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Unformatted text preview: IE 495 Lecture 12 October 5, 2000 Reading for This Lecture Primary ¡ Horowitz and Sahni, Chapter 2, Section 3 ¡ Kozen, Lectures 811 Review From Last Time Binomial Trees The binomial tree of rank i ( B i ) is defined recursively. B i consists of a root with i children B 0 , . . ., B i1 . B B 3 B 2 B 1 Binomial Heaps A binomial heap is a collection of heap ordered binomial trees and a pointer to the overall max/min. No more than one tree of each rank is allowed. The children of each vertex are maintained in a circular linked list . The basic operation is linking . Two trees of rank i can be combined into one tree of rank i+1 in constant time. Eager Meld We can combine two heaps by performing a meld() reminiscent of binary addition. Successively link trees of equal rank and " carry " one if necessary. Must track the position of the new min/max element. This operation takes O ( log n ) time. Inserting into a Binomial Heap To insert() an element: ¡ Make a new heap from the single element to be inserted....
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This note was uploaded on 08/06/2008 for the course IE 495 taught by Professor Linderoth during the Fall '08 term at Lehigh University .
 Fall '08
 Linderoth
 Operations Research

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