描述
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 1:
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] ]
Note:
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.
解析
根据题意，观察 grid 的上面（或下面）得到每一列的最高值列表 max_top ，从左面（或右面）观察 grid 的最高值列表 max_left ，然后构造新的 gridNew ，每个元素是所在位置的对应的行最高值和列最高值的较小值即可，这样不会影响不同方向的天际线发生变化，然后计算 gridNew 与 grid 对应位置的增长高度和即可。
解答
class Solution(object):
def maxIncreaseKeepingSkyline(self, grid):
"""
:type grid: List[List[int]]
:rtype: int
"""
m = len(grid)
n = len(grid[0])
max_left = [max(row) for row in grid]
max_top = [max(col) for col in zip(*grid)]
res = 0
for i in range(m):
for j in range(n):
res += min(max_left[i] ,max_top[j]) - grid[i][j]
return res
运行结果
Runtime: 56 ms, faster than 69.76% of Python online submissions for Max Increase to Keep City Skyline.
Memory Usage: 13.6 MB, less than 20.62% of Python online submissions for Max Increase to Keep City Skyline.
原题链接：leetcode.com/problems/ma…
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