<p>You are given two <code>m x n</code> binary matrices <code>grid1</code> and <code>grid2</code> containing only <code>0</code>&#39;s (representing water) and <code>1</code>&#39;s (representing land). An <strong>island</strong> is a group of <code>1</code>&#39;s connected <strong>4-directionally</strong> (horizontal or vertical). Any cells outside of the grid are considered water cells.</p>

<p>An island in <code>grid2</code> is considered a <strong>sub-island </strong>if there is an island in <code>grid1</code> that contains <strong>all</strong> the cells that make up <strong>this</strong> island in <code>grid2</code>.</p>

<p>Return the <em><strong>number</strong> of islands in </em><code>grid2</code> <em>that are considered <strong>sub-islands</strong></em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/10/test1.png" style="width: 493px; height: 205px;" />
<pre>
<strong>Input:</strong> grid1 = [[1,1,1,0,0],[0,1,1,1,1],[0,0,0,0,0],[1,0,0,0,0],[1,1,0,1,1]], grid2 = [[1,1,1,0,0],[0,0,1,1,1],[0,1,0,0,0],[1,0,1,1,0],[0,1,0,1,0]]
<strong>Output:</strong> 3
<strong>Explanation: </strong>In the picture above, the grid on the left is grid1 and the grid on the right is grid2.
The 1s colored red in grid2 are those considered to be part of a sub-island. There are three sub-islands.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/03/testcasex2.png" style="width: 491px; height: 201px;" />
<pre>
<strong>Input:</strong> grid1 = [[1,0,1,0,1],[1,1,1,1,1],[0,0,0,0,0],[1,1,1,1,1],[1,0,1,0,1]], grid2 = [[0,0,0,0,0],[1,1,1,1,1],[0,1,0,1,0],[0,1,0,1,0],[1,0,0,0,1]]
<strong>Output:</strong> 2 
<strong>Explanation: </strong>In the picture above, the grid on the left is grid1 and the grid on the right is grid2.
The 1s colored red in grid2 are those considered to be part of a sub-island. There are two sub-islands.
</pre>

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

<ul>
	<li><code>m == grid1.length == grid2.length</code></li>
	<li><code>n == grid1[i].length == grid2[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 500</code></li>
	<li><code>grid1[i][j]</code> and <code>grid2[i][j]</code> are either <code>0</code> or <code>1</code>.</li>
</ul>

class UnionFind {
public:
    UnionFind(int size)
    {
        m_data.resize(size, -1);
        m_children_count.resize(size, 0);
    }

    void merge(int idx0, int idx1)
    {
        auto u0 = get_union(idx0);
        auto u1 = get_union(idx1);
        if (u0 != u1)
        {
            if (m_children_count[u0] >= m_children_count[u1])
            {
                m_data[u1] = u0;
                m_children_count[u0] += 1 + m_children_count[u1];
            }
            else
            {
                m_data[u0] = u1;
                m_children_count[u1] += 1 + m_children_count[u0];
            }
        }
    }

    int get_union(int idx) {
        int parent = m_data[idx];
        int current_idx = idx;
        int prev_current = current_idx;
        while (parent != -1) {
            //path compression
            //m_children_count[m_data[prev_current]] -= 1 + m_children_count[prev_current];
            //m_data[prev_current] = parent;
            //m_children_count[parent] += 1 + m_children_count[prev_current];
            prev_current = current_idx;
            current_idx = parent;
            parent = m_data[parent];
        }

        return current_idx;
    }

private:
    std::vector<int> m_data;
    std::vector<int> m_children_count;
};

class Solution {
public:
    int countSubIslands(vector<vector<int>>& grid1,
                        vector<vector<int>>& grid2) {
        const int rows = grid2.size();
        const int cols = grid2[0].size();
        UnionFind grid2unionFind{rows * cols};
        for (int row = 0; row < rows; ++row) {
            for (int col = 0; col < cols; ++col) {
                const auto grid2_value = grid2[row][col];
                if (grid2_value == 1) {
                    int idx = row * cols + col;
                    if ((col + 1) < cols)
                    {
                        const auto right_value = grid2[row][col + 1];
                        if (right_value == 1) {
                            int right_idx = idx + 1;
                            grid2unionFind.merge(idx, right_idx);
                        }
                    }

                    if ((row + 1) < rows)
                    {
                        const auto down_value = grid2[row + 1][col];
                        if (down_value == 1) {
                            int down_idx = idx + cols;
                            grid2unionFind.merge(idx, down_idx);
                        }
                    }
                }
            }
        }

        std::vector<std::vector<int>> grid2_islands;
        grid2_islands.resize(rows * cols);

        for (int row = 0; row < rows; ++row) {
            for (int col = 0; col < cols; ++col) {
                const auto grid2_value = grid2[row][col];
                if (grid2_value == 1) {
                    int idx = row * cols + col;
                    auto island_idx = grid2unionFind.get_union(idx);
                    grid2_islands[island_idx].push_back(idx);
                }
            }
        }

        int sub_island_count = 0;
        for (int i = 0; i < grid2_islands.size(); ++i) {
            const auto& grid2_island = grid2_islands[i];
            if (!grid2_island.size()) {
                continue;
            }
            bool is_sub_island = true;
            for (const auto island_cell : grid2_island) {
                int row = island_cell / cols;
                int col = island_cell % cols;
                if (grid1[row][col] == 0) {
                    is_sub_island = false;
                    break;
                }
            }
            if (is_sub_island) {
                ++sub_island_count;
            }
        }

        return sub_island_count;
    }
};
139527