/*
    Given matrix, if element 0, set entire row/col to 0

    Use 1st row/col as flag to determine if entire row/col 0

    Time: O(mn)
    Space: O(1)
*/

class Solution {
public:
    void setZeroes(vector<vector<int>>& matrix) {
        int m = matrix.size();
        int n = matrix[0].size();
        
        bool isFirstRowZero = false;
        bool isFirstColZero = false;
        
        for (int i = 0; i < m; i++) {
            if (matrix[i][0] == 0) {
                isFirstColZero = true;
                break;
            }
        }
        
        for (int j = 0; j < n; j++) {
            if (matrix[0][j] == 0) {
                isFirstRowZero = true;
                break;
            }
        }
        
        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 (isFirstColZero) {
            for (int i = 0; i < m; i++) {
                matrix[i][0] = 0;
            }
        }
        
        if (isFirstRowZero) {
            for (int j = 0; j < n; j++) {
                matrix[0][j] = 0;
            }
        }
    }
};