We present a simple $O(n^4)$-time algorithm for computing optimal search trees with two-way comparisons. The only previous solution to this problem, by Anderson et al., has the same running time, but is significantly more complicated and is restricted to the variant where only successful queries are allowed. Our algorithm extends directly to solve the standard full variant of the problem, which also allows unsuccessful queries and for which no polynomial-time algorithm was previously known. The correctness proof of our algorithm relies on a new structural theorem for two-way-comparison search trees.

中文翻译：

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具有双向比较的最优搜索树的简单算法

我们提出了一种简单的$ O（n ^ 4）$时间算法，用于通过双向比较来计算最佳搜索树。Anderson等人以前针对该问题的唯一解决方案具有相同的运行时间，但运行起来却复杂得多，并且仅限于仅允许成功查询的变量。我们的算法直接扩展为解决问题的标准完全变体，它还允许不成功的查询，并且以前没有多项式时间算法是已知的。我们算法的正确性证明依赖于双向比较搜索树的新结构定理。