The execution of BINOMIAL-HEAP-UNION. (a) Binomial heaps H1 and H2.
(b) Binomial heap H is the output of BINOMIAL-HEAP-MERGE(H1, H2). Initially, x is the first root on the root list of H . Because both x and next-x have degree 0 and
key[x] < key[next-x], case 3 applies.
(c) After the link occurs, x is the first of three roots with the same degree, so case 2 applies.
(d) After all the pointers move down one position in the root list, case 4 applies, since x is the first of two roots of equal degree.
(e) After the link occurs, case 3 applies.
(f) After another link, case 1 applies, because x has degree 3 and next-x has degree 4.this iteration of the while loop is the last, because after the pointers move down one position in the root list, next-x = NIL.
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