# 3142. Check if Grid Satisfies Conditions

## Description

You are given a 2D matrix grid of size m x n. You need to check if each cell grid[i][j] is:

• Equal to the cell below it, i.e. grid[i][j] == grid[i + 1][j] (if it exists).
• Different from the cell to its right, i.e. grid[i][j] != grid[i][j + 1] (if it exists).

Return true if all the cells satisfy these conditions, otherwise, return false.

Example 1:

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

Output: true

Explanation:

All the cells in the grid satisfy the conditions.

Example 2:

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

Output: false

Explanation:

All cells in the first row are equal.

Example 3:

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

Output: false

Explanation:

Cells in the first column have different values.

Constraints:

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

## Solutions

### 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.

The time complexity is $O(m \times n)$, where $m$ and $n$ are the number of rows and columns of the matrix grid respectively. The space complexity is \$O(1).

• class Solution {
public boolean satisfiesConditions(int[][] grid) {
int m = grid.length, n = grid[0].length;
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
if (i + 1 < m && grid[i][j] != grid[i + 1][j]) {
return false;
}
if (j + 1 < n && grid[i][j] == grid[i][j + 1]) {
return false;
}
}
}
return true;
}
}

• class Solution {
public:
bool satisfiesConditions(vector<vector<int>>& grid) {
int m = grid.size(), n = grid[0].size();
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
if (i + 1 < m && grid[i][j] != grid[i + 1][j]) {
return false;
}
if (j + 1 < n && grid[i][j] == grid[i][j + 1]) {
return false;
}
}
}
return true;
}
};

• 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


• func satisfiesConditions(grid [][]int) bool {
m, n := len(grid), len(grid[0])
for i, row := range grid {
for j, x := range row {
if i+1 < m && x != grid[i+1][j] {
return false
}
if j+1 < n && x == grid[i][j+1] {
return false
}
}
}
return true
}

• function satisfiesConditions(grid: number[][]): boolean {
const [m, n] = [grid.length, grid[0].length];
for (let i = 0; i < m; ++i) {
for (let j = 0; j < n; ++j) {
if (i + 1 < m && grid[i][j] !== grid[i + 1][j]) {
return false;
}
if (j + 1 < n && grid[i][j] === grid[i][j + 1]) {
return false;
}
}
}
return true;
}

`