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Why is there a need to scan each root node of the binomial trees in a binomial heap to find the minimum?

For example, why can't the true root of the binomial heap, the one that leads to the root nodes of the binomial trees, be the minimum? If it is not the minimum, then what value should it be?

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  • $\begingroup$ Just because the minimum could be at a particular root doesn't mean it is guaranteed to be at that place. $\endgroup$ – D.W. Mar 15 '18 at 19:31
  • $\begingroup$ Does that mean for the root that connects to all the roots of the binomial trees, it doesn't actually have a value? if there is a value, (e.g. 13 nodes in such a heap, 1 root, +8 from 1 binomial tree and +4 from another binomial tree). How do you get the value of that 1 root? and how is it chosen? $\endgroup$ – oldselflearner1959 Mar 15 '18 at 19:48
  • $\begingroup$ I don't understand what you are asking. Perhaps it would help if you edited the question to provide more context, show an example, etc. Please define all terms. I don't know what you mean by a "true root". I don't know what you mean by "doesn't actually have a value". Perhaps it would help if you found a textbook that describes binomial heaps and read that. Don't just rely on Wikipedia as your only source; it's often not an ideal source for self-learning. $\endgroup$ – D.W. Mar 15 '18 at 20:00

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