> ## 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.

# Max Increase to Keep City Skyline

> Tested Python solution for LeetCode 807 with 22 pytest cases. Generate a practice environment with lcpy.

LeetCode 807, [Medium](/catalog/medium). Topics: [Array](/catalog/topics/array), [Greedy](/catalog/topics/greedy), [Matrix](/catalog/topics/matrix). [View on LeetCode](https://leetcode.com/problems/max-increase-to-keep-city-skyline/description/).

Generate this problem as a practice environment: tested reference solution, 22 [parametrized pytest cases](/practice/testing), and a playground notebook:

```bash theme={"theme":{"light":"github-light","dark":"github-dark"}}
lcpy gen -n 807   # by problem number
lcpy gen -s max_increase_to_keep_city_skyline   # by problem name
```

## Problem

There is a city composed of `n x n` blocks, where each block contains a single building shaped like a vertical square prism. You are given a **0-indexed** `n x n` integer matrix `grid` where `grid[r][c]` represents the **height** of the building located in the block at row `r` and column `c`.

A city's **skyline** is the outer contour formed by all the building when viewing the side of the city from a distance. The **skyline** from each cardinal direction north, east, south, and west may be different.

We are allowed to increase the height of **any number of buildings by any amount** (the amount can be different per building). The height of a `0`-height building can also be increased. However, increasing the height of a building should **not** affect the city's **skyline** from any cardinal direction.

Return *the **maximum total sum** that the height of the buildings can be increased by **without** changing the city's **skyline** from any cardinal direction*.

### Examples

![Example 1](https://assets.leetcode.com/uploads/2021/06/21/807-ex1.png)

```
Input: grid = [[3,0,8,4],[2,4,5,7],[9,2,6,3],[0,3,1,0]]
Output: 35
Explanation: The building heights are shown in the center of the above image.
The skylines when viewed from each cardinal direction are drawn in red.
The grid after increasing the height of buildings without affecting skylines is:
gridNew = [ [8, 4, 8, 7],
            [7, 4, 7, 7],
            [9, 4, 8, 7],
            [3, 3, 3, 3] ]
```

```
Input: grid = [[0,0,0],[0,0,0],[0,0,0]]
Output: 0
Explanation: Increasing the height of any building will result in the skyline changing.
```

### Constraints

* n == grid.length
* n == grid\[r].length
* 2 \<= n \<= 50
* 0 \<= grid\[r]\[c] \<= 100

## Solution

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

```python theme={"theme":{"light":"github-light","dark":"github-dark"}}
class Solution:
    # Time: O(n^2)
    # Space: O(n)
    def max_increase_keeping_skyline(self, grid: list[list[int]]) -> int:
        row_max = [max(row) for row in grid]
        col_max = [max(col) for col in zip(*grid, strict=True)]
        return sum(
            min(row_max[r], col_max[c]) - grid[r][c]
            for r, row in enumerate(grid)
            for c in range(len(row))
        )
```

## Complexity

| Time | Space |
| - | - |
| O(n^2) | O(n) |

## Tags


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