For example construction of a binomial heap with 13 nodes-

1. First write its binary representation,like for 13, its 1101.

2. So,we'll have trees 0,2,3 that is B0,B2,B3 with B0->1, B2->4 AND B3-> 8 nodes.


A binomial heap H with n = 13 nodes.

 (a) The heap consists of binomial trees B0, B2, and B3, which have 1, 4, and 8 nodes respectively, totaling n = 13 nodes. Since each binomial tree is min-heap-ordered, the key of any node is no less than the key of its parent. Also shown is the root list, which is a linked list of roots in order of increasing degree. 

(b) A more detailed representation of binomial heap H . Each binomial tree is stored in the left child, right-sibling representation, and each node stores its degree.

This heap consists of at most [lg n]+1 binomial trees i.e. 3+1=4.                                  

                                                                               continue representation-of-binomial-heaps.php

                                                                                                                                                                                                                                                                         binomial-trees-properties.php

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