So I’m doing this problem, and in the solution it says this:
Because of the constraints of the DP state, the beginning and ending squares are uniquely determined by their row.
But they… aren’t.
There are multiple ways to get from, say, row 4 to row 10 traversing only 7 squares. So why do they say this?
Well… seconds after posting this question, I realized the answer and I’m going to post it for any other people who have the same question.
There’s only 1 way to get from row 4 to row 10 while traversing only 7 squares due to the palindrome condition- the moves have to be sort of “centered” around the diagonal, or else it wouldn’t be a palindrome.
Ah, the classic “not figuring out a solution for hours and then figuring it out seconds after asking someone” situation. Glad you figured it out.