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• /**

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.

*/

public class Max_Increase_to_Keep_City_Skyline {

class Solution {
public int maxIncreaseKeepingSkyline(int[][] grid) {

if (grid == null || grid[0].length == 0) {
return 0;
}

int[] xMax = new int[grid[0].length];
int[] yMax = new int[grid.length];

for (int i = 0; i < grid.length; i++) {
for (int j  = 0; j < grid[0].length; j++) {
xMax[j] = Math.max(xMax[j], grid[i][j]);
yMax[i] = Math.max(yMax[i], grid[i][j]);
}
}

int result = 0;
for (int i = 0; i < grid.length; i++) {
for (int j = 0; j < grid[0].length; j++) {
result += Math.min(xMax[j], yMax[i]) - grid[i][j];
}
}

return result;
}
}
}

############

class Solution {
public int maxIncreaseKeepingSkyline(int[][] grid) {
int m = grid.length, n = grid[0].length;
int[] rmx = new int[m];
int[] cmx = new int[n];
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
rmx[i] = Math.max(rmx[i], grid[i][j]);
cmx[j] = Math.max(cmx[j], grid[i][j]);
}
}
int ans = 0;
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
ans += Math.min(rmx[i], cmx[j]) - grid[i][j];
}
}
return ans;
}
}

• // OJ: https://leetcode.com/problems/max-increase-to-keep-city-skyline/
// Time: O(MN)
// Space: O(max(M, N))
class Solution {
public:
int maxIncreaseKeepingSkyline(vector<vector<int>>& grid) {
int M = grid.size(), N = grid[0].size(), ans = 0;
vector<int> maxHeightPerRow(M, 0), maxHeightPerCol(N, 0);
for (int i = 0; i < M; ++i) {
for (int j = 0; j < N; ++j) {
maxHeightPerRow[i] = max(maxHeightPerRow[i], grid[i][j]);
}
}
for (int j = 0; j < N; ++j) {
for (int i = 0; i < M; ++i) {
maxHeightPerCol[j] = max(maxHeightPerCol[j], grid[i][j]);
}
}
for (int i = 0; i < M; ++i) {
for (int j = 0; j < N; ++j) {
ans += max(0, min(maxHeightPerRow[i], maxHeightPerCol[j]) - grid[i][j]);
}
}
return ans;
}
};

• class Solution:
def maxIncreaseKeepingSkyline(self, grid: List[List[int]]) -> int:
rmx = [max(row) for row in grid]
cmx = [max(col) for col in zip(*grid)]
return sum(
(min(rmx[i], cmx[j]) - grid[i][j])
for i in range(len(grid))
for j in range(len(grid[0]))
)

############

class Solution(object):
def maxIncreaseKeepingSkyline(self, grid):
"""
:type grid: List[List[int]]
:rtype: int
"""
gridNew = [[0] * len(grid[0]) for _ in range(len(grid))]
top = [max(grid[rows][cols] for rows in range(len(grid))) for cols in range(len(grid[0]))]
left = [max(grid[rows][cols] for cols in range(len(grid[0]))) for rows in range(len(grid))]
for row, row_max in enumerate(left):
for col, col_max in enumerate(top):
gridNew[row][col] = min(row_max, col_max)
return sum(gridNew[row][col] - grid[row][col] for row in range(len(left)) for col in range(len(top)))

• func maxIncreaseKeepingSkyline(grid [][]int) int {
m, n := len(grid), len(grid[0])
rmx := make([]int, m)
cmx := make([]int, n)
for i := 0; i < m; i++ {
for j := 0; j < n; j++ {
rmx[i] = max(rmx[i], grid[i][j])
cmx[j] = max(cmx[j], grid[i][j])
}
}
ans := 0
for i := 0; i < m; i++ {
for j := 0; j < n; j++ {
ans += min(rmx[i], cmx[j]) - grid[i][j]
}
}
return ans
}

func max(a, b int) int {
if a > b {
return a
}
return b
}

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

• function maxIncreaseKeepingSkyline(grid: number[][]): number {
let rows = grid.map(arr => Math.max(...arr)),
cols = [];
let m = grid.length,
n = grid[0].length;
for (let j = 0; j < n; ++j) {
cols[j] = grid[0][j];
for (let i = 1; i < m; ++i) {
cols[j] = Math.max(cols[j], grid[i][j]);
}
}

let ans = 0;
for (let i = 0; i < m; ++i) {
for (let j = 0; j < n; ++j) {
ans += Math.min(rows[i], cols[j]) - grid[i][j];
}
}
return ans;
}


• class Solution {
public int maxIncreaseKeepingSkyline(int[][] grid) {
if (grid == null || grid.length == 0 || grid[0].length == 0)
return 0;
int rows = grid.length, columns = grid[0].length;
int[] skylineRows = new int[rows];
int[] skylineColumns = new int[columns];
for (int i = 0; i < rows; i++) {
for (int j = 0; j < columns; j++) {
int height = grid[i][j];
skylineRows[i] = Math.max(skylineRows[i], height);
skylineColumns[j] = Math.max(skylineColumns[j], height);
}
}
int increase = 0;
for (int i = 0; i < rows; i++) {
for (int j = 0; j < columns; j++) {
int height = grid[i][j];
int maxHeight = Math.min(skylineRows[i], skylineColumns[j]);
increase += maxHeight - height;
}
}
return increase;
}
}

############

class Solution {
public int maxIncreaseKeepingSkyline(int[][] grid) {
int m = grid.length, n = grid[0].length;
int[] rmx = new int[m];
int[] cmx = new int[n];
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
rmx[i] = Math.max(rmx[i], grid[i][j]);
cmx[j] = Math.max(cmx[j], grid[i][j]);
}
}
int ans = 0;
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
ans += Math.min(rmx[i], cmx[j]) - grid[i][j];
}
}
return ans;
}
}

• // OJ: https://leetcode.com/problems/max-increase-to-keep-city-skyline/
// Time: O(MN)
// Space: O(max(M, N))
class Solution {
public:
int maxIncreaseKeepingSkyline(vector<vector<int>>& grid) {
int M = grid.size(), N = grid[0].size(), ans = 0;
vector<int> maxHeightPerRow(M, 0), maxHeightPerCol(N, 0);
for (int i = 0; i < M; ++i) {
for (int j = 0; j < N; ++j) {
maxHeightPerRow[i] = max(maxHeightPerRow[i], grid[i][j]);
}
}
for (int j = 0; j < N; ++j) {
for (int i = 0; i < M; ++i) {
maxHeightPerCol[j] = max(maxHeightPerCol[j], grid[i][j]);
}
}
for (int i = 0; i < M; ++i) {
for (int j = 0; j < N; ++j) {
ans += max(0, min(maxHeightPerRow[i], maxHeightPerCol[j]) - grid[i][j]);
}
}
return ans;
}
};

• class Solution:
def maxIncreaseKeepingSkyline(self, grid: List[List[int]]) -> int:
rmx = [max(row) for row in grid]
cmx = [max(col) for col in zip(*grid)]
return sum(
(min(rmx[i], cmx[j]) - grid[i][j])
for i in range(len(grid))
for j in range(len(grid[0]))
)

############

class Solution(object):
def maxIncreaseKeepingSkyline(self, grid):
"""
:type grid: List[List[int]]
:rtype: int
"""
gridNew = [[0] * len(grid[0]) for _ in range(len(grid))]
top = [max(grid[rows][cols] for rows in range(len(grid))) for cols in range(len(grid[0]))]
left = [max(grid[rows][cols] for cols in range(len(grid[0]))) for rows in range(len(grid))]
for row, row_max in enumerate(left):
for col, col_max in enumerate(top):
gridNew[row][col] = min(row_max, col_max)
return sum(gridNew[row][col] - grid[row][col] for row in range(len(left)) for col in range(len(top)))

• func maxIncreaseKeepingSkyline(grid [][]int) int {
m, n := len(grid), len(grid[0])
rmx := make([]int, m)
cmx := make([]int, n)
for i := 0; i < m; i++ {
for j := 0; j < n; j++ {
rmx[i] = max(rmx[i], grid[i][j])
cmx[j] = max(cmx[j], grid[i][j])
}
}
ans := 0
for i := 0; i < m; i++ {
for j := 0; j < n; j++ {
ans += min(rmx[i], cmx[j]) - grid[i][j]
}
}
return ans
}

func max(a, b int) int {
if a > b {
return a
}
return b
}

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

• function maxIncreaseKeepingSkyline(grid: number[][]): number {
let rows = grid.map(arr => Math.max(...arr)),
cols = [];
let m = grid.length,
n = grid[0].length;
for (let j = 0; j < n; ++j) {
cols[j] = grid[0][j];
for (let i = 1; i < m; ++i) {
cols[j] = Math.max(cols[j], grid[i][j]);
}
}

let ans = 0;
for (let i = 0; i < m; ++i) {
for (let j = 0; j < n; ++j) {
ans += Math.min(rows[i], cols[j]) - grid[i][j];
}
}
return ans;
}