How hard is LeetCode 2088. Count Fertile Pyramids in a Land?

LeetCode 2088. Count Fertile Pyramids in a Land is rated Hard on LeetCode.

What topics does LeetCode 2088. Count Fertile Pyramids in a Land cover?

LeetCode 2088. Count Fertile Pyramids in a Land is tagged Array, Dynamic Programming and Matrix on LeetCode.

Count Fertile Pyramids in a Land — LeetCode 2088 Python Solution

HardArrayDynamic ProgrammingMatrix

Problem: #2088
Pattern: Matrix and Grid
Reading time: 4 min
Source: leetcode.com

The problem

A farmer has a rectangular grid of land with m rows and n columns that can be divided into unit cells. Each cell is either fertile (represented by a 1) or barren (represented by a 0).

Example

Input: grid = [[0,1,1,0],[1,1,1,1]]
Output: 2
Explanation: The 2 possible pyramidal plots are shown in blue and red respectively.

Python solution

Python

class Solution:
    def countPyramids(self, grid: List[List[int]]) -> int:
        m, n = len(grid), len(grid[0])
        f = [[0] * n for _ in range(m)]
        ans = 0
        for i in range(m - 1, -1, -1):
            for j in range(n):
                if grid[i][j] == 0:
                    f[i][j] = -1
                elif not (i == m - 1 or j == 0 or j == n - 1):
                    f[i][j] = min(f[i + 1][j - 1], f[i + 1][j], f[i + 1][j + 1]) + 1
                    ans += f[i][j]
        for i in range(m):
            for j in range(n):
                if grid[i][j] == 0:
                    f[i][j] = -1
                elif i == 0 or j == 0 or j == n - 1:
                    f[i][j] = 0
                else:
                    f[i][j] = min(f[i - 1][j - 1], f[i - 1][j], f[i - 1][j + 1]) + 1
                    ans += f[i][j]
        return ans

Complexity

Measure	Complexity
Time	O(n·m) (typical)
Space	O(n·m) or optimized auxiliary

Pattern: Matrix and Grid

Treat a 2-D grid as a graph whose neighbours are the four adjacent cells. LeetCode 2088. Count Fertile Pyramids in a Land is filed here because LeetCode tags it Matrix, which is the vocabulary this hub collects.

The matrix and grid guide has the Python template for the pattern and the 216 LeetCode problems that use it.

Frequently asked questions

How hard is LeetCode 2088. Count Fertile Pyramids in a Land?: LeetCode 2088. Count Fertile Pyramids in a Land is rated Hard on LeetCode.
What topics does LeetCode 2088. Count Fertile Pyramids in a Land cover?: LeetCode 2088. Count Fertile Pyramids in a Land is tagged Array, Dynamic Programming and Matrix on LeetCode.