# Java code with explanation

• This is a generic solution that should work on any nn board (where n is a perfect square). The idea is to imagine a section that is sqrt(9). So we need to check the uniqueness for a row, col and inside the section of 3x3 region. To traverse each region, we need to loop between 0-3 to cover reach region on row and col side. After that we run two loops for m and n to cover each row and col inside that region. It is easy to guess that m and n should be relative to i and j therefore. The formula will be
m=3
i to 3i + 3
n = 3
j to 3*j + 3

``````  public boolean isValidSudoku(char[][] board)
{
int section = (int) Math.sqrt(board.length);
// validate rows.
for (int i = 0; i < board.length; i++)
{
Set<Character> rows = new HashSet<>();
for (int j = 0; j < board[i].length; j++)
{
if (board[i][j] != '.' && !rows.add(board[i][j]))
{
return false;
}
}
}
// validate cols.
for (int i = 0; i < board[0].length; i++)
{
Set<Character> cols = new HashSet<>();
for (int j = 0; j < board.length; j++)
{
if (board[j][i] != '.' && !cols.add(board[j][i]))
{
return false;
}
}
}
/**
* We have board.length sections altogether.  Each section
* is Math.sqrt(board.lenth)*Math.sqrt(board.length) long. To solve this
* problem, we will break both rows and cols into Math.sqrt(board.length)
* regions and iterate over each one of them. One iteration of i and  j
* should cover one section. For example, for a 4*4 sukodo, we have 2 regions
* each for for rows and cols. Here are the regions:

* region#1: (0,0) to (1,1)
* region#2: (0,2) to (1,3)
* region# 3: (2,0) to (3,1)
* region# 4: (3,1) to (3,3)
*
* Use i an j to traverse to each region. We also need two variables
* m and n to go through each element of a region.
* m = Math.sqrt(board.length) + Math.sqrt(board.length)*i
* n = Math.sqrt(board.length) + Math.sqrt(board.length)*j
*
*/
for (int i = 0; i < section; i++)
{
for (int j = 0; j < section; j++)
{
Set<Character> cubeSet = new HashSet<>();
for (int m = section * i; m < section + section * i; m++)
{
for (int n = section * j; n < section + section * j; n++)
{
if (board[m][n] != '.' && !cubeSet.add(board[m][n]))
{
return false;
}
}
}
}
}
return true;
}

``````

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