Leetcode #2768: Number of Black Blocks
In this guide, we solve Leetcode #2768 Number of Black Blocks 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 two integers m and n representing the dimensions of a 0-indexed m x n grid. You are also given a 0-indexed 2D integer matrix coordinates, where coordinates[i] = [x, y] indicates that the cell with coordinates [x, y] is colored black.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Array, Hash Table, Enumeration
Intuition
Fast membership checks and value lookups are the heart of this problem, which makes a hash map the natural choice.
By storing what we have already seen (or counts/indexes), we can answer the question in one pass without backtracking.
Approach
Scan the input once, using the map to detect when the condition is satisfied and to update state as you go.
This keeps the solution linear while remaining easy to explain in an interview setting.
Steps:
- Initialize a hash map for seen items or counts.
- Iterate through the input, querying/updating the map.
- Return the first valid result or the final computed value.
Example
Input: m = 3, n = 3, coordinates = [[0,0]]
Output: [3,1,0,0,0]
Explanation: The grid looks like this:
There is only 1 block with one black cell, and it is the block starting with cell [0,0].
The other 3 blocks start with cells [0,1], [1,0] and [1,1]. They all have zero black cells.
Thus, we return [3,1,0,0,0].
Python Solution
class Solution:
def countBlackBlocks(
self, m: int, n: int, coordinates: List[List[int]]
) -> List[int]:
cnt = Counter()
for x, y in coordinates:
for a, b in pairwise((0, 0, -1, -1, 0)):
i, j = x + a, y + b
if 0 <= i < m - 1 and 0 <= j < n - 1:
cnt[(i, j)] += 1
ans = [0] * 5
for x in cnt.values():
ans[x] += 1
ans[0] = (m - 1) * (n - 1) - len(cnt.values())
return ans
Complexity
The time complexity is O(n). The space complexity is O(n).
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.