Introduction

In this blog post, we will explore how to solve the LeetCode problem "807" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

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. 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. Example 1: 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] ] Example 2: 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

Explanation

Here's the solution:

• Find Skyline: Determine the maximum height for each row and each column. These represent the skylines when viewed from the north/south and east/west, respectively.
• Calculate Increase: For each building, find the minimum of its row's maximum height and its column's maximum height. This is the maximum height the building can be increased to without affecting the skyline.

• Sum the Increase: Calculate the difference between the new height (minimum of row/col max) and the original height of the building, and accumulate the sum of these differences.

• Runtime Complexity: O(n^2) , Storage Complexity: O(n)

Code

    def maxIncreaseKeepingSkyline(grid: list[list[int]]) -> int:
    """
    Calculates the maximum total sum that the height of the buildings can be increased by
    without changing the city's skyline from any cardinal direction.

    Args:
        grid: A 2D list representing the height of buildings in the city.

    Returns:
        The maximum possible increase in building heights.
    """

    n = len(grid)
    row_maxes = [0] * n
    col_maxes = [0] * n

    # Find the maximum height for each row and column
    for i in range(n):
        for j in range(n):
            row_maxes[i] = max(row_maxes[i], grid[i][j])
            col_maxes[j] = max(col_maxes[j], grid[i][j])

    total_increase = 0
    # Calculate the increase for each building
    for i in range(n):
        for j in range(n):
            total_increase += min(row_maxes[i], col_maxes[j]) - grid[i][j]

    return total_increase