# 3127. Make a Square with the Same Color

## Description

You are given a 2D matrix grid of size 3 x 3 consisting only of characters 'B' and 'W'. Character 'W' represents the white color, and character 'B' represents the black color.

Your task is to change the color of at most one cell so that the matrix has a 2 x 2 square where all cells are of the same color.

Return true if it is possible to create a 2 x 2 square of the same color, otherwise, return false.

Example 1:

Input: grid = [["B","W","B"],["B","W","W"],["B","W","B"]]

Output: true

Explanation:

It can be done by changing the color of the grid[0][2].

Example 2:

Input: grid = [["B","W","B"],["W","B","W"],["B","W","B"]]

Output: false

Explanation:

It cannot be done by changing at most one cell.

Example 3:

Input: grid = [["B","W","B"],["B","W","W"],["B","W","W"]]

Output: true

Explanation:

The grid already contains a 2 x 2 square of the same color.

Constraints:

• grid.length == 3
• grid[i].length == 3
• grid[i][j] is either 'W' or 'B'.

## Solutions

### Solution 1: Enumeration

We can enumerate each $2 \times 2$ square, count the number of black and white cells. If the counts are not equal, then we can construct a square of the same color, and return true.

Otherwise, return false after the traversal.

The time complexity is $O(1)$, and the space complexity is $O(1)$.

• class Solution {
public boolean canMakeSquare(char[][] grid) {
final int[] dirs = {0, 0, 1, 1, 0};
for (int i = 0; i < 2; ++i) {
for (int j = 0; j < 2; ++j) {
int cnt1 = 0, cnt2 = 0;
for (int k = 0; k < 4; ++k) {
int x = i + dirs[k], y = j + dirs[k + 1];
cnt1 += grid[x][y] == 'W' ? 1 : 0;
cnt2 += grid[x][y] == 'B' ? 1 : 0;
}
if (cnt1 != cnt2) {
return true;
}
}
}
return false;
}
}

• class Solution {
public:
bool canMakeSquare(vector<vector<char>>& grid) {
int dirs[5] = {0, 0, 1, 1, 0};
for (int i = 0; i < 2; ++i) {
for (int j = 0; j < 2; ++j) {
int cnt1 = 0, cnt2 = 0;
for (int k = 0; k < 4; ++k) {
int x = i + dirs[k], y = j + dirs[k + 1];
cnt1 += grid[x][y] == 'W';
cnt2 += grid[x][y] == 'B';
}
if (cnt1 != cnt2) {
return true;
}
}
}
return false;
}
};

• class Solution:
def canMakeSquare(self, grid: List[List[str]]) -> bool:
for i in range(0, 2):
for j in range(0, 2):
cnt1 = cnt2 = 0
for a, b in pairwise((0, 0, 1, 1, 0)):
x, y = i + a, j + b
cnt1 += grid[x][y] == "W"
cnt2 += grid[x][y] == "B"
if cnt1 != cnt2:
return True
return False


• func canMakeSquare(grid [][]byte) bool {
dirs := [5]int{0, 0, 1, 1, 0}
for i := 0; i < 2; i++ {
for j := 0; j < 2; j++ {
cnt1, cnt2 := 0, 0
for k := 0; k < 4; k++ {
x, y := i+dirs[k], j+dirs[k+1]
if grid[x][y] == 'W' {
cnt1++
} else {
cnt2++
}
}
if cnt1 != cnt2 {
return true
}
}
}
return false
}

• function canMakeSquare(grid: string[][]): boolean {
const dirs: number[] = [0, 0, 1, 1, 0];
for (let i = 0; i < 2; ++i) {
for (let j = 0; j < 2; ++j) {
let [cnt1, cnt2] = [0, 0];
for (let k = 0; k < 4; ++k) {
const [x, y] = [i + dirs[k], j + dirs[k + 1]];
if (grid[x][y] === 'W') {
++cnt1;
} else {
++cnt2;
}
}
if (cnt1 !== cnt2) {
return true;
}
}
}
return false;
}