This paper presents a gentle tutorial and a structured reformulation of Bock's 1971 Algol procedure for constructing minimum directed spanning trees. Our aim is to make the original algorithm readable and reproducible for modern readers, while highlighting its relevance as an exact decoder for nonprojective graph based dependency parsing. We restate the minimum arborescence objective in Bock's notation and provide a complete line by line execution trace of the original ten node example, extending the partial trace given in the source paper from initialization to termination. We then introduce a structured reformulation that makes explicit the procedure's phase structure, maintained state, and control flow, while preserving the logic of the original method. As a further illustration, we include a worked example adapted from {jurafsky-martin-2026-book} for dependency parsing, showing how a maximum weight arborescence problem is reduced to Bock's minimum cost formulation by a standard affine transformation and traced under the same state variables.

翻译：本文提供Bock于1971年提出的构造最小有向生成树的Algol过程的温和教程与结构化重构。我们的目标是使该原始算法对现代读者具备可读性与可复现性，同时强调其作为非投影图基依存句法分析精确解码器的现实意义。我们以Bock的符号体系重新表述最小树状图目标，并给出原始十节点示例的完整逐行执行轨迹（将源论文中从初始化到终止的部分轨迹加以扩展）。继而引入结构化重构方法，在保持原始逻辑的前提下，明确揭示了该过程的阶段结构、维护状态及控制流。为进一步阐释，我们改编自Jurafsky与Martin（2026版教材）的依存句法分析示例，展示了如何通过标准仿射变换将最大权重树状图问题归约至Bock的最小代价框架，并在相同状态变量下完成完整轨迹追踪。