避免锯齿形的有效路径查找算法

Your current algorithm finds a shortest path, Pmin, but the improved algorithm should find a shortest path that takes minimum number of turns (Pmin, Tmin). General solution requires that you work with pair of numbers instead of a single number. If newly found Pnew is smaller than current Pmin OR if it is equal but Tnew is smaller than Tmin then take (Pnew, Tnew) as new minimal path.

If the board is small enough you could still use a single number as you currently use, but this number must be a compound number C = P * N + T, where N is sufficiently large and sufficiently small constant number. It must be larger than largest possible T for that board, which is almost the total number of tiles in the board. It must be also small enough so that there is no integer overflow when algorithm happens to handle the largest path in the board, which is also the total number of tiles in the board. So N must satisfy these two terms (B is total number of tiles in the board):

N > B
B * N < INT_MAX

If B is larger than SQRT(INT_MAX) then this system is unsolvable, and you should go with pair of values. N should be SQRT(INT_MAX), which for 2³² is 2¹⁶.

现在的主要问题是如何计算所有匝数，但这取决于您使用的算法。添加该部分应该不会太困难。