ProjectionAreaOf3DShapes.java

package math;
/**
 * Created by gouthamvidyapradhan on 09/05/2019
 *
 * <p>On a N * N grid, we place some 1 * 1 * 1 cubes that are axis-aligned with the x, y, and z
 * axes.
 *
 * <p>Each value v = grid[i][j] represents a tower of v cubes placed on top of grid cell (i, j).
 *
 * <p>Now we view the projection of these cubes onto the xy, yz, and zx planes.
 *
 * <p>A projection is like a shadow, that maps our 3 dimensional figure to a 2 dimensional plane.
 *
 * <p>Here, we are viewing the "shadow" when looking at the cubes from the top, the front, and the
 * side.
 *
 * <p>Return the total area of all three projections.
 *
 * <p>Example 1:
 *
 * <p>Input: [[2]] Output: 5 Example 2:
 *
 * <p>Input: [[1,2],[3,4]] Output: 17 Explanation: Here are the three projections ("shadows") of the
 * shape made with each axis-aligned plane.
 *
 * <p>Example 3:
 *
 * <p>Input: [[1,0],[0,2]] Output: 8 Example 4:
 *
 * <p>Input: [[1,1,1],[1,0,1],[1,1,1]] Output: 14 Example 5:
 *
 * <p>Input: [[2,2,2],[2,1,2],[2,2,2]] Output: 21
 *
 * <p>Note:
 *
 * <p>1 <= grid.length = grid[0].length <= 50 0 <= grid[i][j] <= 50
 *
 * <p>Solution O(N x N) project the view on all three different planes. For top view its pretty
 * simple because area of each cube is just 1 * 1, for all other planes take the maximum value of
 * each grid. Sum up values on each planes
 */
public class ProjectionAreaOf3DShapes {
  public static void main(String[] args) {
    //
  }

  public int projectionArea(int[][] grid) {
    int area = 0;
    for (int i = 0; i < grid.length; i++) {
      for (int j = 0; j < grid.length; j++) {
        area += (grid[i][j] > 0 ? 1 : 0);
      }
    }

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

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

    return area;
  }
}