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Say you've found places for the first $$$i$$$ knights and are looking for spots for the $$$i + 1$$$-th knight. How many of the previous knights do you actually care about in terms of where the $$$i + 1$$$-th knight can go?
The dimensions:
dp[rows][3][5][5][7]
If you think you know what to do, good luck, and I recommend recursion. Create the states in a way that will make it convenient to "shift" each knight when you place another one.
Thank you galen_colin! I tried to implement the idea again with the optimization you mentioned but unfortunately I got
TLE
!Here is my implementation including both top-down and bottom-up approaches
I appreciate your help.