807. Max Increase to Keep City Skyline #

Problem #

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 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

Summary #

In the two-dimensional array grid, grid[i][j] represents the height of the building located at a certain position. We are allowed to increase the height of any number of buildings (the amount may be different for different buildings). Height 0 is also considered a building.

Finally, the “skyline” viewed from all four directions of the new array (that is, top, bottom, left, and right) must be the same as the skyline of the original array. A city’s skyline is the outer contour of the rectangle formed by all buildings when viewed from a distance. Please see the example below.

What is the maximum total sum by which the building heights can be increased?

Solution Approach #

• Calculate topBottomSkyline by viewing the “skyline” from the vertical direction of the array (that is, top and bottom)
• Calculate leftRightSkyline by viewing the “skyline” from the horizontal direction of the array (that is, left and right)
• Calculate the difference between each element in grid and the smaller value of the corresponding topBottomSkyline and leftRightSkyline
• Sum all differences into ans and return it

Code #

package leetcode

func maxIncreaseKeepingSkyline(grid [][]int) int {
	n := len(grid)
	topBottomSkyline := make([]int, 0, n)
	leftRightSkyline := make([]int, 0, n)
	for i := range grid {
		cur := 0
		for _, v := range grid[i] {
			if cur < v {
				cur = v
			}
		}
		leftRightSkyline = append(leftRightSkyline, cur)
	}
	for j := range grid {
		cur := 0
		for i := 0; i < len(grid[0]); i++ {
			if cur < grid[i][j] {
				cur = grid[i][j]
			}
		}
		topBottomSkyline = append(topBottomSkyline, cur)
	}
	var ans int
	for i := range grid {
		for j := 0; j < len(grid[0]); j++ {
			ans += min(topBottomSkyline[j], leftRightSkyline[i]) - grid[i][j]
		}
	}
	return ans
}

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}