#3142

Easy

LeetCode Problem Workspace

Check if Grid Satisfies Conditions

Check if a grid satisfies given conditions by analyzing array and matrix structure with specific checks on values.

Problem Statement

You are given a 2D matrix grid with m rows and n columns. Your task is to check if each cell in the grid satisfies specific conditions, such as verifying that all elements in a row or column are identical.

Return true if all the conditions are satisfied across the entire grid; otherwise, return false.

Examples

Example 1

Input: grid = [[1,0,2],[1,0,2]]

Output: true

All the cells in the grid satisfy the conditions.

Example 2

Input: grid = [[1,1,1],[0,0,0]]

Output: false

All cells in the first row are equal.

Example 3

Input: grid = [[1],[2],[3]]

Output: false

Cells in the first column have different values.

Constraints

1 <= n, m <= 10
0 <= grid[i][j] <= 9

Solution Approach

Check each row

The first step is to ensure that each row of the grid has the same values for every element. Iterate through each row and check if all elements are identical.

Check each column

After verifying the rows, check each column to ensure that all elements in a column are the same. This ensures the condition is satisfied for both rows and columns.

Return result

Once both the row and column conditions are validated, return true if all conditions are met; otherwise, return false.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time complexity depends on the approach used. A direct comparison of all elements in rows and columns leads to O(m * n) time complexity, where m is the number of rows and n is the number of columns. The space complexity is O(1) as no additional storage is required beyond the input grid.

What Interviewers Usually Probe

Look for an approach that involves iterating through rows and columns to check for uniformity.
Ensure the candidate efficiently handles the grid with a simple comparison for correctness.
Test whether the candidate identifies the pattern of checking rows and columns in grid validation.

Common Pitfalls or Variants

Common pitfalls

Not correctly iterating through each row or column to check for uniformity.
Misunderstanding the constraints and mistakenly returning incorrect results for non-uniform cells.
Overcomplicating the solution by introducing unnecessary operations or data structures.

Follow-up variants

Consider cases where grid elements may be different but still satisfy conditions.
Try solving the problem by verifying one condition first and then moving to the next step for optimization.
Explore optimization for larger grids when applicable by considering reduced time complexity solutions.

FAQ

What is the key pattern to solve the 'Check if Grid Satisfies Conditions' problem?

The key pattern involves checking if all elements in each row and column of the grid are identical, either row-wise or column-wise.

What approach should be used to check if grid elements satisfy the conditions?

You should iterate through each row and column to check if all elements within each are identical and then return the result based on this verification.

Can this problem be solved in less than O(m * n) time?

No, since we need to check every element in the grid to ensure it satisfies the conditions, a solution with O(m * n) time complexity is optimal.

How can I check if the elements in a grid are the same across rows and columns?

You can check if all elements in each row are the same first, then do the same for columns by comparing the elements in the same column across all rows.

What are the constraints for solving the 'Check if Grid Satisfies Conditions' problem?

The grid must have dimensions between 1 and 10 for both rows and columns, and the values of the elements are between 0 and 9.

terminal

Solution

Solution 1: Simulation

We can iterate through each cell and determine whether it meets the conditions specified in the problem. If there is a cell that does not meet the conditions, we return `false`, otherwise, we return `true`.

1

2

3

4

5

6

7

8

9

10

class Solution:
    def satisfiesConditions(self, grid: List[List[int]]) -> bool:
        m, n = len(grid), len(grid[0])
        for i, row in enumerate(grid):
            for j, x in enumerate(row):
                if i + 1 < m and x != grid[i + 1][j]:
                    return False
                if j + 1 < n and x == grid[i][j + 1]:
                    return False
        return True

Continue Practicing

#3148 maximum difference score in a grid #3127 make a square with the same color #3122 minimum number of operations to satisfy conditions