Set Matrix Zeroes

Description

Given an m x n integer matrix matrix, if an element is 0, set its entire row and column to 0‘s.

You must do it in place.

Example 1:

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

Example 2:

Input: matrix = [[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]]

Constraints:

• m == matrix.length
• n == matrix[0].length
• 1 <= m, n <= 200
• -231 <= matrix[i][j] <= 231 - 1

Follow up:

• A straightforward 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?

Code

row 0 和 col 0 的資訊會衝突，因此只能選一個，另外一個就用 col0 來記錄。

關鍵在於 row 0 & col 0，所以 for loop 必須要由 i = 1, j = 1 開始 iterate。row 0 & col 0 的元素要另外紀錄，不能因為其中一個為零就將其他人設為 0 ，因為這樣會導致 i = 1, j = 1 之後的元素被錯誤的設為 0。

class Solution {
public:
    void setZeroes(vector<vector<int>>& matrix) {
        int zeroCol = 0, zeroRow = 0, n = matrix.size(), m = matrix[0].size();
        
        for(int i = 0; i < n; i++) {
            if(matrix[i][0] == 0) zeroCol = 1;
        }
 
        for(int j = 0; j < m; j++) {
            if(matrix[0][j] == 0) zeroRow = 1;
        }
 
        
        for(int i = 1; i < n; i++) {
            for(int j = 1; j < m; j++) {
                if(matrix[i][j] == 0) {
                    matrix[i][0] = 0;
                    matrix[0][j] = 0;
                }
            }
        }
 
        for(int i = 1; i < n; i++) {
            for(int j = 1; j < m; j++) {
                if(matrix[i][0] == 0 || matrix[0][j] == 0) {
                    matrix[i][j] = 0;
                }
            }
        }
        
        for(int i = 0; i < n; i++) {
            if(zeroCol) matrix[i][0] = 0;
        }
 
        for(int j = 0; j < m; j++) {
            if(zeroRow) matrix[0][j] = 0;
        }
    }
};

其實可以再進一步縮減需要紀錄的資訊，只需要紀錄 col0 即可，但就要注意先後順序。要從右下角填回左上角，因為記錄是否為 0 的資訊都儲存在左邊和上面。

class Solution {
public:
    void setZeroes(vector<vector<int>>& matrix) {
 
        int col0 = 1;
        for(int i = 0; i < matrix.size(); i++) {
            if(matrix[i][0] == 0) col0 = 0;
            for(int j = 1; j < matrix[i].size(); j++) {
                if(matrix[i][j] == 0) {
                    matrix[i][0] = matrix[0][j] = 0;
                }
            }
        }
 
        
        for(int i = matrix.size() - 1; i >= 0; i--) {
            for(int j = matrix[i].size() - 1; j >= 1; j--) {
                if(matrix[i][0] == 0 || matrix[0][j] == 0) 
                    matrix[i][j] = 0;
            }
        }
 
        for(int i = 0; i < matrix.size(); i++) {
            if(col0 == 0) matrix[i][0] = 0;
        }
    }
};

Source

• Set Matrix Zeroes - LeetCode