标题： 一种关于数独求解算法的研究：回溯法和启发式方法 显示英文标题

标题： A Study Of Sudoku Solving Algorithms: Backtracking and Heuristic

摘要： 本文提出了对数独求解策略的比较分析，重点研究递归回溯和基于启发式的约束传播方法。 使用包含五个难度等级（初级到专家级）的500个谜题的数据集，我们根据平均求解时间评估了性能。 启发式方法始终优于回溯法，在初级谜题中加速比达到1.27倍，在专家级谜题中达到2.91倍。 这些发现强调了启发式策略的有效性，尤其是在处理不同难度等级的复杂谜题时。 显示英文摘要

摘要： This paper presents a comparative analysis of Sudoku-solving strategies, focusing on recursive backtracking and a heuristic-based constraint propagation method. Using a dataset of 500 puzzles across five difficulty levels (Beginner to Expert), we evaluated performance based on average solving time. The heuristic approach consistently outperformed backtracking, achieving speedup ratios ranging from 1.27x in Beginner puzzles to 2.91x in Expert puzzles. These findings underscore the effectiveness of heuristic strategies, particularly in tackling complex puzzles across varying difficulty levels.