<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:
    int bfs(vector<vector<int>>&grid, int i, int j) {
        int row = grid.size();
        int col = grid[0].size();
        stack<pair<int, int>>stk;
        stk.push({i,j});

        vector<pair<int,int>>directions ={{1,0},{-1,0},{0,1},{0,-1}};
        // mark starting point as traversed;
        grid[i][j] = 0;
        // contiguous land area. given that this is a first land set1;
        int land = 1;
        while(!stk.empty()){
          auto [x,y] = stk.top();
          stk.pop();
          for(auto& dir: directions){
            int newX = x + dir.first;
            int newY = y + dir.second;
            if(newX >=0&&newX<row&&newY>=0&&newY<col&&grid[newX][newY]==1){
                land++;
                grid[newX][newY]=0;
                stk.push({newX,newY});
            }
          }
        }
        return land;
    };

    int maxAreaOfIsland(vector<vector<int>>&grid) {
        int row = grid.size();
        int col = grid[0].size();
        int maxLand = 0;
        for(int i = 0; i< row; ++i){
            for(int j = 0; j < col; ++j){
                if(grid[i][j] == 1){
                    int currentArea = bfs(grid,i,j);
                    maxLand = max(maxLand,currentArea);
                }
            }
        }
        return maxLand;
    }
};
31290