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leetcode/0807.Max-Increase-to-Keep-City-Skyline/README.md

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+# [807. Max Increase to Keep City Skyline](https://leetcode-cn.com/problems/max-increase-to-keep-city-skyline/)
+
+## 题目
+
+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**:
+
+![https://assets.leetcode.com/uploads/2021/06/21/807-ex1.png](https://assets.leetcode.com/uploads/2021/06/21/807-ex1.png)
+
+    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
+
+## 题目大意
+
+在二维数组grid中，grid[i][j]代表位于某处的建筑物的高度。 我们被允许增加任何数量（不同建筑物的数量可能不同）的建筑物的高度。 高度 0 也被认为是建筑物。
+
+最后，从新数组的所有四个方向（即顶部，底部，左侧和右侧）观看的“天际线”必须与原始数组的天际线相同。 城市的天际线是从远处观看时，由所有建筑物形成的矩形的外部轮廓。 请看下面的例子。
+
+建筑物高度可以增加的最大总和是多少？
+
+## 解题思路
+
+- 从数组竖直方向（即顶部，底部）看“天际线”计算出topBottomSkyline
+- 从数组水平方向（即左侧，右侧）看“天际线”计算出leftRightSKyline
+- 计算grid中每个元素与对应的topBottomSkyline和leftRightSKyline中较小值的差值
+- 统计所有差值的总和ans并返回
+
+## 代码
+
+```go
+package leetcode
+
+func maxIncreaseKeepingSkyline(grid [][]int) int {
+	var topBottomSkyline []int
+	var leftRightSKyline []int
+	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
+}
+```