How do you solve Max Increase to Keep City Skyline on LeetCode?

Max Increase to Keep City Skyline (LeetCode #807) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n²) time complexity and O(n) space complexity. Key insight: The maximum height of each building is constrained by the maximum heights of its corresponding row and column.

What is the brute force solution for Max Increase to Keep City Skyline?

The brute force approach for Max Increase to Keep City Skyline is Brute Force, with O(n²) time complexity and O(n) space complexity. The brute force approach involves calculating the maximum possible height for each building based on the skyline constraints from all four directions. This means for each building, we will determine the minimum height it can be increased to without affecting the skyline. The optimal Optimal Solution approach improves this to O(n²).

What algorithm or data structure is used to solve Max Increase to Keep City Skyline?

Max Increase to Keep City Skyline uses the following concepts: Array, Greedy, Matrix. The recommended patterns to study are: Array, Greedy.

What are the interview tips for Max Increase to Keep City Skyline?

Always clarify the problem constraints and requirements before diving into coding. Think about edge cases, such as grids with all zeros or grids where all buildings are already at maximum height. Explain your thought process clearly while coding; it helps the interviewer understand your reasoning.

What are common mistakes when solving Max Increase to Keep City Skyline?

Students often forget to consider the skyline constraints from both rows and columns, leading to incorrect calculations. Some may attempt to directly modify the grid, which can lead to unintended consequences in the skyline.

#807

Max Increase to Keep City Skyline

Medium

ArrayGreedyMatrixArrayGreedy

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n²)
Space	O(n)	O(n)

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Intuition

Time O(n²)Space O(n)

The optimal solution leverages the same principles as the brute force but calculates the maximum heights for rows and columns in a single pass. This reduces the number of iterations needed to compute the total increase.

⚙️

Algorithm

3 steps

1Step 1: Initialize maxRow and maxCol arrays to store the maximum heights for each row and column.
2Step 2: Iterate through the grid once to fill maxRow and maxCol simultaneously.
3Step 3: Calculate the total increase in a single pass using the precomputed maxRow and maxCol.

solution.py13 lines

1def maxIncreaseKeepingSkyline(grid):
2    n = len(grid)
3    maxRow = [0] * n
4    maxCol = [0] * n
5    totalIncrease = 0
6    for r in range(n):
7        for c in range(n):
8            maxRow[r] = max(maxRow[r], grid[r][c])
9            maxCol[c] = max(maxCol[c], grid[r][c])
10    for r in range(n):
11        for c in range(n):
12            totalIncrease += min(maxRow[r], maxCol[c]) - grid[r][c]
13    return totalIncrease

ℹ

Complexity note: The time complexity remains O(n²) due to iterating through the grid, but we optimize the process by combining the height calculations into fewer iterations. The space complexity is O(n) for storing max heights.

1The maximum height of each building is constrained by the maximum heights of its corresponding row and column.
2The skyline from each direction must remain unchanged, which means we can only increase heights up to the minimum of the maximum row and column heights.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.