On a 2D plane, we place stones at some integer coordinate points.  Each coordinate point may have at most one stone.

Now, a move consists of removing a stone that shares a column or row with another stone on the grid.

What is the largest possible number of moves we can make?

Example 1:

Input: stones = [[0,0],[0,1],[1,0],[1,2],[2,1],[2,2]]
Output: 5

Example 2:

Input: stones = [[0,0],[0,2],[1,1],[2,0],[2,2]]
Output: 3

Example 3:

Input: stones = [[0,0]]

At very first I read this problem, the MOVE operation is described as confusing as heck. I read some explanations on the discussboard, and then finally got the actual meaning.

We can treat each coordinate as two parts (x and y), and can maintain an Union-Find in order to calculate how many groups in the entire field.

 class Solution:
    def removeStones(self, stones: List[List[int]]) -> int:
        UF = {}
        
        def find(x):
            if x != UF[x]:
                UF[x] = find(UF[x])
            return UF[x]
        
        def union(x, y):
            UF.setdefault(x, x)
            UF.setdefault(y, y)
            UF[find(x)] = find(y)


        for i, j in stones:
            print(i, j, ~j)
            union(i, ~j)
            
        return len(stones) - len({find(x) for x in UF})