Lecture 10

Fibonacci Heaps

Note

• A Fibonacci heapis a collection of min-heap-ordered trees.
• Trees within Fibonacci heaps are rooted but unordered.

Note

\[ \Phi(H) = t(H) + 2 m(H) \]

Note

We assume that there is a known upper bound \(D(n)\) on the maximum degree of any node in ann-node Fibonacci heap.

Mergeable-heap operations

Note

FIB-HEAP-INSERT(H,X)

x.degree = 0, x.p = NULL
x.child = NULL， x.mark = FALSE

if H.min == NIL
    create a root list for H contianing just x
    H.min = x
else insert x into H's root list
    if x.key < H.min.key
        H.min= x
H.n += 1

Just Insert a node into root list.

Uniting

H = MAKE-FIB-HEAP()
H.min = H1.min
concatenate the root lists of H2 and H
if(H1.min == NIL) or (H2.min != NIL and H2.min.key < H1.min.key)
    H.min=H2.min
H.n=H1.n+H2.n
return H