It seems that some information/constraints are missing from the question. It does not specify the boundary/limits of the coordinates which we need to consider. Like what is the max unit on the x and y axis which we need to consider;
Grand Temple problem : extra information needed
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If the constraints for x and y are so high, then I think the answer to the given answer should also be quite a big number since if lets say there are towers at the given points, the temple can be made starting from a length/breadth till the limit of x/y.
My query is that the output will not be 2 for the given test case if the king has such huge amount of land (100001 on both x and y axis). Only 3 coordinates with rivers flowing at (1,1), (2,4) and (5,2). By drawing a diagram it seems that a huge area is empty towards the right side (x-axis) and upper side (Y-axis). I think the constraints should be a lower number to arrive at this answer.
hey @shubh17, it will be 2 only. constraints x[100001],y[100001] means maximum 100001 coordinates of river are given.