> For the complete documentation index, see [llms.txt](https://gl01.gitbook.io/gfg-editorials/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://gl01.gitbook.io/gfg-editorials/2023/09-2023-sep-29/30-boolean-matrix.md).

# 30. Boolean Matrix

The problem can be found at the following link: [Question Link](https://practice.geeksforgeeks.org/problems/boolean-matrix-problem-1587115620/1)

## My Approach

Simple problem just Identify the rows and columns containing at least one `1` and then completely replace all the elements in those rows and columns with `1`.

Here are the steps to do so:

* Create two vectors `r` and `c` to keep track of rows and columns that should be converted to all 1s.
* Iterate through the matrix to find cells with the value `1`.
  * For each cell with the value 1, set the corresponding entry in the `r` and `c` vectors to 1.
* Iterate through the `r` vector and convert rows to all 1s where `r[i]` is 1.
* Iterate through the `c` vector and convert columns to all 1s where `c[j]` is 1.

## Time and Auxiliary Space Complexity

* **Time Complexity**: `O(N*M)`, where `N` is the number of rows and `M` is the number of columns in the matrix.
* **Auxiliary Space Complexity**: `O(N+M)`, where `N` is the number of rows and `M` is the number of columns in the matrix.

## Code (C++)

```cpp
class Solution {
public:
    void booleanMatrix(vector<vector<int> > &matrix) {
        int n = matrix.size();
        int m = matrix[0].size();
        vector<bool> r(n, 0), c(m, 0);

        for (int i = 0; i < n; ++i)
            for (int j = 0; j < m; ++j)
                if (matrix[i][j]) {
                    r[i] = true;
                    c[j] = true;
                }

        for (int i = 0; i < n; ++i)
            if (r[i])
                for (int j = 0; j < m; ++j)
                    matrix[i][j] = 1;

        for (int j = 0; j < m; ++j)
            if (c[j])
                for (int i = 0; i < n; ++i)
                    matrix[i][j] = 1;
    }
};
```

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