> ## Documentation Index
> Fetch the complete documentation index at: https://leetcode-py.wisl.dev/llms.txt
> Use this file to discover all available pages before exploring further.

> ## Agent Instructions
> leetcode-py is a Python LeetCode practice environment generator with one CLI: lcpy. It is not a service or platform.
> Each problem is a directory under leetcode/ with README.md, solution.py, test_solution.py, helpers.py, and playground.ipynb. lcpy gen creates them from JSON templates bundled with the package.
> Examples are backed by tests; copy them verbatim.

# Best Meeting Point Python Solution with Tests

> Tested Python solution for LeetCode 296 with 12 pytest cases. Generate a practice environment with lcpy.

LeetCode 296, [Hard](/catalog/hard). Topics: [Array](/catalog/topics/array), [Math](/catalog/topics/math), [Matrix](/catalog/topics/matrix), [Sorting](/catalog/topics/sorting). [View on LeetCode](https://leetcode.com/problems/best-meeting-point/description/).

Generate this problem as a practice environment: tested reference solution, 12 [parametrized pytest cases](/practice/testing), and a playground notebook:

```bash theme={"theme":{"light":"github-light","dark":"github-dark"}}
lcpy gen -n 296   # by problem number
lcpy gen -s best_meeting_point   # by problem name
```

## Problem

Given an `m x n` binary `grid` where each `1` marks the home of one friend, return *the minimal **total travel distance***.

The **total travel distance** is the sum of the distances between the houses of the friends and the meeting point.

The distance is calculated using Manhattan Distance, where `distance(p1, p2) = |p2.x - p1.x| + |p2.y - p1.y|`.

### Examples

![Example 1](https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0200-0299/0296.Best%20Meeting%20Point/images/meetingpoint-grid.jpg)

```
Input: grid = [[1,0,0,0,1],[0,0,0,0,0],[0,0,1,0,0]]
Output: 6
Explanation: Given three friends living at (0,0), (0,4), and (2,2).
The point (0,2) is an ideal meeting point, as the total travel distance of 2 + 2 + 2 = 6 is minimal.
So return 6.
```

```
Input: grid = [[1,1]]
Output: 1
```

### Constraints

* `m == grid.length`
* `n == grid[i].length`
* `1 <= m, n <= 200`
* `grid[i][j]` is either `0` or `1`.
* There will be **at least two** friends in the `grid`.

## Solution

Reference implementation from [solution.py on GitHub](https://github.com/wislertt/leetcode-py/blob/main/leetcode/best_meeting_point/solution.py), full suite in [test\_solution.py](https://github.com/wislertt/leetcode-py/blob/main/leetcode/best_meeting_point/test_solution.py):

```python theme={"theme":{"light":"github-light","dark":"github-dark"}}
class Solution:
    # Time: O(m*n + f log f) where f is the friend count
    # Space: O(f)
    def min_total_distance(self, grid: list[list[int]]) -> int:
        rows: list[int] = []
        cols: list[int] = []
        for r in range(len(grid)):
            for c in range(len(grid[0])):
                if grid[r][c] == 1:
                    rows.append(r)
                    cols.append(c)
        cols.sort()
        median_row = rows[len(rows) // 2]
        median_col = cols[len(cols) // 2]
        return sum(abs(r - median_row) for r in rows) + sum(abs(c - median_col) for c in cols)
```

## Complexity

| Time | Space |
| - | - |
| O(m\*n + f log f) where f is the friend count | O(f) |

## Tags

[NeetCode All](/catalog/neetcode).


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