Set Matrix Zeros ****

Given a m x n matrix, if an element is 0, set its entire row and column to 0. Do it in place.

click to show follow up.

Follow up:

Did you use extra space?
A straight forward solution using O(mn) space is probably a bad idea.
A simple improvement uses O(m + n) space, but still not the best solution.
Could you devise a constant space solution?

 

Analyse: O(m + n) space

class Solution {
public:
    void setZeroes(vector<vector<int>>& matrix) {
        if (matrix.empty() || matrix[0].empty()) return;
        // bool: rows[] stores the rows needed to be replaced by 0
        // bool: cols[] stores the cols needed to be replaced by 0
        int m = matrix.size(), n = matrix[0].size();
        vector<int> rows(m, false);
        vector<int> cols(n, false);
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (!matrix[i][j]) {
                    rows[i] = true;
                    cols[j] = true;
                }
            }
        }
        
        // replace the matrix accordingly
        for (int i = 0; i < m; i++) {
            if (rows[i]) {
                for (int j = 0; j < n; j++)
                    matrix[i][j] = 0;
            }
        }
        for (int j = 0; j < n; j++) {
            if (cols[j]) {
                for (int i = 0; i < m; i++)
                    matrix[i][j] = 0;
            }
        }
    }
};

Analyse: O(1) space.

-- Scan the matrix, when it comes to 0, set all 1 in its row and column as 2. Scan the matrix again, replace all 2 with 0. However, we may encounter the situation where 2 has already been used in the matrix...

-- Use the first row and first column to store the information. Solution should be as the same. A very smart solution can be viewed at:

class Solution {
public:
    void setZeroes(vector<vector<int> > &matrix) {
        int col0 = 1, rows = matrix.size(), cols = matrix[0].size();

        for (int i = 0; i < rows; i++) {
            if (matrix[i][0] == 0) col0 = 0;
            for (int j = 1; j < cols; j++)
                if (matrix[i][j] == 0)
                    matrix[i][0] = matrix[0][j] = 0;
        }

        for (int i = rows - 1; i >= 0; i--) {
            for (int j = cols - 1; j >= 1; j--)
                if (matrix[i][0] == 0 || matrix[0][j] == 0)
                    matrix[i][j] = 0;
            if (col0 == 0) matrix[i][0] = 0;
        }
　　}
};