# [542\. 01 Matrix](https://leetcode.com/problems/01-matrix/)

:::spoiler Solution - BFS

class Solution {
public:
    vector<vector<int>> updateMatrix(vector<vector<int>>& mat)
    {
        int m = mat.size(), n = mat[0].size();
        
        queue<vector<int>> q;
        set<pair<int, int>> seen;
        
        for (int i = 0; i < m; i++)
        {
            for (int j = 0; j < n; j++)
            {
                if (mat[i][j] == 0)
                {
                    q.push({i, j, 0});
                    seen.insert({i, j});
                }
            }
        }

        vector<vector<int>> res = mat;
        vector<vector<int>> directions = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}};
        
        while (!q.empty())
        {
            auto node = q.front(); q.pop();
            for (const auto& dir : directions)
            {
                int new_i = node[0] + dir[0];
                int new_j = node[1] + dir[1];
                int dist = node[2] + 1;

                if (new_i < 0 || new_j < 0 || new_i >= m || new_j >= n || seen.count({new_i, new_j})) continue;
                q.push({new_i, new_j, dist});
                seen.insert({new_i, new_j});
                res[new_i][new_j] = dist;
            }
        }
        return res;
    }
};

- T: $O(M \cdot N)$
- S: $O(M \cdot N)$
:::