Set Matrix Zeroes

Given an m x n integer matrix matrix, if an element is 0, set its entire row and column to 0’s, and return the matrix.You must do it in place.

Brute Force

• For every 0 in matrix we set its entire row and column to -1(if all values are positive).
• We are setting value -1 because, setting value 0 might affect other rows and columns.
• after whole matrix is traversed, we set all -1 to 0;
• Time Complexity: O(m*n) * (m+n)
  • m*n : to traverse the array
  • m+n : to traverse the row and column for the element.
• Space Complexity: O(1)

Optimization using extra space

• We take 2 vectors/set 1 for rows and 1 for columns.
• We traverse in matrix and if the element is 0, we set the corresponding row and column vector index to 0.
• After the traversal, we again traverse the matrix and if any of the row or column vector at that index is 0, we set the element to 0.
• Time complexity: 2*O(N*M) –> O(N*M)
• Space complexity: O(N), N = max(m,n)

Code

// codestudio
#include <bits/stdc++.h>
void setZeros(vector<vector<int>> &matrix)
{
    set<int> rows, cols;
    int n = matrix.size();
    int m = matrix[0].size();
    for(int i = 0 ; i< n ; i++){
        for(int j = 0 ; j < m ; j++){
            if(matrix[i][j]==0){
                rows.insert(i);
                cols.insert(j);
            }
        }
    }
    for(auto x:rows){
        for(int j = 0; j < m; j++){
            matrix[x][j] = 0;
        }
    }
    for(auto x:cols){
        for(int i = 0; i < n; i++){
            matrix[i][x] = 0;
        }
    }
}

O(1) Space Optimization

• Instead of creating 2 new vectors for row and column we can take first row and first column of matrix for marking.
• We traverse the whole array and if the element is 0, we set the corresponding row and column vector index to 0.
• For the first col there is one special case, if we set first col to 0 so the row will unnecessarily have 0’s in them.
• to tackle this case we take col variable and set it true initially. while traversing the array if we got any 0 in first column so we change col = false.
• Now we traverse from bottom-right to top-left and if we found 0 in any marker vector we set current element to 0.
• for the first column, if col==false we set it to 0.
• Time complexity: 2*O(N*M) –> O(N*M)
• Space complexity: O(1)

Code

// leetcode
class Solution {
public:
    void setZeroes(vector<vector<int>>& matrix)
    {
        int r = matrix.size(), c = matrix[0].size();
        bool col = true;

        for (int i = 0; i < r; i++) { // Traverse all rows
            if (matrix[i][0] == 0) col = false; // if Element of first column is 0, set col = false
            for (int j = 1; j < c; j++) // Traverse all cols except first
                if (matrix[i][j] == 0) {
                    matrix[i][0] = 0;
                    matrix[0][j] = 0;
                }
        }

        // traverse from backwards
        for (int i = r - 1; i >= 0; i--) {
            for (int j = c - 1; j >= 1; j--)
                if (matrix[i][0] == 0 || matrix[0][j] == 0) // if any marker array has 0 set i,j th Element to 0
                    matrix[i][j] = 0;
            // if col = false, means whole col is 0.
            if (col == false) matrix[i][0] = 0;
        }
    }
};