> For the complete documentation index, see [llms.txt](https://mayanktyagi3111.gitbook.io/interview-prep/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mayanktyagi3111.gitbook.io/interview-prep/hashmap-and-hashset-and-sliding-window/flip-columns-for-maximum-number-of-equal-rows.md).

# Flip Columns For Maximum Number of Equal Rows

Given a `matrix` consisting of 0s and 1s, we may choose any number of columns in the matrix and flip **every** cell in that column.  Flipping a cell changes the value of that cell from 0 to 1 or from 1 to 0.

Return the maximum number of rows that have all values equal after some number of flips.

1.

**Example 1:**

```
Input: [[0,1],[1,1]]
Output: 1
Explanation: After flipping no values, 1 row has all values equal.
```

**Example 2:**

```
Input: [[0,1],[1,0]]
Output: 2
Explanation: After flipping values in the first column, both rows have equal values.
```

**Example 3:**

```
Input: [[0,0,0],[0,0,1],[1,1,0]]
Output: 2
Explanation: After flipping values in the first two columns, the last two rows have equal values.
```

**Note:**

1. `1 <= matrix.length <= 300`
2. `1 <= matrix[i].length <= 300`
3. All `matrix[i].length`'s are equal
4. `matrix[i][j]` is `0` or `1`

```java
class Solution {
    public int maxEqualRowsAfterFlips(int[][] matrix) {
        // We can make a single row into full 1s OR 0s
        if (matrix.length == 1)
            return 1;
        Map<String, Integer> map = new HashMap<>();
        int max = 0;
        // Observation -> 2 rows which are opposite of each other will become full on
        // same column flips
        for (int i = 0; i < matrix.length; i++) {
            StringBuilder str1 = new StringBuilder();
            StringBuilder str2 = new StringBuilder();
            for (int j = 0; j < matrix[i].length; j++) {
                str1.append(1 - matrix[i][j]);
                str2.append(matrix[i][j]);
            }
            String key1 = str1.toString(), key2 = str2.toString();
            map.put(key1, map.getOrDefault(key1, 0) + 1);
            max = Math.max(max, map.get(key1));
            map.put(key2, map.getOrDefault(key2, 0) + 1);
            max = Math.max(max, map.get(key2));
        }
        return max;
    }
}
```


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