<p>You are given an <code>n x n</code> binary matrix <code>grid</code>. You are allowed to change <strong>at most one</strong> <code>0</code> to be <code>1</code>.</p>

<p>Return <em>the size of the largest <strong>island</strong> in</em> <code>grid</code> <em>after applying this operation</em>.</p>

<p>An <strong>island</strong> is a 4-directionally connected group of <code>1</code>s.</p>

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

<pre>
<strong>Input:</strong> grid = [[1,0],[0,1]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> Change one 0 to 1 and connect two 1s, then we get an island with area = 3.
</pre>

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

<pre>
<strong>Input:</strong> grid = [[1,1],[1,0]]
<strong>Output:</strong> 4
<strong>Explanation: </strong>Change the 0 to 1 and make the island bigger, only one island with area = 4.</pre>

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

<pre>
<strong>Input:</strong> grid = [[1,1],[1,1]]
<strong>Output:</strong> 4
<strong>Explanation:</strong> Can&#39;t change any 0 to 1, only one island with area = 4.
</pre>

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

<ul>
	<li><code>n == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= n &lt;= 500</code></li>
	<li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li>
</ul>

class Solution {
public:
    vector<vector<pair<int,int>>> parent;
    vector<vector<int>> size;
    int dx[4] = {1,0,-1,0};
    int dy[4] = {0,-1,0,1};
    bool valid(vector<int> a,vector<vector<int>> b){
        for(auto it:b){
            if(it==a){
                return false;
            }
        }
        return true;
    }
    vector<int> find_parent(int i,int j){
        if(parent[i][j].first==i && parent[i][j].second==j){
            return {i,j};
        }
        auto ans = find_parent(parent[i][j].first,parent[i][j].second);
        parent[i][j] = {ans[0],ans[1]};
        return ans;
    }
    void do_union(vector<int> a,vector<int> b){
        a = find_parent(a[0],a[1]);
        b = find_parent(b[0],b[1]);
        if(a!=b){
            parent[b[0]][b[1]] = {a[0],a[1]};
            size[a[0]][a[1]]+=size[b[0]][b[1]];
        }
    }
    void initialize(int n,int m){
        parent.resize(n);
        size.resize(n);
        for(int i=0;i<n;i++){
            parent[i].resize(m);
            size[i].resize(m);
        }
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                parent[i][j] = {i,j};
                size[i][j]=1;
            }
        }
    }
    void dfs(int i,int j,vector<vector<int>>& grid,vector<vector<int>> &vis){
        vis[i][j]=1;
        for(int x=0;x<4;x++){
            int new_i = i+dx[x];
            int new_j = j+dy[x];
            if(new_i>=0 && new_j>=0 && new_i<grid.size() && new_j < grid[0].size() && grid[new_i][new_j]==1 && vis[new_i][new_j]==0){
                do_union({i,j},{new_i,new_j});
                dfs(new_i,new_j,grid,vis);
            }
        }
    }
    int largestIsland(vector<vector<int>>& grid) {
        int n = grid.size();
        int m = grid[0].size();
        initialize(n,m);
        vector<vector<int>> vis(n,vector<int>(m,0));
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(vis[i][j]==0 && grid[i][j]==1){
                dfs(i,j,grid,vis);}
            }
        }
        int ans = 0;
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                ans = max(ans,size[i][j]);
                // cout<<parent[i][j].first<<" "<<parent[i][j].second<<"....";
                cout<<size[i][j]<<" ";
                if(grid[i][j]==0){
                    int curr = 0;
                    vector<vector<int>> curr_parent_array;
                    if(i-1>=0 && grid[i-1][j]==1){
                        auto curr_parent = find_parent(i-1,j);
                        curr_parent_array.push_back(curr_parent);
                        auto curr_size = size[curr_parent[0]][curr_parent[1]];
                        curr = curr + curr_size;
                    }
                    if(j+1<grid[0].size() && grid[i][j+1]==1){
                        if(valid(find_parent(i,j+1),curr_parent_array)){
                           auto curr_parent = find_parent(i,j+1);
                           curr_parent_array.push_back(curr_parent);
                           auto curr_size = size[curr_parent[0]][curr_parent[1]];
                           curr = curr + curr_size;
                        }
                    }
                    if(i+1<grid.size() && grid[i+1][j]==1){
                        if(valid(find_parent(i+1,j),curr_parent_array)){
                           auto curr_parent = find_parent(i+1,j);
                           curr_parent_array.push_back(curr_parent);
                           auto curr_size = size[curr_parent[0]][curr_parent[1]];
                           curr = curr + curr_size;
                        }
                    }
                    if(j-1>=0 && grid[i][j-1]==1){
                        if(valid(find_parent(i,j-1),curr_parent_array)){
                           auto curr_parent = find_parent(i,j-1);
                           curr_parent_array.push_back(curr_parent);
                           auto curr_size = size[curr_parent[0]][curr_parent[1]];
                           curr = curr + curr_size;
                        }
                    }
                    ans = max(ans,curr+1);
                }
                
            }
            cout<<endl;
        }
        return ans;
    }
};
312721