807.MaxIncreasetoKeepCitySkyline.py

"""
    In a 2 dimensional array grid, each value grid[i][j] represents the height 
    of a building located there. We are allowed to increase the height of any 
    number of buildings, by any amount (the amounts can be different for 
    different buildings). Height 0 is considered to be a building as well. 

    At the end, the "skyline" when viewed from all four directions of the grid, 
    i.e. top, bottom, left, and right, must be the same as the skyline of the 
    original grid. A city's skyline is the outer contour of the rectangles 
    formed by all the buildings when viewed from a distance. See the following 
    example.

    What is the maximum total sum that the height of the buildings can be 
    increased?

    Example:
    Input: grid = [[3,0,8,4],[2,4,5,7],[9,2,6,3],[0,3,1,0]]
    Output: 35
    Explanation: 
    The grid is:
    [ [3, 0, 8, 4], 
      [2, 4, 5, 7],
      [9, 2, 6, 3],
      [0, 3, 1, 0] ]

    The skyline viewed from top or bottom is: [9, 4, 8, 7]
    The skyline viewed from left or right is: [8, 7, 9, 3]

    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] ]

    Notes:
        - 1 < grid.length = grid[0].length <= 50.
        - All heights grid[i][j] are in the range [0, 100].
        - All buildings in grid[i][j] occupy the entire grid cell: that is, 
          they are a 1 x 1 x grid[i][j] rectangular prism.
"""
#Difficulty: Medium
#133 / 133 test cases passed.
#Runtime: 64 ms
#Memory Usage: 14.2 MB

#Runtime: 64 ms, faster than 97.89% of Python3 online submissions for Max Increase to Keep City Skyline.
#Memory Usage: 14.2 MB, less than 7.78% of Python3 online submissions for Max Increase to Keep City Skyline.

class Solution:
    def maxIncreaseKeepingSkyline(self, grid: List[List[int]]) -> int:
        total_increase = 0
        horozontal = len(grid)
        vertical = len(grid[0])
        top_bottom = [float(-inf)] * vertical
        left_right = [float(-inf)] * horozontal
        for i in range(horozontal):
            left_right[i] = max(grid[i])
            for j in range(vertical):
                top_bottom[j] = max(top_bottom[j], grid[i][j])
        for i in range(horozontal):
            for j in range(vertical):
                total_increase += min(left_right[i], top_bottom[j]) - grid[i][j]
        return total_increase