<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>

struct Position {
  int row;
  int col;

  bool operator<(const Position &other) const {
    return tie(row, col) < tie(other.row, other.col);
  }
};

class Solution {
private:
  set<Position> visitedIslands{};
  int maxRow{0};
  int maxCol{0};
  int area{0};
  int maxArea{0};

  void markIslandAsVisited(int row, int col) {
    visitedIslands.insert({row, col});
  }

  bool didVisitIsland(int row, int col) {
    return visitedIslands.find({row, col}) != visitedIslands.end();
  }

  void getIslandArea(int row, int col, vector<vector<int>> &grid) {
    markIslandAsVisited(row, col);
    area += 1;

    if (row > 0 && grid[row - 1][col] == 1 && !didVisitIsland(row - 1, col))
      getIslandArea(row - 1, col, grid); // North
    if (row < maxRow && grid[row + 1][col] == 1 &&
        !didVisitIsland(row + 1, col))
      getIslandArea(row + 1, col, grid); // South
    if (col < maxCol && grid[row][col + 1] == 1 &&
        !didVisitIsland(row, col + 1))
      getIslandArea(row, col + 1, grid); // East
    if (col > 0 && grid[row][col - 1] == 1 && !didVisitIsland(row, col - 1))
      getIslandArea(row, col - 1, grid); // West
  }

public:
  int maxAreaOfIsland(vector<vector<int>> &grid) {
    maxRow = grid.size() - 1;
    maxCol = grid[0].size() - 1;

    for (int row{0}; row < size(grid); ++row) {
      for (int col{0}; col < size(grid[0]); ++col) {
        int gridItem = grid[row][col];
        if (gridItem == 1 && !didVisitIsland(row, col)) {
          area = 0;
          getIslandArea(row, col, grid);
          if (area > maxArea) {
            maxArea = area;
          }
        }
      }
    }

    return maxArea;
  }
};


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