Algorithm for Fibonacci Heap and Operations on it

Make-Fibonacci-Heap()

n[H] := 0

min[H] := NIL

return H

Fibonacci-Heap-Minimum(H)

return min[H]

Fibonacci-Heap-Link(H,y,x)

remove y from the root list of H

make y a child of x

degree[x] := degree[x] + 1

mark[y] := FALSE

CONSOLIDATE(H)

for i:=0 to D(n[H])

     Do A[i] := NIL

for each node w in the root list of H

    do x:= w

       d:= degree[x]

       while A[d] <> NIL

           do y:=A[d]

              if key[x]>key[y]

               then exchange x<->y

              Fibonacci-Heap-Link(H, y, x)

              A[d]:=NIL

             d:=d+1

       A[d]:=x

min[H]:=NIL

for i:=0 to D(n[H])

    do if A[i]<> NIL

          then add A[i] to the root list of H

               if min[H] = NIL or key[A[i]]<key[min[H]]

                  then min[H]:= A[i]

Fibonacci-Heap-Union(H1,H2)

H := Make-Fibonacci-Heap()

min[H] := min[H1]

Concatenate the root list of H2 with the root list of H

if (min[H1] = NIL) or (min[H2] <> NIL and min[H2] < min[H1])

   then min[H] := min[H2]

n[H] := n[H1] + n[H2]

free the objects H1 and H2

return H

Fibonacci-Heap-Insert(H,x)

degree[x] := 0

p[x] := NIL

child[x] := NIL

left[x] := x

right[x] := x

mark[x] := FALSE

concatenate the root list containing x with root list H

if min[H] = NIL or key[x]<key[min[H]]

        then min[H] := x

n[H]:= n[H]+1

Fibonacci-Heap-Extract-Min(H)

z:= min[H]

if x <> NIL

        then for each child x of z

                do add x to the root list of H

                   p[x]:= NIL

             remove z from the root list of H

             if z = right[z]

                then min[H]:=NIL

                else min[H]:=right[z]

                     CONSOLIDATE(H)

             n[H] := n[H]-1

return z

Fibonacci-Heap-Decrease-Key(H,x,k)

if k > key[x]

   then error "new key is greater than current key"

key[x] := k

y := p[x]

if y <> NIL and key[x]<key[y]

   then CUT(H, x, y)

        CASCADING-CUT(H,y)    

if key[x]<key[min[H]]

   then min[H] := x

CUT(H,x,y)

Remove x from the child list of y, decrementing degree[y]

Add x to the root list of H

p[x]:= NIL

mark[x]:= FALSE

CASCADING-CUT(H,y)

z:= p[y]

if z <> NIL

  then if mark[y] = FALSE

       then mark[y]:= TRUE

       else CUT(H, y, z)

            CASCADING-CUT(H, z)

Fibonacci-Heap-Delete(H,x)

Fibonacci-Heap-Decrease-Key(H,x,-infinity)

Fibonacci-Heap-Extract-Min(H)