find second smallest element in Fibonacci Heap

Question

I need to describe an algorithm that finds the second smallest element in a Fibonacci-Heap using the Operations: Insert, ExtractMin, DecreaseKey and GetMin. The last one is an algorithm previously implemented to find and return the smallest element of the heap.

I thought I'd start by extracting the minimum, which results in its children becoming roots. I could then use GetMin to find the second smallest element. But it seems to me that I'm overlooking other cases because I don't know when to use Insert and DecreaseKey, and the way the question is phrased seems to suggest I should need them.

• ratchet freak: a=extractMin; res=getMin; insert(a);return res
• Longeyes: Why do I need to insert a again? And also, does it not matter that I still haven't used DecreaseKey then?
• ratchet freak: only if you want to keep the heap unchanged after the call to getSecondMin, and no it doesn't matter that you didn't use it
• C.B.: @ratchetfreak : Why not post your comment as an answer? :)

Answer 1

a=extractMin; res=getMin; insert(a);return res;

[Folks: when answers are posted as comments, would you please add them as an answer and close the question. Thanks]