Problem

On a N * N grid, we place some 1 * 1 * 1 cubes that are axis-aligned with the x, y, and z axes.

Each value v = grid[i][j] represents a tower of v cubes placed on top of grid cell (i, j).

Now we view the projection of these cubes onto the xy, yz, and zx planes.

A projection is like a shadow, that maps our 3 dimensional figure to a 2 dimensional plane.

Here, we are viewing the “shadow” when looking at the cubes from the top, the front, and the side.

Return the total area of all three projections.

Example 1:

Input: [[2]]
Output: 5

Example 2:

Input: [[1,2],[3,4]]
Output: 17
Explanation: 
Here are the three projections ("shadows") of the shape made with each axis-aligned plane.

Example 3:

Input: [[1,0],[0,2]]
Output: 8

Example 4:

Input: [[1,1,1],[1,0,1],[1,1,1]]
Output: 14

Example 5:

Input: [[2,2,2],[2,1,2],[2,2,2]]
Output: 21

Note:

Solution: Brute Force

Sum of max heights for each cols / rows + # of non-zero-height bars.

Time complexity: O(mn)

Space complexity: O(1)

C++

// Author: Huahua

// Running time : 4 ms

class Solution {

public:

int projectionArea(vector<vector<int>>& grid) {

int n = grid.size();

int m = grid[0].size();

int ans = 0;

for (int i = 0; i < n; ++i) {

int h = 0;

for (int j = 0; j < m; ++j) {

h = max(h, grid[i][j]);

if (grid[i][j] != 0) ++ans;

}

ans += h;

}

for (int j = 0; j < m; ++j) {

int h = 0;

for (int i = 0; i < n; ++i)

h = max(h, grid[i][j]);

ans += h;

}

return ans;

}

};