Leetcode: 73 Set Matrix Zeroes

Published at

1/10/2025

Intuition

In a naive solution, we can keep track of all the rows and columns to be made zero.

Approach

In the naive solution, we can use hash sets or sets to keep track of rows and columns to make zero using one iteration. In the second phase, we can iterate through our sets to set the saved rows and columns to zero.

Space complexity for Naive Solution: O(M+N)
Naive solution code:

class Solution {
    public void setRowZero(int[][] matrix, int row){
        for(int i = 0;i<matrix[0].length;i++){
            matrix[row][i] = 0;
        }
   }
    public void setColZero(int[][] matrix, int col){
        for(int i = 0;i<matrix.length;i++){
            matrix[i][col] = 0;
        }
    }
    public void setZeroes(int[][] matrix) {
        Set<Integer> rowSet = new HashSet<>();
        Set<Integer> colSet = new HashSet<>();
        for(int i =0;i<matrix.length;i++){
            for(int j = 0;j<matrix[i].length;j++){
                if(matrix[i][j] == 0){
                    rowSet.add(i);
                    colSet.add(j);
                }
            }
        }
        for(int ele: rowSet){
            setRowZero(matrix,ele);
        }
        for(int ele: colSet){
            setColZero(matrix,ele);
        }     
    }
}

In the below solution which is optimized, I have marked the first row and first column if we encounter any zero in the submatrix

[ (1, rows): (1, cols) ]

We can use two boolean variables to keep track of the first row and first column for any zero.

Complexity

Time complexity: O(M * N)
Space complexity: O(1)

Code

class Solution {
    public void setZeroes(int[][] matrix) {
        int rows = matrix.length;
        int cols = matrix[0].length;

        boolean first_row_has_zero = false;
        boolean first_col_has_zero = false;

        // check if first row has any zero
        for(int c = 0;c<cols;c++){
            if(matrix[0][c] == 0){
                first_row_has_zero = true;
                break;
            }
        }

        // check if first col has any zero
        for(int r = 0;r<rows;r++){
            if(matrix[r][0] == 0){
                first_col_has_zero = true;
                break;
            }
        }
        // checking for zero elsewhere and keeping track of it in the first row and first column
        for(int r = 1;r<rows;r++){
            for(int c = 1;c<cols;c++){
                if(matrix[r][c] == 0){
                    matrix[r][0] = 0;
                    matrix[0][c] = 0;
                }
            }
        }

        // checking and setting respcted row to zero
        for(int c = 1;c<cols; c++){
            if(matrix[0][c] == 0){
                for(int r = 0;r<rows;r++){
                    matrix[r][c] = 0;
                }
            }
        }

        // checking and setting respcted cols to zero
        for(int r = 1;r<rows; r++){
            if(matrix[r][0] == 0){
                for(int c = 0;c<cols;c++){
                    matrix[r][c] = 0;
                }
            }
        }

        if(first_row_has_zero == true){
            for(int c = 0;c<cols;c++){
                matrix[0][c] = 0;
            }
        }

        if(first_col_has_zero == true){
            for(int r = 0;r<rows;r++){
                matrix[r][0] = 0;
            }
        }

    }
}