recursion - Minimizing cheating of students -

given matrix of size m * n, place k students in such way cheating in exam minimized

what thought :

with brute force approach , create possible combination of students placements , return 1 minimum cheating score, while cheating score defined sum of manhattan distances between each 2 students.

the time & space complexity of approach bad, better solution ?

1) geometric intuition -- perhaps try placing first 4 @ outer corners of square, spiral inwards there?

this approx work "pythagorean distance", maybe can adapt "manhattan distance" equivalent of inward spiralling path & place students linearly along that.

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2) or, place students sequentially @ next cheating-minima; then, once students placed, perturb locations achieve "overall minima".

i 2) best approach.