Flags are distributed randomly on a large board. Starting from the corner position your goal is to capture as many flags as possible in at most N moves.
The board is described by a matrix B with 1's at the flag positions, and 0's otherwise.
B = [0 0 1 1; 0 0 1 1; 0 0 1 0];
N = 6;
You are starting at the top-left corner (row=1, col=1) and are allowed N steps (steps are up/down/left/right movements, no diagonal movements allowed).
Return a trajectory attempting to maximize the number of flags captured. The output of your function should be a Nx2 matrix of the form [row, col] (not including the initial [1,1] position) visiting as many flags as possible.
path = [1 2; 1 3; 1 4; 2 4; 2 3; 3 3];
This solution captures all 5 flags on the board.
Your function will receive a score equal to the number of non-visited flags across all 50 of the testsuite problems. You need to leave at most 10,000 flags univisited (among 50,000 total flags) to pass this problem.
The boards and number of movements allowed will be large. Optimizing over all possible trajectories is very likely to time out.