<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 {
public:
    int removeStones(vector<vector<int>>& stones) {
        unordered_map<int, vector<int>> xmap; // x, node
        unordered_map<int, vector<int>> ymap; // y, node

        vector<pair<int, int>> edges;
        for (int i = 0; i < stones.size(); i ++) {
            int x = stones[i][0];
            int y = stones[i][1];
            if (xmap.find(x) == xmap.end()) {
                vector<int> v = {i};
                xmap.insert({x, v});
            } else {
                xmap[x].push_back(i);
            }
            if (ymap.find(y) == ymap.end()) {
                vector<int> v = {i};
                ymap.insert({y, v});
            } else {
                ymap[y].push_back(i);
            }
        }

        // cout << xmap[1].size() << " " << ymap[0].size() << endl;

        for (int i = 0; i < stones.size(); i ++) {
            int x = stones[i][0];
            int y = stones[i][1];
            // cout << x << " " << y << "!!" << endl;

            if (xmap.find(x) != xmap.end()) {
                for (int j = 0; j < xmap[x].size(); j ++) {
                    // cout << xmap[x][j] << endl;
                    if (xmap[x][j] != i) {
                        edges.push_back({xmap[x][j], i});
                        break;
                    }
                }
            }
            if (ymap.find(y) != ymap.end()) {
                
                for (int j = 0; j < ymap[y].size(); j ++) {
                    
                    if (ymap[y][j] != i) {
                        // cout << ymap[y][j] << " " << i << "sdfsfsd" << endl;
                        edges.push_back({ymap[y][j], i});
                        break;
                    }
                }
            }
        }

        unordered_map<int, vector<int>> graph;
        buildGraph(graph, edges);

        int cnt = 0;
        vector<bool> visited(stones.size(), false);
        for (int i = 0; i < stones.size(); i ++) {
            if (visited[i]) {
                continue;
            }

            // cout << i << endl;

            dfs(i, graph, visited);
            cnt ++;
        }
        return stones.size() - cnt;
    }

    void buildGraph(unordered_map<int, vector<int>>& graph, vector<pair<int, int>>& edges) {
        for (int i = 0; i < edges.size(); i ++) {
            int n1 = edges[i].first;
            int n2 = edges[i].second;
            // cout << n1 << " " << n2 << endl;
            if (graph.find(n1) == graph.end()) {
                vector<int> v;
                graph.insert({n1, v});
            }
            if (graph.find(n2) == graph.end()) {
                vector<int> v;
                graph.insert({n2, v});
            }

            graph[n1].push_back(n2);
            graph[n2].push_back(n1);
        }
    }

    void dfs(int node, unordered_map<int, vector<int>>& graph, vector<bool>& visited) {
        // cout << node << endl;
        visited[node] = true;
        if (graph.find(node) == graph.end()) {
            return;
        }
        for (int i = 0; i < graph[node].size(); i ++) {
            if (!visited[graph[node][i]]) {
                dfs(graph[node][i], graph, visited);
            }
        }
    }
};

// 1 1 0
// 1 0 1
// 0 1 1
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