Leetcode #807: Max Increase to Keep City Skyline
In this guide, we solve Leetcode #807 Max Increase to Keep City Skyline in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Greedy, Array, Matrix
Intuition
A locally optimal choice leads to a globally optimal result for this structure.
That means we can commit to decisions as we scan without backtracking.
Approach
Sort or preprocess if needed, then repeatedly take the best available local choice.
Maintain the minimal state necessary to validate the greedy decision.
Steps:
- Sort or preprocess as needed.
- Iterate and pick the best local option.
- Track the current solution.
Example
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] ]
Python Solution
class Solution:
def maxIncreaseKeepingSkyline(self, grid: List[List[int]]) -> int:
row_max = [max(row) for row in grid]
col_max = [max(col) for col in zip(*grid)]
return sum(
min(row_max[i], col_max[j]) - x
for i, row in enumerate(grid)
for j, x in enumerate(row)
)
Complexity
The time complexity is , and the space complexity is , where is the side length of the matrix . The space complexity is , where is the side length of the matrix .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.