How a Chinese Drama Illustrates Data Structures, Algorithms, and Time Complexity

Big Data Analogy and Recommendation Algorithm

The "Great Archive Technique" (大案牍术) described in the drama is a structured repository of historical case files. By indexing these archival records and applying a recommendation algorithm, the system can quickly retrieve relevant cases, support inference, and suggest actions—functionally similar to modern big‑data platforms.

Map of Chang’an and Time‑Complexity Analysis

Villains initially attempt a brute‑force search for a target across the city. Scanning every sector for every possible target yields a quadratic time complexity O(n²), where n is the number of distinct city sectors.

When they obtain a detailed city map, the problem becomes a single linear pass over the map, reducing the complexity to O(n).

The protagonist treats the city as a three‑dimensional graph (streets, canals, rooftops). By using a “space‑for‑time” strategy—jumping across walls and rooftops—he can perform a divide‑and‑conquer traversal analogous to binary search, achieving logarithmic time O(log n). This demonstrates how a different data structure (3‑D adjacency) and algorithm dramatically improve performance.

Watchtower Communication and Simple Encryption

The series depicts a network of eight‑zhang (≈2.7 m) watchtowers distributed throughout Chang’an. After a drum signal, each tower displays a pattern of squares formed by lanterns. The patterns are publicly visible, but their semantic meaning is defined in a secret codebook known only to authorized personnel. This constitutes a basic substitution cipher: the visual pattern is the ciphertext, and the codebook provides the mapping to plaintext.