After reading, I have two questions pending on this approach:

a. I could understand that for 1-d scenario, it is optimal to find "median". However, this approach applies this theory to 2-d senario: "Then we calculate the total distance as the sum of two independent 1D problems."

How to prove 1-d scenario correctness to a 2-d scenario? Or more generally, may I apply 1-d scenario correctness to an n-d scenario?

b. Honestly, the solution specifically said that "in the code above we **do not need to sort rows**". Could anyone give me some clue on why we ignore this soring on rows?

Thanks a lot !!