算法导论[Exercises 14.2-4]

红黑树节点字段更新

最新推荐文章于 2022-09-14 20:37:13 发布

最新推荐文章于 2022-09-14 20:37:13 发布 · 86 阅读

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#算法 #F#

本文探讨了在红黑树中维护一个额外字段f的方法，该字段存储从根到每个节点路径上的所有a值的累积结果。通过保持不变式f(x)=f(left[x])*a[x]*f(right[x])，文章详细说明了如何在旋转操作中高效更新这些值，并扩展到顺序统计树的大小字段。

Exercises 14.2-4: ⋆

Let * be an associative binary operator, and let a be a field maintained in each node of a red-black tree. Suppose that we want to include in each node x an additional field f such that f[x] = a[x₁] * a[x₂] * ··· * a[x_m], where x₁, x₂,..., x_m is the inorder listing of nodes in the subtree rooted at x. Show that the f fields can be properly updated in O(1) time after a rotation. Modify your argument slightly to show that the size fields in order-statistic trees can be maintained in O(1) time per rotation.