Daily Archives: 29 March,09

Warshall algorithm

 1 /* Assume a function edgeCost(i,j) which returns the cost of the edge from i to j
 2    (infinity if there is none).
 3    Also assume that n is the number of vertices and edgeCost(i,i)=0
 4 */
 5
 6 int path[][];
 7 /* A 2-dimensional matrix. At each step in the algorithm, path[i][j] is the shortest path
 8    from i to j using intermediate vertices (1..k-1).  Each path[i][j] is initialized to
 9    edgeCost(i,j) or infinity if there is no edge between i and j.
10 */
11
12 procedure FloydWarshall ()
13    for k: = 1 to n
14       for each (i,j) in {1,..,n}2
15          path[i][j] = min ( path[i][j], path[i][k]+path[k][j] );

Kruskal algorithm

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void kruskal ( )

{

int i,x,b[MAX_NODE],top,w,v;

int min_wt,y,f_wt[MAX_NODE],bentuk;

node *ptr1;

f_node *ptr2;

f_list=NULL;

for(i=1;i<=totNodes;i++)

status[i]=unseen;

x=1;

status[x]=intree;

top=0;

bentuk=0;

while( (top <= (totNodes-1)) && (!bentuk

{

ptr1=adj[x];

while(ptr1!=NULL)

{

y=ptr1->vertex;

w=ptr1->weight;

if((status[y]==fringe) && (w<f_wt[y]))

{

b[y]=x;

f_wt[y]=w;

}

else if(status[y]==unseen)

{

status[y]=fringe;

b[y]=x;

f_wt[y]=w;

Insert_Beg(y);

}

ptr1=ptr1->next;

}

if(f_list==NULL)

bentuk=1;

else

{

x=f_list->vertex;

min_wt=f_wt[x];

ptr2=f_list->next;

while(ptr2!=NULL)

{

w=ptr2->vertex;

if(f_wt[w] < min_wt)

{

x=w;

min_wt=f_wt[w];

}

ptr2=ptr2->next;

}

del(x);

status[x]=intree;

top++;

}

}

for(x=2;x<=totNodes;x++)

cout<<”(“<<x<<”,”<<b[x]<<”)\n”;

delay(10);

}

Prim algorithm

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Procedure Prim(input G : graf, output T : pohon)

{ Membentuk pohon merentang minimum T dari

graf terhubung G.

Masukan : graf-berbobot terhubung G = (V, E),

dimana V = n

Keluaran : pohon rentang minimum T = (V, E’)

}

Deklarasi

i, p, q, u, v : integer

Algoritma

Cari sisi (p,q) dari E yang berbobot terkecil

T {(p,q)}

for i 1 to n-2 do

Pilih sisi (u,v) dari E yang bobotnya terkecil

namun bersisian dengan suatu simpul di

dalam T

T T {(u,v)}

endfor

Bellman Ford algorithm

procedure BellmanFord(list vertices, list edges, vertex source)
   // This implementation takes in a graph, represented as lists of vertices
   // and edges, and modifies the vertices so that their distance and
   // predecessor attributes store the shortest paths.

   // Step 1: Initialize graph
   for each vertex v in vertices:
       if v is source then v.distance := 0
       else v.distance := infinity
       v.predecessor := null

   // Step 2: relax edges repeatedly
   for i from 1 to size(vertices)-1:       
       for each edge uv in edges: // uv is the edge from u to v
           u := uv.source
           v := uv.destination             
           if v.distance > u.distance + uv.weight:
               v.distance := u.distance + uv.weight
               v.predecessor := u

   // Step 3: check for negative-weight cycles
   for each edge uv in edges:
       u := uv.source
       v := uv.destination
       if v.distance > u.distance + uv.weight:
           error "Graph contains a negative-weight cycle"

DFS & BFS algorithm

algoritma DFS

dfs(graph G)
{
  list L = empty
  tree T = empty
  choose a starting vertex x
  search(x)
  while(L is not empty)
  {
    remove edge (v, w) from beginning of L
    if w not yet visited
    {
      add (v, w) to T
      search(w)
    }
  }
}

search(vertex v)
{
  visit v
  for each edge (v, w)
    add edge (v, w) to the beginning of L
}

BFS algoritma


 
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 Inisialisasi Matriks Boolean yang diset false 

Inisialisasi
Sebuah Antrian Kosong 

Buat Simpul
Asal 

Masukkan
Simpul Asal ke dalam Antrian 

Buat Simpul
Tujuan 

Boolean
ketemu=false 

int jarak =
1 

While
AntrianTidakKosong and not ketemu do  

Ambil simpul n dari antrian  

if n=simpul_tujuan then

ketemu=true   

output(jarak)   

return solusi  

else

increment
(level)   

Bangkitkan
suksesor n  dari n   

for setiap
suksesor n  dari n  

if(dikunjungi[posisi  x  dari 

n ][posisi  y  dari  n
]=false) 

then

Set parent dari n  menjadi n 

Masukkan
n  ke dalam antrian 

endfor

endwhile