<p>You are given an <code>m x n</code> binary matrix <code>grid</code>. An island is a group of <code>1</code>&#39;s (representing land) connected <strong>4-directionally</strong> (horizontal or vertical.) You may assume all four edges of the grid are surrounded by water.</p>

<p>The <strong>area</strong> of an island is the number of cells with a value <code>1</code> in the island.</p>

<p>Return <em>the maximum <strong>area</strong> of an island in </em><code>grid</code>. If there is no island, return <code>0</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/05/01/maxarea1-grid.jpg" style="width: 500px; height: 310px;" />
<pre>
<strong>Input:</strong> grid = [[0,0,1,0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1,1,1,0,0,0],[0,1,1,0,1,0,0,0,0,0,0,0,0],[0,1,0,0,1,1,0,0,1,0,1,0,0],[0,1,0,0,1,1,0,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,1,1,0,0,0],[0,0,0,0,0,0,0,1,1,0,0,0,0]]
<strong>Output:</strong> 6
<strong>Explanation:</strong> The answer is not 11, because the island must be connected 4-directionally.
</pre>

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

<pre>
<strong>Input:</strong> grid = [[0,0,0,0,0,0,0,0]]
<strong>Output:</strong> 0
</pre>

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

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 50</code></li>
	<li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li>
</ul>

class Solution {
public:
    map<pair<int,int>, int> mp;
    int maxSize = 0,size = 0;
    bool print = false;
   
    void traverse(vector<vector<int>>& newGrid, pair<int,int> pr){
        int r = pr.first, c = pr.second;
        if(mp[pr]==1)return;
        mp[pr]=1;size+=1;
        if(size>maxSize)maxSize=size;
        if(print==true){
            cout<<"size:"<<size<<"\tr:"<<r<<"\tc:"<<c<<endl;
        }
        if(newGrid[r+1][c]==1){//Down
            traverse(newGrid, make_pair(r+1, c));
        }
        if(newGrid[r][c+1]==1){//Right
            traverse(newGrid, make_pair(r, c+1));
        }
        if(newGrid[r-1][c]==1){//Up
            traverse(newGrid, make_pair(r-1, c));
        }
        if(newGrid[r][c-1]==1){//Left
            traverse(newGrid, make_pair(r, c-1));
        }
        // cout<<"elsePart\n"<<endl; 
        return;
        
    };

    int maxAreaOfIsland(vector<vector<int>>& grid) {
        int row = grid.size(), col = grid[0].size();
        
        // add two rows and columns to new grid
        vector<vector<int>> newGrid(row+2, vector<int>(col+2, 0));
        
        for(int r=1;r<=row;r++){
            for(int c=1;c<=col;c++){
                newGrid[r][c]=grid[r-1][c-1];
            }
        }
        for(int r=1;r<=row;r++){
            for(int c=1;c<=col;c++){
                if(newGrid[r][c]==1){
                    // if(r==4 && c==9)print=true;
                    // else false;
                    pair<int, int> pr = make_pair(r,c);
                    size = 0;
                    traverse(newGrid, pr);
                }
            }
        }
        return maxSize;
    }
};
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