一种生成策略可解数独线索的精确方法
Exact Method for Generating Strategy-Solvable Sudoku Clues
摘要：
数独谜题通常在首字母数字的排列上有一个规则的模式，通常可以用已知的解决方法来解决，称为策略。在本文中，我们考虑生成这样的数独实例的问题。我们引入了一个严格的框架来讨论数独实例的策略可解性。这使得我们不仅可以处理已知的策略，而且可以在一些合理的假设下处理一般策略。我们提出了一个精确的方法来确定数独线索的一组给定的线索位置，是可解的一组给定的策略。这是第一个精确的方法，除了一个平凡的蛮力搜索。除了线索生成，我们提出了一个应用程序，我们的方法来确定最小数量的战略可解的数独线索的问题。我们进行实验，以评估我们的方法，不同的位置和数量的线索随机。对于许多网格，我们的方法在$1$分钟内终止。然而，随着线索的数量越来越接近$20$，运行时间迅速增加，并超过设置为$600$秒的时间限制。我们还评估了我们的方法与$17$线索的位置，从已知的最小数独的几个实例，看看效率决定不可解性。
英文摘要：
A Sudoku puzzle often has a regular pattern in the arrangement of initial digits and it is typically made solvable with known solving techniques, called strategies. In this paper, we consider the problem of generating such Sudoku instances. We introduce a rigorous framework to discuss solvability for Sudoku instances with respect to strategies. This allows us to handle not only known strategies but also general strategies under a few reasonable assumptions. We propose an exact method for determining Sudoku clues for a given set of clue positions that is solvable with a given set of strategies. This is the first exact method except for a trivial brute-force search. Besides the clue generation, we present an application of our method to the problem of determining the minimum number of strategy-solvable Sudoku clues. We conduct experiments to evaluate our method, varying the position and the number of clues at random. Our method terminates within $1$ minutes for many grids. However, as the number of clues gets closer to $20$, the running time rapidly increases and exceeds the time limit set to $600$ seconds. We also evaluate our method for several instances with $17$ clue positions taken from known minimum Sudokus to see the efficiency for deciding unsolvability.
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