# lec13 - Analysis Of Binomial Heaps Leftist trees O(log n...

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Analysis Of Binomial Heaps Binomial heaps Leftist trees Actual Amortized Insert O(log n) O(1) O(1) Remove min (or max) O(log n) O(n) O(log n) Meld O(log n) O(1) O(1)

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Operations Insert Add a new min tree to top-level circular list. Meld Combine two circular lists. Remove min Pairwise combine min trees whose roots have equal degree. O(MaxDegree + s) , where s is number of min trees following removal of min element but before pairwise combining.
Binomial Trees B 1 B 3

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All Trees In Binomial Heap Are Binomial Trees Initially, all trees in system are Binomial trees (actually, there are no trees initially). Assume true before an operation, show true after the operation. Insert creates a B . Meld does not create new trees. Remove Min Reinserted subtrees are binomial trees. Pairwise combine takes two trees of equal degree and makes one a subtree of the other.
Complexity of Remove Min Let n be the number of operations performed.

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• Spring '10
• sartajsahani
• binomial heap, Amortized analysis, Potential method, accounting method, remove min

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