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Binomial heap
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=== Find minimum === To find the '''minimum''' element of the heap, find the minimum among the roots of the binomial trees. This can be done in <math>O(\log n)</math> time, as there are just <math>O(\log n)</math> tree roots to examine.<ref name="clrs" /> By using a pointer to the binomial tree that contains the minimum element, the time for this operation can be reduced to <math>O(1)</math>. The pointer must be updated when performing any operation other than finding the minimum. This can be done in <math>O(\log n)</math> time per update, without raising the overall asymptotic running time of any operation.{{cn|date=October 2019}}
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