C C++ 算法实例大全

2020-01-06 16:05:16王旭


var
a:array[1..maxn,1..maxn] of integer;
b:array[1..maxn] of integer; {b[i]指顶点i到源点的最短路径}
mark:array[1..maxn] of boolean; 

procedure bhf;
var
best,best_j:integer;
begin
fillchar(mark,sizeof(mark),false);
mark[1]:=true; b[1]:=0;{1为源点}
repeat
best:=0;
for i:=1 to n do
If mark[i] then {对每一个已计算出最短路径的点}
for j:=1 to n do
if (not mark[j]) and (a[i,j]>0) then 
if (best=0) or (b[i]+a[i,j]<best) then begin
best:=b[i]+a[i,j]; best_j:=j;
end;
if best>0 then begin
b[best_j]:=best;mark[best_j]:=true;
end;
until best=0;
end;{bhf}

B.Floyed算法求解所有顶点对之间的最短路径:


procedure floyed;
begin
for I:=1 to n do
for j:=1 to n do
if a[I,j]>0 then p[I,j]:=I else p[I,j]:=0; {p[I,j]表示I到j的最短路径上j的前驱结点}
for k:=1 to n do {枚举中间结点}
for i:=1 to n do
for j:=1 to n do
if a[i,k]+a[j,k]<a[i,j] then begin
a[i,j]:=a[i,k]+a[k,j];
p[I,j]:=p[k,j];
end;
end; 

C. Dijkstra 算法:


var
a:array[1..maxn,1..maxn] of integer;
b,pre:array[1..maxn] of integer; {pre[i]指最短路径上I的前驱结点}
mark:array[1..maxn] of boolean;
procedure dijkstra(v0:integer);
begin
fillchar(mark,sizeof(mark),false);
for i:=1 to n do begin
d[i]:=a[v0,i];
if d[i]<>0 then pre[i]:=v0 else pre[i]:=0;
end;
mark[v0]:=true;
repeat {每循环一次加入一个离1集合最近的结点并调整其他结点的参数}
min:=maxint; u:=0; {u记录离1集合最近的结点}
for i:=1 to n do
if (not mark[i]) and (d[i]<min) then begin
u:=i; min:=d[i];
end;
if u<>0 then begin
mark[u]:=true; 
for i:=1 to n do
if (not mark[i]) and (a[u,i]+d[u]<d[i]) then begin
d[i]:=a[u,i]+d[u];
pre[i]:=u;
end;
end;
until u=0;
end;

3.计算图的传递闭包


Procedure Longlink;
Var
T:array[1..maxn,1..maxn] of boolean;
Begin
Fillchar(t,sizeof(t),false);
For k:=1 to n do
For I:=1 to n do
For j:=1 to n do T[I,j]:=t[I,j] or (t[I,k] and t[k,j]);
End; 

4.无向图的连通分量

A.深度优先


procedure dfs ( now,color: integer);
begin
for i:=1 to n do
if a[now,i] and c[i]=0 then begin {对结点I染色}
c[i]:=color;
dfs(I,color);
end;
end; 

B 宽度优先(种子染色法)


5.关键路径

几个定义: 顶点1为源点,n为汇点。
a. 顶点事件最早发生时间Ve[j], Ve [j] = max{ Ve [j] + w[I,j] },其中Ve (1) = 0;
b. 顶点事件最晚发生时间 Vl[j], Vl [j] = min{ Vl[j] – w[I,j] },其中 Vl(n) = Ve(n);
c. 边活动最早开始时间 Ee[I], 若边I由<j,k>表示,则Ee[I] = Ve[j];
d. 边活动最晚开始时间 El[I], 若边I由<j,k>表示,则El[I] = Vl[k] – w[j,k];
若 Ee[j] = El[j] ,则活动j为关键活动,由关键活动组成的路径为关键路径。
求解方法:
a. 从源点起topsort,判断是否有回路并计算Ve;