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The concept of binomial trees and binomial heaps, focusing on their definition, merge operation, and insertion process. Binomial trees are recursively defined structures with the heap-order property, while binomial heaps are sets of binomial trees with different ranks. The merge operation is used to combine two trees, with rule i for trees of different sizes and rule ii for trees of the same size. The insertion operation recursively applies the merge rules. Useful for students in computer science or mathematics, particularly those studying data structures and algorithms.
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Binomial Tree Definition • B 0 is a single node
Bk B 0 Bk- Binomial heap is a set of binomial trees with different ranks
Binomial Tree Binomial Heap Yes Yes
Yes Yes
No No
No Yes
B
B
B
B
Rule II: Merge two trees with same size Select the one with the smallest root, and attach the other one to the root as the right most child example 1:
example2:
Insert 6:
1.2. Find the Min RootDelete the Root
Deleting the min:
Merging: Step1:
