# 73. Set Matrix Zeroes

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

Example 1:

Input: 
[
  [1,1,1],
  [1,0,1],
  [1,1,1]
]
Output: 
[
  [1,0,1],
  [0,0,0],
  [1,0,1]
]

Example 2:

Input: 
[
  [0,1,2,0],
  [3,4,5,2],
  [1,3,1,5]
]
Output: 
[
  [0,0,0,0],
  [0,4,5,0],
  [0,3,1,0]
]

Follow up:

  • 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?

# Solution

Approach 1: Mark the zero information in the first row and column.

# Code (Python)

Approach 1:

# Code (C++)

Approach 1:

class Solution {
public:
    void setZeroes(vector<vector<int>>& matrix) {
        int rowSize = matrix.size();
        if (rowSize == 0)
            return;
        int colSize = matrix[0].size();
        // Mark which row/column will be zero.
        bool firstRowZero = false;
        for (int col = 0; col < colSize; ++col)
        {
            if (matrix[0][col] == 0)
            {
                firstRowZero = true;
                break;
            }
        }
        for (int row = 1; row < rowSize; ++row)
        {
            for (int col = 0; col < colSize; ++col)
            {
                if (matrix[row][col] == 0)
                {
                    matrix[row][0] = 0;
                    matrix[0][col] = 0;
                }
            }
        }
        // Zero the identified row/column (need to scan reversely).
        for (int row = rowSize - 1; row > 0; --row)
        {
            for (int col = colSize - 1; col >= 0; --col)
            {
                if (matrix[row][0] == 0 || matrix[0][col] == 0)
                    matrix[row][col] = 0;
            }
        }
        if (firstRowZero)
        {
            for (int col = 0; col < colSize; ++col)
                matrix[0][col] = 0;
        }
    }
};