Analysis Of Fibonacci Heaps
Actual
Amortized
Insert O(1) O(1)
Remove min (or max)
O(n) O(log n)
Meld O(1) O(1)
Remove O(n) O(log n)
Decrease key (or
increase) O(n) O(1)
MaxDegree
• Let Ni = min # of nodes in any min (sub)tree
whose root has i children.
• N0 = 1.
• N1 = 2.
6
9
5
Ni , i > 1
• Children of b are labeled in the order in which they
became children of b.
c1became a child before c2 did, and so on.
• So, when ck became a child of b, degree(b) >= k –1.
• degree(ck) at the time when ckbecame a child of b
= degree(b) at the time when ckbecame a child of b
>= k – 1.
b
c1c2… … ci
Ni , i > 1
• So, current degree(ck) >= max{0, k – 2}.
• So, Ni = N0 + (Σ0<=q<=i-2Nq) + 1
= (Σ0<=q<=i-2Nq) + 2.
b
c1c2… … ci
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