Let be an associative binary operator, and let a be an attribute maintained in each node of a red black tree Suppose that we want to include in each node x an additional attribute f such that x f x 1 a x 2 a x m a, where x 1 x 2 , ,x m is the inorder listing of nodes in the subtree rooted at x Show how to update the f attributes in O(1) time after a rotation Modify your argument slightly to apply it to the size attributes in order statistic trees

Question: Let be an associative binary operator, and let a be an attribute maintained in each node of a red-black tree. Suppose that we want

Let ⊗ be an associative binary operator, and let a be an attribute maintained in each node of a red-black tree. Suppose that we want to include in each node x an additional attribute f such that x.f = x₁.a ⊗ x₂.a ⊗ …⊗ x_m.a, where x₁. x₂, . . . ,x_m is the inorder listing of nodes in the subtree rooted at x. Show how to update the f attributes in O(1) time after a rotation. Modify your argument slightly to apply it to the size attributes in order-statistic trees.

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Answer We firstly define the pivot point of a tree if this pivot point holds then the tree has some perfect cycle Now to update the pivot points We us... View full answer

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