Solving puzzle problems using computer-aided methods is becoming more common with applications in forensic science, restoration, banking system, and multimedia. However, only a few surveys have been published on this topic, the most recent being more than a decade old. The scope of 2D puzzle problems is extensive, and the number of computer-aided methods has increased in recent years. In this paper, we have presented a comprehensive survey to pave a roadmap for researchers dealing with puzzle problems. This study classifies 2D puzzle problems in a novel way, considering many examples such as dissection, combinatorial and double-sided puzzles and reclassifies computer-aided methods to cover the studies carried out in recent years. Various strategies (pre-grouping and global consistency approach) have been investigated to solve the puzzle problem effectively. The computer-aided methods have been examined deeply, including many recent methods related to squared jigsaw puzzles, torn photographs, banknotes, and fragmented documents, and they are compared to each other. In addition, new topics such as combining mosaic pieces and Islamic architectural motif puzzle problems have been proposed to the interest of researchers. In conclusion, our study shows many research opportunities that are not yet solved by any computer-aided method.

使用计算机辅助方法解决难题在法医学、修复、银行系统和多媒体领域的应用中变得越来越普遍。然而，关于这个主题的调查只有几项，最近的调查已有十多年的历史了。二维拼图问题的范围很广泛，近年来计算机辅助方法的数量也在增加。在本文中，我们提出了一项全面的调查，为研究人员处理难题提供了路线图。这项研究以一种新颖的方式对二维拼图问题进行了分类，考虑了解剖、组合和双面拼图等许多例子，并对计算机辅助方法进行了重新分类，以涵盖近年来进行的研究。人们已经研究了各种策略（预分组和全局一致性方法）来有效解决难题。计算机辅助方法已被深入研究，包括许多最近与方形拼图、撕裂的照片、钞票和碎片文件相关的方法，并将它们相互比较。此外，诸如组合马赛克碎片和伊斯兰建筑主题拼图问题等新主题也引起了研究人员的兴趣。总之，我们的研究显示了许多计算机辅助方法尚未解决的研究机会。诸如组合马赛克碎片和伊斯兰建筑主题拼图问题等新主题已经引起了研究人员的兴趣。总之，我们的研究显示了许多计算机辅助方法尚未解决的研究机会。诸如组合马赛克碎片和伊斯兰建筑主题拼图问题等新主题已经引起了研究人员的兴趣。总之，我们的研究显示了许多计算机辅助方法尚未解决的研究机会。