Is Maximum Consistent Columns in a Grid easy or hard?

Maximum Consistent Columns in a Grid is generally classified as a hard problem because the main challenge is identifying the correct normalization strategy. The brute force solution is straightforward, but deriving the optimal hashing approach requires stronger pattern recognition skills.

Maximum Consistent Columns in a Grid Python/Java solution

Python solutions usually store column signatures as tuples or strings inside a dictionary. Java implementations commonly use HashMap or integer bitmasks for binary grids. Both approaches achieve O(m * n) complexity.

How to solve Maximum Consistent Columns in a Grid in O(n)?

The standard optimized solution is effectively O(m * n) because every grid value must be read at least once. Build a normalized signature for each column and store it in a hash map. The highest frequency of any signature gives the maximum consistent columns.

What is the best approach for Maximum Consistent Columns in a Grid?

The best approach uses a hash map to group normalized column patterns. Each column is converted into a compact signature, and matching signatures are counted in O(1) average lookup time. This reduces the overall complexity to O(m * n).

Is Maximum Consistent Columns in a Grid asked at Google/Amazon/Meta?

Grid normalization and hash-based grouping problems appear frequently in interviews at Google, Amazon, and Meta. Variants involving row flips, column patterns, and binary matrix transformations are common in hard-level rounds.

What data structure is used in Maximum Consistent Columns in a Grid?

The primary data structure is a hash map that stores column signatures and their frequencies. Some optimized implementations also use bitmasks to compress binary column states into integers for faster lookup.

What is the time complexity of Maximum Consistent Columns in a Grid?

The optimal hashing solution runs in O(m * n) time, where m is the number of rows and n is the number of columns. Every cell is processed once while constructing column signatures. Space complexity is typically O(n) for storing frequencies.

Description Hints 5 Video 13:41

3989. Maximum Consistent Columns in a Grid

Hard68.7% acceptance

You are given a 2D integer array grid of size m x n, and an integer limit.

You may remove zero or more columns from the grid, but at least one column must remain. The relative order of the remaining columns must be preserved.

A grid is called consistent if for every row i, and for every pair of adjacent remaining columns a and b with a < b, the following holds: |grid[i][b] - grid[i][a]| <= limit.

Return the maximum number of columns that can remain such that the resulting grid is consistent.

Example 1:

Input: grid = [[-2,0,3]], limit = 2

Output: 2

Explanation:

Remove column 2 and keep columns 0 and 1, which gives |grid[0][1] − grid[0][0]| = |0 − (−2)| = 2 <= limit.
Thus, the maximum number of columns that can remain is 2.

Example 2:

Input: grid = [[1,-1,1],[2,2,2]], limit = 1

Output: 2

Explanation:

Remove column 1 and keep columns 0 and 2, which gives
- |grid[0][2] − grid[0][0]| = |1 − 1| = 0 <= limit and
- |grid[1][2] − grid[1][0]| = |2 − 2| = 0 <= limit.
Thus, the maximum number of columns that can remain is 2.

Example 3:

Input: grid = [[-5,5]], limit = 9

Output: 1

Explanation:

Remove either column 0 or column 1, since |grid[0][1] − grid[0][0]| = |5 − (−5)| = 10 > limit.
Thus, the maximum number of columns that can remain is 1.

Constraints:

1 <= m == grid.length <= 250
1 <= n == grid[i].length <= 250
-10⁵ <= grid[i][j] <= 10⁵
0 <= limit <= 10⁵

Topics

Hints open one at a time

Hint 1

Think of each column as one item in a subsequence. Two columns a and b with a < b can be adjacent in the remaining grid only if |grid[i][b] - grid[i][a]| <= limit for every row i.

Hint 2

Precompute whether every pair of columns (a, b) is compatible.

Hint 3

Let dp[j] be the maximum number of columns in a valid remaining grid whose last column is j.

Hint 4

For each j, try all previous columns i < j. If columns i and j are compatible, update dp[j] = max(dp[j], dp[i] + 1).

Hint 5

The answer is the maximum value of dp[j].

LanguageLoading editor…

1class Solution:
2    def maxConsistentColumns(self, grid: List[List[int]], limit: int) -> int:
3        

Starter codePython 3Spaces: 4

Examples

Case 1Case 2Case 3

Input

[[-2,0,3]]
2

Input

[[1,-1,1],[2,2,2]]
1

Input

[[-5,5]]
9

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