Editing Binomial heap
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* A node in a binomial tree can have more than two children. | * A node in a binomial tree can have more than two children. | ||
* Binomial trees are fully max-heap-ordered, rather than simply left-max-heap-ordered like power-of-two trees. | * Binomial trees are fully max-heap-ordered, rather than simply left-max-heap-ordered like power-of-two trees. | ||
− | A binomial tree of height 0 is a single node. A binomial tree of height <math>k > 0</math> consists of a root node with <math>k</math> children. | + | A binomial tree of height 0 is a single node. A binomial tree of height <math>k > 0</math> consists of a root node with <math>k</math> children. The subtree rooted at each child is a tree of a different height. |
When we merge two binomial trees of the same size, we simply make the smaller root the child of the larger root. Observe that this instantly gives a binomial tree of twice the size (whose height is then one greater than the heights of the two original trees). When we split a binomial tree of height <math>k > 0</math>, we simply detach the subtree of height <math>k-1</math>, giving two binomial trees of size <math>k-1</math>. | When we merge two binomial trees of the same size, we simply make the smaller root the child of the larger root. Observe that this instantly gives a binomial tree of twice the size (whose height is then one greater than the heights of the two original trees). When we split a binomial tree of height <math>k > 0</math>, we simply detach the subtree of height <math>k-1</math>, giving two binomial trees of size <math>k-1</math>. | ||