MHB Comparing Binomial & Binary Heaps: What's the Difference?

AI Thread Summary
Binomial heaps are priority queue data structures that differ from binary heaps in their structure and merging capabilities. Unlike binary heaps, which have a maximum of two child nodes per node, binomial heaps can have a varying number of children based on the depth of the node, specifically $\binom n d$ children at depth $d$. The union operation in binomial heaps allows for the merging of two heaps of order $k-1$ into a single heap of order $k$ by attaching one heap as a left child to the other, facilitating efficient merging and maintaining the properties of the heap.
mathmari
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Hey! :o

I am reading about binomial heaps. They are priority queue data structures similar to the binary heap, right? (Wondering) Which is the difference between these two heaps? (Wondering)
I haven't really understood the operation of the binomial heaps Union. Could you explain it to me? (Wondering)
 
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mathmari said:
Hey! :o

I am reading about binomial heaps. They are priority queue data structures similar to the binary heap, right? (Wondering) Which is the difference between these two heaps? (Wondering)
I haven't really understood the operation of the binomial heaps Union. Could you explain it to me? (Wondering)

Well... apparently a binomial heap does not have up to 2 child nodes at each node, but an amount depending on how high we are in the tree. In particular that means that we have $\binom n d$ children at depth $d$ instead of $2^d$.
A "merge" of two binomial heaps of order $k-1$ leads trivially to a binomial heap of order $k$ by adding one heap as a left child to the other tree.
 
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