Leetcode #883: Projection Area of 3D Shapes
In this guide, we solve Leetcode #883 Projection Area of 3D Shapes in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
You are given an n x n grid where we place some 1 x 1 x 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 the cell (i, j).
Quick Facts
- Difficulty: Easy
- Premium: No
- Tags: Geometry, Array, Math, Matrix
Intuition
There is a mathematical invariant or formula that directly leads to the result.
Using math avoids unnecessary loops and reduces complexity.
Approach
Derive the formula or update rule, then compute the answer directly.
Handle edge cases like overflow or zero carefully.
Steps:
- Identify the math relationship.
- Compute the result with a loop or formula.
- Handle edge cases.
Example
Input: grid = [[1,2],[3,4]]
Output: 17
Explanation: Here are the three projections ("shadows") of the shape made with each axis-aligned plane.
Python Solution
class Solution:
def projectionArea(self, grid: List[List[int]]) -> int:
xy = sum(v > 0 for row in grid for v in row)
yz = sum(max(row) for row in grid)
zx = sum(max(col) for col in zip(*grid))
return xy + yz + zx
Complexity
The time complexity is , where is the side length of the grid grid. The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.