论文标题
自动方程和有效的随机生成二进制树
Holonomic equations and efficient random generation of binary trees
论文作者
论文摘要
弹能方程是递归方程，可以有效地计算组合对象的数量。 r {é}我表明，与二进制树相关的载体方程产生了有效的二进制树的线性随机发生器。 我将此范式扩展到motzkin树和schr {Ö} der树，并表明，尽管有微小的差异，但我的算法会生成随机的schr {Ö} der树具有线性的预期复杂性，并且我的算法在O（n）中产生motzkin树的算法在O（n）的预期复杂性中才能实现特定的Oracle与O（1）复杂性实现特定的Oracle。 对于Motzkin树，我提出了一个解决方案，该解决方案适用于现实的值（多达100万人），并产生有效的算法。
Holonomic equations are recursive equations which allow computing efficiently numbers of combinatoric objects. R{é}my showed that the holonomic equation associated with binary trees yields an efficient linear random generator of binary trees. I extend this paradigm to Motzkin trees and Schr{ö}der trees and show that despite slight differences my algorithm that generates random Schr{ö}der trees has linear expected complexity and my algorithm that generates Motzkin trees is in O(n) expected complexity, only if we can implement a specific oracle with a O(1) complexity. For Motzkin trees, I propose a solution which works well for realistic values (up to size ten millions) and yields an efficient algorithm.
