Reordering Variables using ‘Contribution Number' Strategy to Neutralize Sudoku Sets

Humans tend to form decisions intuitively, often based on experience, and without considering optimality; sometimes, search algorithms and their strategies apply the same approach. For example, the minimum remaining values (MRV) strategy selects Sudoku squares based on their remaining values; squares with less number of values are selected first, and the search algorithm continues solving squares until the Sudoku rule is violated. Then, the algorithm reverses the steps and attempts different values. The MRV strategy reduces the backtracking rate; however, when there are two or more blank squares with the same number of minimum values, such strategy selects any of these blank squares randomly. In addition, MRV continues to target squares with minimum values, ignoring that some of those squares could be considered ‘solved’ when they have no influence on other squares. Hence, we aim to introduce a new strategy called Contribution Number (CtN) with the ability to evaluate squares based on their influence on others candidates to reduce squares explorations and the backtracking rate. The results show that the CtN strategy behaves in a more disciplined manner and outperforms MRV in most cases.