How do I calculate the surface area of cubes in this problem?

Each cube contributes 6 units to the surface area, but you must subtract the area covered by adjacent cubes based on their relative height.

What is the optimal approach for solving the Surface Area of 3D Shapes problem?

Traverse the grid, calculating the exposed surface for each cube while accounting for adjacent cubes. Use efficient comparisons to minimize redundant calculations.

What are the key pitfalls in solving the Surface Area of 3D Shapes problem?

Common pitfalls include overlooking hidden sides, unnecessary complexity in the approach, and not considering edge cases like minimal or zero-height towers.

How does adjacency affect the surface area calculation in this problem?

Adjacent cubes reduce the visible surface area by covering shared sides. The difference in height between adjacent cubes determines how much surface is hidden.

Can I solve this problem with a brute-force approach?

While a brute-force approach is possible, it may not be efficient. Optimizing the calculation of exposed surfaces by considering height differences between adjacent cubes can improve performance.

#892

Easy

auto_awesome数组·数学

LeetCode 题解工作台

三维形体的表面积

给你一个 n * n 的网格 grid ，上面放置着一些 1 x 1 x 1 的正方体。每个值 v = grid[i][j] 表示 v 个正方体叠放在对应单元格 (i, j) 上。放置好正方体后，任何直接相邻的正方体都会互相粘在一起，形成一些不规则的三维形体。请你返回最终这些形体的总表面积。注…

数组数学几何矩阵

题目描述

给你一个 n * n 的网格 grid ，上面放置着一些 1 x 1 x 1 的正方体。每个值 v = grid[i][j] 表示 v 个正方体叠放在对应单元格 (i, j) 上。

放置好正方体后，任何直接相邻的正方体都会互相粘在一起，形成一些不规则的三维形体。

请你返回最终这些形体的总表面积。

注意：每个形体的底面也需要计入表面积中。

示例 1：

输入：grid = [[1,2],[3,4]]
输出：34

示例 2：

输入：grid = [[1,1,1],[1,0,1],[1,1,1]]
输出：32

示例 3：

输入：grid = [[2,2,2],[2,1,2],[2,2,2]]
输出：46

提示：

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

lightbulb

解题思路

方法一：遍历，逐个累加

时间复杂度 $O(n^2)$ ，空间复杂度 $O(1)$ 。

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class Solution:
    def surfaceArea(self, grid: List[List[int]]) -> int:
        ans = 0
        for i, row in enumerate(grid):
            for j, v in enumerate(row):
                if v:
                    ans += 2 + v * 4
                    if i:
                        ans -= min(v, grid[i - 1][j]) * 2
                    if j:
                        ans -= min(v, grid[i][j - 1]) * 2
        return ans

speed

复杂度分析

指标	值
时间	Depends on the final approach
空间	Depends on the final approach

psychology

面试官常问的追问

外企场景

question_mark
Look for understanding of how adjacency affects surface area calculations.
question_mark
Evaluate if the candidate considers optimizations for repeated calculations.
question_mark
Check if the solution correctly handles edge cases like adjacent towers of equal or differing heights.

warning

常见陷阱

外企场景

error
Failing to account for hidden sides between adjacent cubes.
error
Overcomplicating the solution when a direct traversal of the grid is sufficient.
error
Not handling edge cases like empty or minimal grids (e.g., n = 1 or towers with height 0).

swap_horiz

进阶变体

外企场景

arrow_right_alt
Consider cases where some cells contain zero cubes.
arrow_right_alt
What happens when the grid contains large numbers or is very sparse?
arrow_right_alt
Can this problem be generalized to irregular 3D shapes?

help

常见问题

外企场景

继续练习

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