73. Set Matrix Zeroes

class Solution {
public:
    void setZeroes(vector<vector<int>>& matrix)
    {
        int m = matrix.size(), n = matrix[0].size();

        bool firstRow = false, firstCol = false;

        for (int i = 0; i < m; ++i)
        {
            if (matrix[i][0] == 0) firstCol = true;
        }

        for (int j = 0; j < n; ++j)
        {
            if (matrix[0][j] == 0) firstRow = true;
        }

        for (int i = 1; i < m; ++i)
        {
            for (int j = 1; j < n; ++j)
            {
                if (matrix[i][j] == 0)
                {
                    matrix[i][0] = 0;
                    matrix[0][j] = 0;
                }
            }
        }

        for (int i = 1; i < m; ++i)
        {
            for (int j = 1; j < n; ++j)
            {
                if (matrix[i][0] == 0 || matrix[0][j] == 0)
                {
                    matrix[i][j] = 0;
                }
            }
        }

        if (firstRow)
        {
            for (int j = 0; j < n; ++j)
            {
                matrix[0][j] = 0;
            }
        }

        if (firstCol)
        {
            for (int i = 0; i < m; ++i)
            {
                matrix[i][0] = 0;
            }
        }
    }
};

• T: $O(M \cdot N)$
• S: $O(1)$