 x2c h5 ya ff1 fs0 fc0 sc0 ls0 ws0">＜d</div><div class="t m0 x2d h3 yb ff3 fs1 fc0 sc0 ls13 ws0">ij</div><div class="t m0 x2e h2 ya ff2 fs0 fc0 sc0 lsf ws0">, 则令 d</div><div class="t m0 xa h3 yb ff3 fs1 fc0 sc0 ls13 ws0">ij</div><div class="t m0 x2f h2 ya ff2 fs0 fc0 sc0 ls3 wsa"> = d</div><div class="t m0 x30 h3 yb ff3 fs1 fc0 sc0 ls1d ws10">ik </div><div class="t m0 x31 h2 ya ff2 fs0 fc0 sc0 ls3 ws0">+ d</div><div class="t m0 x32 h3 yb ff3 fs1 fc0 sc0 ls1f ws0">k j</div><div class="t m0 x33 h2 ya ff2 fs0 fc0 sc0 ls6 ws0">, r</div><div class="t m0 x34 h3 yb ff3 fs1 fc0 sc0 ls11 wsd">ij </div><div class="t m0 x35 h2 ya ff2 fs0 fc0 sc0 ls1a wsa">= k, 转向③. </div><div class="t m0 x2 h2 yc ff1 fs0 fc0 sc0 ls0 ws0">③ 终止判断. 若 d</div><div class="t m0 x36 h3 yd ff3 fs1 fc0 sc0 ls13 ws0">ii</div><div class="t m0 x37 h2 yc ff1 fs0 fc0 sc0 ls0 ws0">＜0, 则存在一条含有顶点 v</div><div class="t m0 x38 h3 yd ff3 fs1 fc0 sc0 ls11 ws0">i</div><div class="t m0 x39 h2 yc ff1 fs0 fc0 sc0 ls0 ws0">的负回路, 终止; 或者 k = n 终止; 否则</div><div class="t m0 x16 h2 ye ff1 fs0 fc0 sc0 ls0 ws0">令 k = k + 1, 转向②. </div><div class="t m0 x2 h5 yf ff1 fs0 fc0 sc0 ls0 ws0">最短路线可由 r</div><div class="t m0 x3a h3 y10 ff3 fs1 fc0 sc0 ls11 ws0">ij</div><div class="t m0 x3b h2 yf ff1 fs0 fc0 sc0 ls0 ws0">得到. </div><div class="t m0 x16 h2 y11 ff2 fs0 fc0 sc0 ls0 ws1"> </div><div class="t m0 x2 h7 y12 ff5 fs0 fc0 sc0 ls0 ws0">例 1 求图 6-4 中任意两点间的最短路. </div><div class="t m0 x16 h2 y13 ff2 fs0 fc0 sc0 ls0 ws1"> </div><div class="t m0 x16 h2 y14 ff2 fs0 fc0 sc0 ls0 ws1"> </div><div class="t m0 x16 h2 y15 ff2 fs0 fc0 sc0 ls0 ws1"> </div><div class="t m0 x16 h2 y16 ff2 fs0 fc0 sc0 ls0 ws1"> </div><div class="t m0 x16 h2 y17 ff2 fs0 fc0 sc0 ls0 ws1"> </div><div class="t m0 x16 h2 y18 ff2 fs0 fc0 sc0 ls0 ws1"> </div><div class="t m0 x16 h2 y19 ff2 fs0 fc0 sc0 ls0 ws1"> </div><div class="t m0 x2 h2 y1a ff7 fs0 fc0 sc0 ls0 ws0">解：用 Warshall-Floyd 算法, MATLAB 程序代码如下： </div><div class="t m0 x16 h8 y1b ff8 fs3 fc0 sc0 ls24 ws0">n=8;A=[0 2 8 1 Inf Inf Inf Inf </div><div class="t m0 x2 h8 y1c ff8 fs3 fc0 sc0 ls24 ws0">2 0 6 Inf 1 Inf Inf Inf </div><div class="t m0 x2 h8 y1d ff8 fs3 fc0 sc0 ls24 ws0">8 6 0 7 5 1 2 Inf </div><div class="t m0 x2 h8 y1e ff8 fs3 fc0 sc0 ls24 ws0">1 Inf 7 0 Inf Inf 9 Inf </div><div class="t m0 x2 h8 y1f ff8 fs3 fc0 sc0 ls26 ws0">Inf 1 5 Inf 0 3 Inf 8 </div><div class="t m0 x2 h8 y20 ff8 fs3 fc0 sc0 ls26 ws0">Inf Inf 1 Inf 3 0 4 6 </div><div class="t m0 x2 h8 y21 ff8 fs3 fc0 sc0 ls26 ws0">Inf Inf 2 9 Inf 4 0 3 </div><div class="t m0 x2 h9 y22 ff8 fs3 fc0 sc0 ls26 ws0">Inf Inf Inf Inf 8 6 3 0]; % MATLAB 中, Inf 表示∞ </div><div class="t m0 x16 h9 y23 ff8 fs3 fc0 sc0 ls2b ws0">D=A; %赋初值 </div><div class="t m0 x16 h9 y24 ff8 fs3 fc2 sc0 ls2d ws0">for(i=1:n)for(j=1:n)R(i,j)=j;end;end %赋路径初值 </div><div class="t m0 x16 h9 y25 ff8 fs3 fc2 sc0 ls2d ws0">for(k=1:n)for(i=1:n)for(j=1:n)if(D(i,k)+D(k,j)<D(i,j))D(i,j)=D(i,k)+D(k,j); %更新 dij </div><div class="t m0 x16 h9 y26 ff8 fs3 fc0 sc0 ls0 ws15"> R(i,j)=k;end;end;end %更新 rij </div><div class="t m0 x16 h9 y27 ff8 fs3 fc0 sc0 ls0 ws15"> k %显示迭代步数 </div><div class="t m0 x16 h9 y28 ff8 fs3 fc0 sc0 ls0 ws15"> D %显示每步迭代后的路长 </div><div class="t m0 x16 h9 y29 ff8 fs3 fc0 sc0 ls0 ws15"> R %显示每步迭代后的路径 </div><div class="t m0 x16 h9 y2a ff8 fs3 fc0 sc0 ls0 ws15"> pd=0;for i=1:n %含有负权时 </div><div class="t m0 x16 h9 y2b ff8 fs3 fc0 sc0 ls0 ws15"> if(D(i,i)<0)pd=1;break;end;end %存在一条含有顶点 vi 的负回路 </div><div class="t m0 x16 h9 y2c ff8 fs3 fc0 sc0 ls0 ws15"> if(pd)break;end %存在一条负回路, 终止程序 </div><div class="t m0 x16 h9 y2d ff8 fs3 fc2 sc0 ls24 ws0">end %程序结束 </div><div class="t m0 x16 h2 y2e ff2 fs0 fc0 sc0 ls0 ws1"> </div><div class="t m0 x3c h2 y2f ff2 fs0 fc0 sc0 ls0 ws1"> </div><div class="t m0 x3d ha y30 ff1 fs3 fc0 sc0 ls0 ws0">图 6-4 </div><div class="c x3e y31 w2 hb"><div class="t m0 x0 h2 y32 ff2 fs0 fc0 sc0 ls0 ws1"> </div></div></div><div class="pi" data-data='{"ctm":[1.610738,0.000000,0.000000,1.610738,0.000000,0.000000]}'></div></div> </body> </html>

<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/622bdb083d2fbb000796acd0/bg2.jpg"><div class="t m0 x16 h2 y33 ff2 fs0 fc0 sc0 ls0 ws1"> </div><div class="t m0 x2 h2 y34 ff2 fs0 fc0 sc0 ls41 ws0">Kruskal 避圈法：将图 G 中的边按权数从小到大逐条考察, 按不构成圈的原则加入到 T</div><div class="t m0 x16 hc y35 ff1 fs0 fc0 sc0 ls0 ws0">中(若有选择时, 不同的选择可能会导致最后生成树的权数不同), 直到 q (T ) = p (G ) − 1 为</div><div class="t m0 x16 hc y36 ff1 fs0 fc0 sc0 ls0 ws0">止, 即 T 的边数= G 的顶点数− 1 为止. </div><div class="t m0 x2 h2 y37 ff2 fs0 fc0 sc0 ls41 ws0">Kruskal 避圈法的 MATLAB 程序代码如下： </div><div class="t m0 x16 h8 yb ff8 fs3 fc0 sc0 ls46 ws0">n=8;A=[0 2 8 1 0 0 0 0 </div><div class="t m0 x2 h8 y38 ff8 fs3 fc0 sc0 ls24 ws0">2 0 6 0 1 0 0 0 </div><div class="t m0 x2 h8 y39 ff8 fs3 fc0 sc0 ls24 ws0">8 6 0 7 5 1 2 0 </div><div class="t m0 x2 h8 y3a ff8 fs3 fc0 sc0 ls24 ws0">1 0 7 0 0 0 9 0 </div><div class="t m0 x2 h8 y3b ff8 fs3 fc0 sc0 ls24 ws0">0 1 5 0 0 3 0 8 </div><div class="t m0 x2 h8 y3c ff8 fs3 fc0 sc0 ls24 ws0">0 0 1 0 3 0 4 6 </div><div class="t m0 x2 h8 y3d ff8 fs3 fc0 sc0 ls24 ws0">0 0 2 9 0 4 0 3 </div><div class="t m0 x2 h8 y3e ff8 fs3 fc0 sc0 ls24 ws0">0 0 0 0 8 6 3 0]; </div><div class="t m0 x16 h9 y3f ff8 fs3 fc0 sc0 ls48 ws0">k=1; %记录 A 中不同正数的个数 </div><div class="t m0 x16 h9 y40 ff8 fs3 fc2 sc0 ls2d ws0">for(i=1:n-1)for(j=i+1:n) %此循环是查找 A 中所有不同的正数 </div><div class="t m0 x16 h9 y41 ff8 fs3 fc0 sc0 ls0 ws15"> if(A(i,j)>0)x(k)=A(i,j); %数组 x 记录 A 中不同的正数 </div><div class="t m0 x16 h9 y42 ff8 fs3 fc0 sc0 ls0 ws15"> kk=1; %临时变量 </div><div class="t m0 x16 h9 y43 ff8 fs3 fc0 sc0 ls0 ws15"> for(s=1:k-1)if(x(k)==x(s))kk=0;break;end;end %排除相同的正数 </div><div class="t m0 x16 h8 y44 ff8 fs3 fc0 sc0 ls0 ws15"> k=k+kk;end;end;end </div><div class="t m0 x16 h9 y45 ff8 fs3 fc0 sc0 ls53 ws0">k=k-1 %显示 A 中所有不同正数的个数 </div><div class="t m0 x16 h9 y46 ff8 fs3 fc2 sc0 ls2d ws0">for(i=1:k-1)for(j=i+1:k) %将 x 中不同的正数从小到大排序 </div><div class="t m0 x16 h8 y47 ff8 fs3 fc0 sc0 ls0 ws15"> if(x(j)<x(i))xx=x(j);x(j)=x(i);x(i)=xx;end;end;end </div><div class="t m0 x16 h9 y48 ff8 fs3 fc0 sc0 ls56 ws0">T(n,n)=0; %将矩阵 T 中所有的元素赋值为 0 </div><div class="t m0 x16 h9 y49 ff8 fs3 fc0 sc0 ls24 ws0">q=0; %记录加入到树 T 中的边数 </div><div class="t m0 x16 h9 y4a ff8 fs3 fc2 sc0 ls2d ws0">for(s=1:k)if(q==n)break;end %获得最小生成树 T, 算法终止 </div><div class="t m0 x16 h9 y4b ff8 fs3 fc0 sc0 ls0 ws15"> for(i=1:n-1)for(j=i+1:n)if (A(i,j)==x(s))T(i,j)=x(s);T(j,i)=x(s); %加入边到树 T 中 </div><div class="t m0 x16 h9 y4c ff8 fs3 fc0 sc0 ls0 ws15"> TT=T; %临时记录 T </div><div class="t m0 x16 h9 y4d ff8 fs3 fc0 sc0 ls0 ws15"> while(1)pd=1; %砍掉 TT 中所有的树枝 </div><div class="t m0 x16 h8 y4e ff8 fs3 fc0 sc0 ls0 ws15"> for(y=1:n)kk=0; </div><div class="t m0 x16 h9 y4f ff8 fs3 fc0 sc0 ls0 ws15"> for(z=1:n)if(TT(y,z)>0)kk=kk+1;zz=z;end;end %寻找 TT 中的树枝 </div><div class="t m0 x16 h9 y50 ff8 fs3 fc0 sc0 ls0 ws15"> if(kk==1)TT(y,zz)=0;TT(zz,y)=0;pd=0;end;end %砍掉 TT 中的树枝 </div><div class="t m0 x16 h9 y1b ff8 fs3 fc0 sc0 ls0 ws15"> if(pd)break;end;end %已砍掉了 TT 中所有的树枝 </div><div class="t m0 x16 h9 y1c ff8 fs3 fc0 sc0 ls0 ws15"> pd=0; %判断 TT 中是否有圈 </div><div class="t m0 x16 h8 y1d ff8 fs3 fc0 sc0 ls0 ws15"> for(y=1:n-1)for(z=y+1:n)if(TT(y,z)>0)pd=1;break;end;end;end </div><div class="t m0 x16 h9 y1e ff8 fs3 fc0 sc0 ls0 ws15"> if(pd)T(i,j)=0;T(j,i)=0; %假如 TT 中有圈 </div><div class="t m0 x16 h8 y1f ff8 fs3 fc0 sc0 ls0 ws15"> else q=q+1;end;end;end;end;end </div><div class="t m0 x16 h9 y20 ff8 fs3 fc0 sc0 ls57 ws0">T %显示近似最小生成树 T, 程序结束 </div><div class="t m0 x16 h2 y51 ff2 fs0 fc0 sc0 ls0 ws1"> </div></div><div class="pi" data-data='{"ctm":[1.610738,0.000000,0.000000,1.610738,0.000000,0.000000]}'></div></div>

<div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/622bdb083d2fbb000796acd0/bg3.jpg"><div class="t m0 x2 h2 y33 ff1 fs0 fc0 sc0 ls0 ws0">求二部图 G 的最大匹配的算法(匈牙利算法), 其基本思想是：从 G 的任意匹配 M 开始, </div><div class="t m0 x16 hc y34 ff1 fs0 fc0 sc0 ls0 ws0">对 X 中所有 M 的非饱和点, 寻找 M −增广路. 若不存在 M −增广路, 则 M 为最大匹配; 若存</div><div class="t m0 x16 hc y35 ff1 fs0 fc0 sc0 ls0 ws0">在 M −增广路 P, 则将 P 中 M 与非 M 的边互换得到比 M 多一边的匹配 M</div><div class="t m0 x3f h6 y52 ff2 fs1 fc0 sc0 ls6 ws0">1 </div><div class="t m0 x40 h2 y35 ff2 fs0 fc0 sc0 lsf ws0">, 再对 M</div><div class="t m0 x41 h6 y52 ff2 fs1 fc0 sc0 ls6 ws0">1</div><div class="t m0 x13 hd y35 ff1 fs0 fc0 sc0 ls0 ws0">重复上</div><div class="t m0 x16 h2 y36 ff1 fs0 fc0 sc0 ls0 ws0">述过程. </div><div class="t m0 x2 h2 y37 ff1 fs0 fc0 sc0 ls0 ws0">设 G = ( X, Y, E )为二部图, 其中 X = {x</div><div class="t m0 x42 h6 y53 ff2 fs1 fc0 sc0 ls6 ws0">1</div><div class="t m0 x43 h2 y37 ff2 fs0 fc0 sc0 ls6 ws0">, x</div><div class="t m0 x44 h6 y53 ff2 fs1 fc0 sc0 ls6 ws0">2</div><div class="t m0 x45 h2 y37 ff2 fs0 fc0 sc0 ls6 ws0">, … , x</div><div class="t m0 x46 h3 y53 ff3 fs1 fc0 sc0 ls6 ws0">n </div><div class="t m0 xa h2 y37 ff2 fs0 fc0 sc0 ls6b ws22">}, Y = { y</div><div class="t m0 x47 h6 y53 ff2 fs1 fc0 sc0 ls6 ws0">1</div><div class="t m0 x48 h2 y37 ff2 fs0 fc0 sc0 ls6 ws0">, y</div><div class="t m0 x49 h6 y53 ff2 fs1 fc0 sc0 ls6 ws0">2</div><div class="t m0 x4a h2 y37 ff2 fs0 fc0 sc0 ls6 ws0">, … , y</div><div class="t m0 x4b h3 y53 ff3 fs1 fc0 sc0 ls6 ws0">n</div><div class="t m0 x4c h2 y37 ff2 fs0 fc0 sc0 ls6d ws24">}. 任取 G 的一初</div><div class="t m0 x16 h2 y54 ff1 fs0 fc0 sc0 ls0 ws0">始匹配 M (如任取 e∈E, 则 M = {e}是一个匹配). </div><div class="t m0 x2 he y55 ff1 fs0 fc0 sc0 ls0 ws0">① 令 S = φ , T = φ , 转向②. </div><div class="t m0 x2 h2 y56 ff1 fs0 fc0 sc0 ls0 ws0">② 若 M 饱和 X \ S的所有点, 则 M 是二部图 G 的最大匹配. 否则, 任取 M 的非饱和点</div><div class="t m0 x16 h2 y57 ff3 fs0 fc0 sc0 ls0 ws0">u∈X \ S , 令 S = S ∪{ u }, 转向③. </div><div class="t m0 x2 hc y58 ff1 fs0 fc0 sc0 ls0 ws0">③ 记 N (S ) = {v | u∈S, uv∈E</div><div class="t m0 x4d h3 y59 ff3 fs1 fc0 sc0 ls0 ws7"> </div><div class="t m0 x4e hc y58 ff2 fs0 fc0 sc0 ls6d ws24">}. 若 N (S ) = T, 转向②. 否则取 y∈N (S ) \ T. 若 y 是 M</div><div class="t m0 x16 h2 y5a ff1 fs0 fc0 sc0 ls0 ws0">的饱和点, 转向④, 否则转向⑤. </div><div class="t m0 x2 h2 y5b ff1 fs0 fc0 sc0 ls0 ws0">④ 设 x y∈M, 则令 S = S ∪{ x }, T = T ∪{ y }, 转向③. </div><div class="t m0 x2 hc y5c ff1 fs0 fc0 sc0 ls0 ws0">⑤ u − y 路是 M−增广路, 设为 P, 并令 M = M⊕P, 转向①. 这里 M⊕P = M∪P \ M∩</div><div class="t m0 x16 h2 y5d ff3 fs0 fc0 sc0 ls5 ws0">P, 是对称差. </div><div class="t m0 x2 hc y5e ff1 fs0 fc0 sc0 ls0 ws0">由于计算 M−增广路 P 比较麻烦, 因此将迭代步骤改为： </div><div class="t m0 x2 h2 y4b ff1 fs0 fc0 sc0 ls0 ws0">① 将 X 中 M 的所有非饱和点(不是 M 中某条边的端点)都给以标号 0 和标记*, 转向②. </div><div class="t m0 x2 h2 y5f ff1 fs0 fc0 sc0 ls0 ws0">② 若 X 中所有有标号的点都已去掉了标记*, 则 M 是 G 的最大匹配. 否则任取 X 中一</div><div class="t m0 x16 h2 y31 ff1 fs0 fc0 sc0 ls0 ws0">个既有标号又有标记*的点 x</div><div class="t m0 x1b h3 y4f ff3 fs1 fc0 sc0 ls11 wsd">i </div><div class="t m0 x1c h2 y31 ff2 fs0 fc0 sc0 lsf ws0">, 去掉 x</div><div class="t m0 x4f h3 y4f ff3 fs1 fc0 sc0 ls11 ws0">i</div><div class="t m0 x50 h2 y31 ff1 fs0 fc0 sc0 ls0 ws0">的标记*, 转向③. </div><div class="t m0 x2 h2 y60 ff1 fs0 fc0 sc0 ls0 ws0">③ 找出在 G 中所有与 x</div><div class="t m0 x51 h3 y1b ff3 fs1 fc0 sc0 ls11 ws0">i</div><div class="t m0 x52 h5 y60 ff1 fs0 fc0 sc0 ls0 ws0">邻接的点 y</div><div class="t m0 x53 h3 y1b ff3 fs1 fc0 sc0 ls11 ws0">j</div><div class="t m0 x54 h2 y60 ff2 fs0 fc0 sc0 ls7 ws2"> (即 x</div><div class="t m0 x55 h3 y1b ff3 fs1 fc0 sc0 ls11 wsd">i </div><div class="t m0 x56 h5 y60 ff3 fs0 fc0 sc0 ls10 ws0">y</div><div class="t m0 x57 h3 y1b ff3 fs1 fc0 sc0 ls11 ws0">j</div><div class="t m0 x58 h2 y60 ff1 fs0 fc0 sc0 ls0 ws0">∈E ), 若所有这样的 y</div><div class="t m0 x59 h3 y1b ff3 fs1 fc0 sc0 ls11 ws0">j</div><div class="t m0 x5a h2 y60 ff1 fs0 fc0 sc0 ls0 ws0">都已有标号, 则转向</div><div class="t m0 x16 h2 y61 ff1 fs0 fc0 sc0 ls0 ws0">②, 否则转向④. </div><div class="t m0 x2 h2 y62 ff1 fs0 fc0 sc0 ls0 ws0">④ 对与x</div><div class="t m0 x5b h3 y63 ff3 fs1 fc0 sc0 ls11 ws0">i</div><div class="t m0 x5c h5 y62 ff1 fs0 fc0 sc0 ls0 ws0">邻接且尚未给标号的y</div><div class="t m0 x5d h3 y63 ff3 fs1 fc0 sc0 ls11 ws0">j</div><div class="t m0 x5e h2 y62 ff1 fs0 fc0 sc0 ls0 ws0">都给定标号i. 若所有的y</div><div class="t m0 x5f h3 y63 ff3 fs1 fc0 sc0 ls11 ws0">j</div><div class="t m0 x47 h2 y62 ff1 fs0 fc0 sc0 ls0 ws0">都是M的饱和点, 则转向⑤, </div><div class="t m0 x16 h2 y64 ff1 fs0 fc0 sc0 ls0 ws0">否则逆向返回. 即由其中 M的任一个非饱和点y</div><div class="t m0 x60 h3 y65 ff3 fs1 fc0 sc0 ls11 ws0">j</div><div class="t m0 x61 h5 y64 ff1 fs0 fc0 sc0 ls0 ws0">的标号i找到x</div><div class="t m0 x62 h3 y65 ff3 fs1 fc0 sc0 ls11 ws0">i</div><div class="t m0 x63 h2 y64 ff2 fs0 fc0 sc0 lsf ws0">, 再由x</div><div class="t m0 x64 h3 y65 ff3 fs1 fc0 sc0 ls11 ws0">i</div><div class="t m0 x65 h5 y64 ff1 fs0 fc0 sc0 ls0 ws0">的标号k 找到y</div><div class="t m0 x66 h3 y65 ff3 fs1 fc0 sc0 ls30 ws2b">k </div><div class="t m0 x67 h2 y64 ff2 fs0 fc0 sc0 lsf ws0">, … , </div><div class="t m0 x16 h5 y66 ff1 fs0 fc0 sc0 ls0 ws0">最后由 y</div><div class="t m0 x68 h3 y67 ff3 fs1 fc0 sc0 ls11 ws0">t</div><div class="t m0 x69 h2 y66 ff1 fs0 fc0 sc0 ls0 ws0">的标号 s 找到标号为 0 的 x</div><div class="t m0 x6a h3 y67 ff3 fs1 fc0 sc0 ls77 ws0">s</div><div class="t m0 x6b hc y66 ff1 fs0 fc0 sc0 ls0 ws0">时结束, 获得M −增广路 x</div><div class="t m0 x63 h3 y67 ff3 fs1 fc0 sc0 ls77 ws2e">s </div><div class="t m0 x6c h5 y66 ff3 fs0 fc0 sc0 ls10 ws0">y</div><div class="t m0 x48 h3 y67 ff3 fs1 fc0 sc0 ls11 ws0">t</div><div class="t m0 x6d h2 y66 ff2 fs0 fc0 sc0 ls0 ws1"> … x</div><div class="t m0 x6e h3 y67 ff3 fs1 fc0 sc0 ls11 wsd">i </div><div class="t m0 x6f h5 y66 ff3 fs0 fc0 sc0 ls10 ws0">y</div><div class="t m0 x70 h3 y67 ff3 fs1 fc0 sc0 ls11 ws0">j</div><div class="t m0 x71 h2 y66 ff2 fs0 fc0 sc0 lsf ws0">, 记P = {x</div><div class="t m0 x72 h3 y67 ff3 fs1 fc0 sc0 ls77 ws2e">s </div><div class="t m0 x73 h5 y66 ff3 fs0 fc0 sc0 ls10 ws0">y</div><div class="t m0 x66 h3 y67 ff3 fs1 fc0 sc0 ls11 ws0">t</div><div class="t m0 x74 h2 y66 ff2 fs0 fc0 sc0 lsf ws0">, … , </div><div class="t m0 x16 h5 y68 ff3 fs0 fc0 sc0 ls10 ws0">x</div><div class="t m0 x75 h3 y69 ff3 fs1 fc0 sc0 ls11 wsd">i </div><div class="t m0 x76 h5 y68 ff3 fs0 fc0 sc0 ls10 ws0">y</div><div class="t m0 x77 h3 y69 ff3 fs1 fc0 sc0 ls11 wsd">j </div><div class="t m0 x78 h2 y68 ff2 fs0 fc0 sc0 ls6b ws22">}, 重新记 M 为 M⊕P, 转向①. </div><div class="t m0 x2 h2 y6a ff1 fs0 fc0 sc0 ls0 ws0">⑤ 将 y</div><div class="t m0 x79 h3 y6b ff3 fs1 fc0 sc0 ls11 ws0">j</div><div class="t m0 x7a h5 y6a ff1 fs0 fc0 sc0 ls0 ws0">在 M 中与之邻接的点 x</div><div class="t m0 x2a h3 y6b ff3 fs1 fc0 sc0 ls30 ws2b">k </div><div class="t m0 x4f h2 y6a ff2 fs0 fc0 sc0 ls7 ws0">(即 x</div><div class="t m0 x7b h3 y6b ff3 fs1 fc0 sc0 ls30 ws2b">k </div><div class="t m0 x7c h5 y6a ff3 fs0 fc0 sc0 ls10 ws0">y</div><div class="t m0 x7d h3 y6b ff3 fs1 fc0 sc0 ls11 ws0">j</div><div class="t m0 x7e h2 y6a ff1 fs0 fc0 sc0 ls0 ws0">∈M), 给以标号 j 和标记*, 转向②. </div><div class="t m0 x16 h2 y6c ff2 fs0 fc0 sc0 ls0 ws1"> </div><div class="t m0 x16 h2 y6d ff2 fs0 fc0 sc0 ls0 ws1"> </div></div><div class="pi" data-data='{"ctm":[1.610738,0.000000,0.000000,1.610738,0.000000,0.000000]}'></div></div>