Formatted question description: https://leetcode.ca/all/883.html

883. Projection Area of 3D Shapes (Easy)

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:

  • 1 <= grid.length = grid[0].length <= 50
  • 0 <= grid[i][j] <= 50

Related Topics:
Math

Solution 1.

// OJ: https://leetcode.com/problems/projection-area-of-3d-shapes/
// Time: O(MN)
// Space: O(1)
class Solution {
public:
    int projectionArea(vector<vector<int>>& grid) {
        int cnt = 0;
        for (int N = grid.size(), i = 0; i < N; ++i) {
            int max1 = 0, max2 = 0;
            for (int j = 0; j < N; ++j) {
                if (grid[i][j]) ++cnt;
                max1 = max(max1, grid[i][j]);
                max2 = max(max2, grid[j][i]);
            }
            cnt += max1 + max2;
        }
        return cnt;
    }
};

Java

  • class Solution {
        public int projectionArea(int[][] grid) {
            int areaTop = 0, areaFront = 0, areaSide = 0;
            int rows = grid.length, columns = grid[0].length;
            int[] maxEachRow = new int[rows];
            int[] maxEachColumn = new int[columns];
            for (int i = 0; i < rows; i++) {
                for (int j = 0; j < columns; j++) {
                    int cell = grid[i][j];
                    if (cell != 0)
                        areaTop++;
                    maxEachRow[i] = Math.max(maxEachRow[i], cell);
                    maxEachColumn[j] = Math.max(maxEachColumn[j], cell);
                }
            }
            for (int num : maxEachRow)
                areaSide += num;
            for (int num : maxEachColumn)
                areaFront += num;
            return areaTop + areaFront + areaSide;
        }
    }
    
  • // OJ: https://leetcode.com/problems/projection-area-of-3d-shapes/
    // Time: O(MN)
    // Space: O(1)
    class Solution {
    public:
        int projectionArea(vector<vector<int>>& grid) {
            int cnt = 0;
            for (int N = grid.size(), i = 0; i < N; ++i) {
                int max1 = 0, max2 = 0;
                for (int j = 0; j < N; ++j) {
                    if (grid[i][j]) ++cnt;
                    max1 = max(max1, grid[i][j]);
                    max2 = max(max2, grid[j][i]);
                }
                cnt += max1 + max2;
            }
            return cnt;
        }
    };
    
  • class Solution(object):
        def projectionArea(self, grid):
            """
            :type grid: List[List[int]]
            :rtype: int
            """
            top, front, side = 0, 0, 0
            n = len(grid)
            for i in range(n):
                x, y = 0, 0
                for j in range(n):
                    if grid[i][j] != 0:
                        top += 1
                    x = max(x, grid[i][j])
                    y = max(y, grid[j][i])
                front += x
                side += y
            return top + front + side
    

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