<p>On a 2D plane, we place <code>n</code> stones at some integer coordinate points. Each coordinate point may have at most one stone.</p>

<p>A stone can be removed if it shares either <strong>the same row or the same column</strong> as another stone that has not been removed.</p>

<p>Given an array <code>stones</code> of length <code>n</code> where <code>stones[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> represents the location of the <code>i<sup>th</sup></code> stone, return <em>the largest possible number of stones that can be removed</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> stones = [[0,0],[0,1],[1,0],[1,2],[2,1],[2,2]]
<strong>Output:</strong> 5
<strong>Explanation:</strong> One way to remove 5 stones is as follows:
1. Remove stone [2,2] because it shares the same row as [2,1].
2. Remove stone [2,1] because it shares the same column as [0,1].
3. Remove stone [1,2] because it shares the same row as [1,0].
4. Remove stone [1,0] because it shares the same column as [0,0].
5. Remove stone [0,1] because it shares the same row as [0,0].
Stone [0,0] cannot be removed since it does not share a row/column with another stone still on the plane.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> stones = [[0,0],[0,2],[1,1],[2,0],[2,2]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> One way to make 3 moves is as follows:
1. Remove stone [2,2] because it shares the same row as [2,0].
2. Remove stone [2,0] because it shares the same column as [0,0].
3. Remove stone [0,2] because it shares the same row as [0,0].
Stones [0,0] and [1,1] cannot be removed since they do not share a row/column with another stone still on the plane.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> stones = [[0,0]]
<strong>Output:</strong> 0
<strong>Explanation:</strong> [0,0] is the only stone on the plane, so you cannot remove it.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= stones.length &lt;= 1000</code></li>
	<li><code>0 &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 10<sup>4</sup></code></li>
	<li>No two stones are at the same coordinate point.</li>
</ul>

class Solution {
    unordered_set<int> removed;
    unordered_map<int, vector<int>> mx, my;
public:
    int removeStones(vector<vector<int>>& stones) {
        int result = 0;
        for (auto &stone: stones) {
            mx[stone[0]].push_back(stone[1]);
            my[stone[1]].push_back(stone[0]);
        }

        for (auto &stone: stones) {
            int k = (stone[0] << 16) | stone[1];
            if (removed.find(k) == removed.end()) {
                removed.insert(k);
                result += dfs(stone[0], stone[1]) - 1;
            }
        }
        return result;
    }

    int dfs(int x, int y) {
        auto dx = my.find(y);
        int count = 0;
        if (dx != my.end()) {
            auto v = dx->second;
            my.erase(y);
            for (auto nx: v) {
                int k = (nx<<16) | y;
                if (removed.find(k) == removed.end()) {
                    removed.insert(k);
                    count += dfs(nx, y);
                }
            }
        }

        auto dy = mx.find(x);
        if (dy != mx.end()) {
            auto v = dy->second;
            mx.erase(x);
            for (auto ny: v) {
                int k = (x<<16) | ny;
                if (removed.find(k) == removed.end()) {
                    removed.insert(k);
                   count += dfs(x, ny);
                }
            }
        }
        return count + 1;
    }
};
29006