constant space Archives - Huahua's Tech Road https://zxi.mytechroad.com/blog/tag/constant-space/ Sat, 09 Feb 2019 19:56:59 +0000 en hourly 1 https://wordpress.org/?v=6.0.8 https://zxi.mytechroad.com/blog/wp-content/uploads/2017/09/cropped-photo-32x32.jpg constant space Archives - Huahua's Tech Road https://zxi.mytechroad.com/blog/tag/constant-space/ 32 32 花花酱 LeetCode 73. Set Matrix Zeroes https://zxi.mytechroad.com/blog/algorithms/array/leetcode-73-set-matrix-zeroes/ https://zxi.mytechroad.com/blog/algorithms/array/leetcode-73-set-matrix-zeroes/#respond Sat, 09 Feb 2019 19:32:10 +0000 https://zxi.mytechroad.com/blog/?p=4806 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],…

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]]> 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 1

Use two arrays to track whether the i-th row / j-th column need to be zeroed.

Time complexity: O(mn)
Space complexity: O(m+n)

C++

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

Solution 2

Use the first row / first col to indicate whether the i-th row / j-th column need be zeroed.

C++

class Solution {
public:
  void setZeroes(vector<vector<int>>& matrix) {
    const int m = matrix.size();
    const int n = matrix[0].size();
    
    bool col0 = false;
    bool row0 = false;
    
    for (int i = 0; i < m; ++i) 
      col0 |= (matrix[i][0] == 0);
    for (int j = 0; j < n; ++j) 
      row0 |= (matrix[0][j] == 0);
    
    for (int i = 1; i < m; ++i)
      for (int j = 1; j < n; ++j)
        if (matrix[i][j] == 0)
          matrix[0][j] = matrix[i][0] = 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 (row0)
      for (int j = 0; j < n; ++j) 
        matrix[0][j] = 0;
    
    if (col0)
      for (int i = 0; i < m; ++i) 
        matrix[i][0] = 0;
  }
};

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